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+Binomial nomenclature ("two-term naming system"), also called binominal nomenclature ("two-name naming system") or binary nomenclature, is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, although they can be based on words from other languages. Such a name is called a binomial name (which may be shortened to just "binomial"), a binomen, binominal name or a scientific name; more informally it is also called a Latin name.
+
+The first part of the name – the generic name – identifies the genus to which the species belongs, while the second part – the specific name or specific epithet – identifies the species within the genus. For example, humans belong to the genus Homo and within this genus to the species Homo sapiens. Tyrannosaurus rex is probably the most widely known binomial.[1] The formal introduction of this system of naming species is credited to Carl Linnaeus, effectively beginning with his work Species Plantarum in 1753.[2] But Gaspard Bauhin, in as early as 1622, had introduced in his book Pinax theatri botanici (English, Illustrated exposition of plants) many names of genera that were later adopted by Linnaeus.[3]
+
+The application of binomial nomenclature is now governed by various internationally agreed codes of rules, of which the two most important are the International Code of Zoological Nomenclature (ICZN) for animals and the International Code of Nomenclature for algae, fungi, and plants (ICNafp). Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences, both in the terminology they use and in their precise rules.
+
+In modern usage, the first letter of the first part of the name, the genus, is always capitalized in writing, while that of the second part is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized when a binomial name occurs in normal text (or underlined in handwriting). Thus the binomial name of the annual phlox (named after botanist Thomas Drummond) is now written as Phlox drummondii.
+
+In scientific works, the authority for a binomial name is usually given, at least when it is first mentioned, and the date of publication may be specified.
+
+The name is composed of two word-forming elements: "bi", a Latin prefix for two, and "-nomial", literally translated as "name". The word "binomium" was used in Medieval Latin to signify one of the terms in a two-term binomial expression in mathematics.[4]
+
+Prior to the adoption of the modern binomial system of naming species, a scientific name consisted of a generic name combined with a specific name that was from one to several words long. Together they formed a system of polynomial nomenclature.[5] These names had two separate functions. First, to designate or label the species, and second, to be a diagnosis or description; however these two goals were eventually found to be incompatible.[6] In a simple genus, containing only two species, it was easy to tell them apart with a one-word genus and a one-word specific name; but as more species were discovered, the names necessarily became longer and unwieldy, for instance, Plantago foliis ovato-lanceolatus pubescentibus, spica cylindrica, scapo tereti ("plantain with pubescent ovate-lanceolate leaves, a cylindric spike and a terete scape"), which we know today as Plantago media.
+
+Such "polynomial names" may sometimes look like binomials, but are significantly different. For example, Gerard's herbal (as amended by Johnson) describes various kinds of spiderwort: "The first is called Phalangium ramosum, Branched Spiderwort; the second, Phalangium non ramosum, Unbranched Spiderwort. The other ... is aptly termed Phalangium Ephemerum Virginianum, Soon-Fading Spiderwort of Virginia".[7] The Latin phrases are short descriptions, rather than identifying labels.
+
+The Bauhins, in particular Caspar Bauhin (1560–1624), took some important steps towards the binomial system, by pruning the Latin descriptions, in many cases to two words.[8] The adoption by biologists of a system of strictly binomial nomenclature is due to Swedish botanist and physician Carl Linnaeus (1707–1778).  It was in Linnaeus's 1753 Species Plantarum that he began consistently using a one-word "trivial name" (nomen triviale) after a generic name (genus name) in a system of binomial nomenclature.[9] Trivial names had already appeared in his Critica Botanica (1737) and Philosophia Botanica (1751). This trivial name is what is now known as a specific epithet (ICNafp) or specific name (ICZN).[9] The Bauhins' genus names were retained in many of these, but the descriptive part was reduced to a single word.
+
+Linnaeus's trivial names introduced an important new idea, namely that the function of a name could simply be to give a species a unique label. This meant that the name no longer need be descriptive; for example both parts could be derived from the names of people. Thus Gerard's Phalangium ephemerum virginianum became Tradescantia virginiana, where the genus name honoured John Tradescant the Younger,[note 1] an English botanist and gardener.[10] A bird in the parrot family was named Psittacus alexandri, meaning "Alexander's parrot", after Alexander the Great, whose armies introduced eastern parakeets to Greece.[11] Linnaeus's trivial names were much easier to remember and use than the parallel polynomial names and eventually replaced them.[2]
+
+The value of the binomial nomenclature system derives primarily from its economy, its widespread use, and the uniqueness and stability of names it generally favors:
+
+Binomial nomenclature for species has the effect that when a species is moved from one genus to another, sometimes the specific name or epithet must be changed as well. This may happen because the specific name is already used in the new genus, or to agree in gender with the new genus. Some biologists have argued for the combination of the genus name and specific epithet into a single unambiguous name, or for the use of uninomials (as used in nomenclature of ranks above species).[18]
+
+Because binomials are unique only within a kingdom, it is possible for two or more species to share the same binomial if they occur in different kingdoms. At least 1241 instances of such binomial duplication occur.[19][20]
+
+Nomenclature (including binomial nomenclature) is not the same as classification, although the two are related. Classification is the ordering of items into groups based on similarities or differences; in biological classification, species are one of the kinds of item to be classified.[21] In principle, the names given to species could be completely independent of their classification. This is not the case for binomial names, since the first part of a binomial is the name of the genus into which the species is placed. Above the rank of genus, binomial nomenclature and classification are partly independent; for example, a species retains its binomial name if it is moved from one family to another or from one order to another, unless it better fits a different genus in the same or different family, or it is split from its old genus and placed in a newly created genus. The independence is only partial since the names of families and other higher taxa are usually based on genera.[citation needed]
+
+Taxonomy includes both nomenclature and classification. Its first stages (sometimes called "alpha taxonomy") are concerned with finding, describing and naming species of living or fossil organisms.[22] Binomial nomenclature is thus an important part of taxonomy as it is the system by which species are named. Taxonomists are also concerned with classification, including its principles, procedures and rules.[23]
+
+A complete binomial name is always treated grammatically as if it were a phrase in the Latin language (hence the common use of the term "Latin name" for a binomial name). However, the two parts of a binomial name can each be derived from a number of sources, of which Latin is only one. These include:
+
+The first part of the name, which identifies the genus, must be a word which can be treated as a Latin singular noun in the nominative case. It must be unique within each kingdom, but can be repeated between kingdoms. Thus Huia recurvata is an extinct species of plant, found as fossils in Yunnan, China,[33] whereas Huia masonii is a species of frog found in Java, Indonesia.[34]
+
+The second part of the name, which identifies the species within the genus, is also treated grammatically as a Latin word. It can have one of a number of forms:
+
+Whereas the first part of a binomial name must be unique within a kingdom, the second part is quite commonly used in two or more genera (as is shown by examples of hodgsonii above). The full binomial name must be unique within a kingdom.
+
+From the early 19th century onwards it became ever more apparent that a body of rules was necessary to govern scientific names. In the course of time these became nomenclature codes. The International Code of Zoological Nomenclature (ICZN) governs the naming of animals,[36] the International Code of Nomenclature for algae, fungi, and plants (ICNafp) that of plants (including cyanobacteria), and the International Code of Nomenclature of Bacteria (ICNB) that of bacteria (including Archaea). Virus names are governed by the International Committee on Taxonomy of Viruses (ICTV), a taxonomic code, which determines taxa as well as names. These codes differ in certain ways, e.g.:
+
+Unifying the different codes into a single code, the "BioCode", has been suggested, although implementation is not in sight. (There is also a code in development for a different system of classification which does not use ranks, but instead names clades. This is called the PhyloCode.)
+
+As noted above, there are some differences between the codes in the way in which binomials can be formed; for example the ICZN allows both parts to be the same, while the ICNafp does not. Another difference is in the way in which personal names are used in forming specific names or epithets. The ICNafp sets out precise rules by which a personal name is to be converted to a specific epithet. In particular, names ending in a consonant (but not "er") are treated as first being converted into Latin by adding "-ius" (for a man) or "-ia" (for a woman), and then being made genitive (i.e. meaning "of that person or persons"). This produces specific epithets like lecardii for Lecard (male), wilsoniae for Wilson (female), and brauniarum for the Braun sisters.[41] By contrast the ICZN does not require the intermediate creation of a Latin form of a personal name, allowing the genitive ending to be added directly to the personal name.[42] This explains the difference between the names of  the plant Magnolia hodgsonii and the bird Anthus hodgsoni. Furthermore, the ICNafp requires names not published in the form required by the code to be corrected to conform to it,[43] whereas the ICZN is more protective of the form used by the original author.[44]
+
+By tradition, the binomial names of species are usually typeset in italics; for example, Homo sapiens.[45] Generally, the binomial should be printed in a font style different from that used in the normal text; for example, "Several more Homo sapiens fossils were discovered." When handwritten, a binomial name should be underlined; for example, Homo sapiens.[46]
+
+The first part of the binomial, the genus name, is always written with an initial capital letter. In current usage, the second part is never written with an initial capital.[47][48] Older sources, particularly botanical works published before the 1950s, use a different convention. If the second part of the name is derived from a proper noun, e.g. the name of a person or place, a capital letter was used. Thus the modern form Berberis darwinii was written as Berberis Darwinii. A capital was also used when the name is formed by two nouns in apposition, e.g. Panthera Leo or Centaurea Cyanus.[49][note 3]
+
+When used with a common name, the scientific name often follows in parentheses, although this varies with publication.[51] For example, "The house sparrow (Passer domesticus) is decreasing in Europe."
+
+The binomial name should generally be written in full. The exception to this is when several species from the same genus are being listed or discussed in the same paper or report, or the same species is mentioned repeatedly; in which case the genus is written in full when it is first used, but may then be abbreviated to an initial (and a period/full stop).[52] For example, a list of members of the genus Canis might be written as "Canis lupus, C. aureus, C. simensis". In rare cases, this abbreviated form has spread to more general use; for example, the bacterium Escherichia coli is often referred to as just E. coli, and Tyrannosaurus rex is perhaps even better known simply as T. rex, these two both often appearing in this form in popular writing even where the full genus name has not already been given.
+
+The abbreviation "sp." is used when the actual specific name cannot or need not be specified. The abbreviation "spp." (plural) indicates "several species". These abbreviations are not italicised (or underlined).[53] For example: "Canis sp." means "an unspecified species of the genus Canis", while "Canis spp." means "two or more species of the genus Canis" (the abbreviations "sp." and "spp." can easily be confused with the abbreviations "ssp." (zoology) or "subsp." (botany), plurals "sspp." or "subspp.", referring to one or more subspecies. See trinomen (zoology) and infraspecific name).
+
+The abbreviation "cf." (i.e. confer in Latin) is used to compare individuals/taxa with known/described species. Conventions for use of the "cf." qualifier vary.[54] In paleontology, it is typically used when the identification is not confirmed.[55] For example, "Corvus cf. nasicus"  was used to indicate "a fossil bird similar to the Cuban crow but not certainly identified as this species".[56] In molecular systematics papers, "cf." may be used to indicate one or more undescribed species assumed related to a described species. For example, in a paper describing the phylogeny of small benthic freshwater fish called darters, five undescribed putative species (Ozark, Sheltowee, Wildcat, Ihiyo, and Mamequit darters), notable for brightly colored nuptial males with distinctive color patterns,[57] were referred to as "Etheostoma cf. spectabile" because they had been viewed as related to, but distinct from, Etheostoma spectabile (orangethroat darter).[58] This view was supported in varying degrees by DNA analysis. The somewhat informal use of taxa names with qualifying abbreviations is referred to as open nomenclature and it is not subject to strict usage codes.
+
+In some contexts the dagger symbol ("†") may be used before or after the binomial name to indicate that the species is extinct.
+
+In scholarly texts, at least the first or main use of the binomial name is usually followed by the "authority" – a way of designating the scientist(s) who first published the name. The authority is written in slightly different ways in zoology and botany. For names governed by the ICZN the surname is usually written in full together with the date (normally only the year) of publication. The ICZN recommends that the "original author and date of a name should be cited at least once in each work dealing with the taxon denoted by that name."[59] For names governed by the ICNafp the name is generally reduced to a standard abbreviation and the date omitted. The International Plant Names Index maintains an approved list of botanical author abbreviations. Historically, abbreviations were used in zoology too.
+
+When the original name is changed, e.g. the species is moved to a different genus, both codes use parentheses around the original authority; the ICNafp also requires the person who made the change to be given. In the ICNafp, the original name is then called the basionym. Some examples:
+
+Binomial nomenclature, as described here, is a system for naming species. Implicitly it includes a system for naming genera, since the first part of the name of the species is a genus name. In a classification system based on ranks there are also ways of naming ranks above the level of genus and below the level of species. Ranks above genus (e.g., family, order, class) receive one-part names, which are conventionally not written in italics. Thus the house sparrow, Passer domesticus, belongs to the family Passeridae. Family names are normally based on genus names, although the endings used differ between zoology and botany.
+
+Ranks below species receive three-part names, conventionally written in italics like the names of species. There are significant differences between the ICZN and the ICNafp. In zoology, the only rank below species is subspecies and the name is written simply as three parts (a trinomen). Thus one of the subspecies of the olive-backed pipit is Anthus hodgsoni berezowskii. In botany, there are many ranks below species and although the name itself is written in three parts, a "connecting term" (not part of the name) is needed to show the rank. Thus the American black elder is Sambucus nigra subsp. canadensis; the white-flowered form of the ivy-leaved cyclamen is Cyclamen hederifolium f. albiflorum.

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+Asterix or The Adventures of Asterix (French: Astérix or Astérix le Gaulois [asteʁiks lə ɡolwa]; lit. "Asterix the Gaul") is a French bande dessinée series about Gaulish warriors, who have adventures and fight the Roman Empire during the era of Julius Caesar. The series first appeared in the Franco-Belgian comics magazine Pilote on 29 October 1959. It was written by René Goscinny and illustrated by Albert Uderzo until Goscinny's death in 1977. Uderzo then took over the writing until 2009, when he sold the rights to publishing company Hachette; he died in 2020. In 2013, a new team consisting of Jean-Yves Ferri (script) and Didier Conrad (artwork) took over. As of 2019[update], 38 volumes have been released, with the most recent released in October 2019.
+
+Each Asterix comic starts with the following introduction:
+
+The year is 50 BC. Gaul is entirely occupied by the Romans. Well, not entirely... One small village of indomitable Gauls still holds out against the invaders. And life is not easy for the Roman legionaries who garrison the fortified camps of Totorum, Aquarium, Laudanum and Compendium...[1][2]
+
+The series follows the adventures of a village of Gauls as they resist Roman occupation in 50 BCE. They do so by means of a magic potion, brewed by their druid Getafix (Panoramix in the French version), which temporarily gives the recipient superhuman strength. The protagonists, the title character Asterix and his friend Obelix, have various adventures. The "-ix" ending of both names (as well as all the other pseudo-Gaulish "-ix" names in the series) alludes to the "-rix" suffix (meaning "king") present in the names of many real Gaulish chieftains such as Vercingetorix, Orgetorix, and Dumnorix.
+
+In many of the stories, they travel to foreign countries, though other tales are set in and around their village. For much of the history of the series (Volumes 4 through 29), settings in Gaul and abroad alternated, with even-numbered volumes set abroad and odd-numbered volumes set in Gaul, mostly in the village.
+
+The Asterix series is one of the most popular Franco-Belgian comics in the world, with the series being translated into 111 languages and dialects as of 2009[update].[3]
+
+The success of the series has led to the adaptation of its books into 13 films: nine animated, and four live action (one of which, Asterix & Obelix: Mission Cleopatra, was a major box office success in France). There have also been a number of games based on the characters, and a theme park near Paris, Parc Astérix. The very first French satellite, Astérix, launched in 1965, was also named after the comics character. As of 2017, 370 million copies of Asterix books have been sold worldwide,[4] with co-creators René Goscinny and Albert Uderzo being France's best-selling authors abroad.[5][6]
+
+Prior to creating the Asterix series, Goscinny and Uderzo had previously had success with their series Oumpah-pah, which was published in Tintin magazine.[8]
+Astérix was originally serialised in Pilote magazine, debuting in the first issue on 29 October 1959.[9] In 1961 the first book was put together, titled Asterix the Gaul. From then on, books were released generally on a yearly basis. Their success was exponential; the first book sold 6,000 copies in its year of publication; a year later, the second sold 20,000. In 1963, the third sold 40,000; the fourth, released in 1964, sold 150,000. A year later, the fifth sold 300,000; 1966's Asterix and the Big Fight sold 400,000 upon initial publication. The ninth Asterix volume, when first released in 1967, sold 1.2 million copies in two days.
+
+Uderzo's first preliminary sketches portrayed Asterix as a huge and strong traditional Gaulish warrior. But Goscinny had a different picture in his mind, visualizing Asterix as a shrewd, compact warrior who would possess intelligence and wit more than raw strength. However, Uderzo felt that the downsized hero needed a strong but dim companion, to which Goscinny agreed. Hence, Obelix was born.[10] Despite the growing popularity of Asterix with the readers, the financial backing for the publication Pilote ceased. Pilote was taken over by Georges Dargaud.[10]
+
+When Goscinny died in 1977, Uderzo continued the series by popular demand of the readers, who implored him to continue. He continued to issue new volumes of the series, but on a less-frequent basis. Many critics and fans of the series prefer the earlier collaborations with Goscinny.[11] Uderzo created his own publishing company, Les Editions Albert-René, which published every album drawn and written by Uderzo alone since then.[10] However, Dargaud, the initial publisher of the series, kept the publishing rights on the 24 first albums made by both Uderzo and Goscinny. In 1990, the Uderzo and Goscinny families decided to sue Dargaud to take over the rights. In 1998, after a long trial, Dargaud lost the rights to publish and sell the albums. Uderzo decided to sell these rights to Hachette instead of Albert-René, but the publishing rights on new albums were still owned by Albert Uderzo (40%), Sylvie Uderzo (20%) and Anne Goscinny (40%).[citation needed]
+
+In December 2008, Uderzo sold his stake to Hachette, which took over the company.[12] In a letter published in the French newspaper Le Monde in 2009, Uderzo's daughter, Sylvie, attacked her father's decision to sell the family publishing firm and the rights to produce new Astérix adventures after his death. She said:
+
+... the co-creator of Astérix, France's comic strip hero, has betrayed the Gaulish warrior to the modern-day Romans – the men of industry and finance.[13][14]
+
+However, René Goscinny's daughter, Anne, also gave her agreement to the continuation of the series and sold her rights at the same time. She is reported to have said that "Asterix has already had two lives: one during my father's lifetime and one after it. Why not a third?".[15] A few months later, Uderzo appointed three illustrators, who had been his assistants for many years, to continue the series.[11] In 2011, Uderzo announced that a new Asterix album was due out in 2013, with Jean-Yves Ferri writing the story and Frédéric Mébarki drawing it.[16] A year later, in 2012, the publisher Albert-René announced that Frédéric Mébarki had withdrawn from drawing the new album, due to the pressure he felt in following in the steps of Uderzo. Comic artist Didier Conrad was officially announced to take over drawing duties from Mébarki, with the due date of the new album in 2013 unchanged.[17][18]
+
+In January 2015, after the murders of seven cartoonists at the satirical Paris weekly Charlie Hebdo, Astérix creator Albert Uderzo came out of retirement to draw two Astérix pictures honouring the memories of the victims.[19]
+
+Numbers 1–24, 32 and 34 are by Goscinny and Uderzo. Numbers 25–31 and 33 are by Uderzo alone. Numbers 35–38 are by Jean-Yves Ferri and Didier Conrad. Years stated are for their initial album release.
+
+Asterix Conquers Rome is a comics adaptation of the animated film The Twelve Tasks of Asterix. It was released in 1976, and was the 23rd volume to be published, but it has been rarely reprinted and is not considered to be canonical to the series. The only English translations ever to be published were in the Asterix Annual 1980 and never an English standalone volume. A picture-book version of the same story was published in English translation as The Twelve Tasks of Asterix by Hodder & Stoughton in 1978.
+
+In 1996, a tribute album in honour of Albert Uderzo was released titled "Uderzo Croqué par ses Amis", a volume containing 21 short stories with Uderzo in Ancient Gaul. This volume was published by Soleil Productions and has not been translated into English
+
+In 2007, Les Editions Albert René released a tribute volume titled Astérix et ses Amis, a 60-page volume of one-to-four-page short stories. It was a tribute to Albert Uderzo on his 80th birthday by 34 European cartoonists. The volume was translated into nine languages. As of 2016[update], it has not been translated into English.[23]
+
+In 2016, the French publisher Hachette, along with Anne Goscinny and Albert Uderzo decided to make the special issue album The XII Tasks of Asterix for the 40th anniversary of the film The Twelve Tasks of Asterix. There was no English edition.
+
+The main setting for the series is an unnamed coastal village (rumoured to be inspired by Erquy[by whom?]) in Armorica (present-day Brittany), a province of Gaul (modern France), in the year 50 BC. Julius Caesar has conquered nearly all of Gaul for the Roman Empire. The little Armorican village, however, has held out because the villagers can gain temporary superhuman strength by drinking a magic potion brewed by the local village druid, Getafix. His chief is Vitalstatistix.
+
+The main protagonist and hero of the village is Asterix, who, because of his shrewdness, is usually entrusted with the most important affairs of the village. He is aided in his adventures by his rather corpulent and slower thinking friend, Obelix, who, because he fell into the druid's cauldron of the potion as a baby, has permanent superhuman strength (because of this, Getafix steadily refuses to allow Obelix to drink the potion, as doing so would have a dangerous and unpredictable result). Obelix is usually accompanied by Dogmatix, his little dog. (Except for Asterix and Obelix, the names of the characters change with the language. For example, Obelix's dog's name is "Dogmatix" in English, but "Idéfix" in the original French edition.)
+
+Asterix and Obelix (and sometimes other members of the village) go on various adventures both within the village and in far away lands. Places visited in the series include parts of Gaul (Lutetia, Corsica etc.), neighbouring nations (Belgium, Spain, Britain, Germany etc.), and far away lands (North America, Middle East, India etc.).
+
+The series employs science-fiction and fantasy elements in the more recent books; for instance, the use of extraterrestrials in Asterix and the Falling Sky and the city of Atlantis in Asterix and Obelix All at Sea.
+
+The humour encountered in the Asterix comics often centers around puns, caricatures, and tongue-in-cheek stereotypes of contemporary European nations and French regions. Much of the humour in the initial Asterix books was French-specific, which delayed the translation of the books into other languages for fear of losing the jokes and the spirit of the story. Some translations have actually added local humour: In the Italian translation, the Roman legionaries are made to speak in 20th-century Roman dialect, and Obelix's famous Ils sont fous ces romains ("These Romans are crazy") is translated properly as Sono pazzi questi romani, humorously alluding to the Roman abbreviation SPQR. In another example: Hiccups are written onomatopoeically in French as hips, but in English as "hic", allowing Roman legionaries in more than one of the English translations to decline their hiccups absurdly in Latin (hic, haec, hoc). The newer albums share a more universal humour, both written and visual.[24]
+
+All the fictional characters in Asterix have names which are puns on their roles or personalities, and which follow certain patterns specific to nationality. Certain rules are followed (most of the time) such as Gauls (and their neighbours) having an "-ix" suffix for the men and ending in "-a" for the women; for example, Chief Vitalstatistix (so called due to his portly stature) and his wife Impedimenta (often at odds with the chief). The male Roman names end in "-us", echoing Latin nominative male singular form, as in Gluteus Maximus, a muscle-bound athlete whose name is literally the butt of the joke. Gothic names (present-day Germany) end in "-ic", after Gothic chiefs such as Alaric and Theoderic; for example Rhetoric the interpreter. Greek names end in "-os" or "-es"; for example, Thermos the restaurateur. British names end in "-ax" and are often puns on the taxation associated with the later United Kingdom; examples include Valuaddedtax the druid, and Selectivemploymentax the mercenary. Other nationalities are treated to pidgin translations from their language, like Huevos y Bacon, a Spanish chieftain (whose name, meaning eggs and bacon, is often guidebook Spanish for tourists), or literary and other popular media references, like Dubbelosix (a sly reference to James Bond's codename "007").
+
+Most of these jokes, and hence the names of the characters, are specific to the translation; for example, the druid named Getafix in English translation - "get a fix", referring to the character's role in dispensing the magic potion - is Panoramix in the original French and Miraculix in German.[25] Even so, occasionally the wordplay has been preserved: Obelix's dog, known in the original French as Idéfix (from idée fixe, a "fixed idea" or obsession), is called Dogmatix in English, which not only renders the original meaning strikingly closely ("dogmatic") but in fact adds another layer of wordplay with the syllable "Dog-" at the beginning of the name.
+
+The name Asterix, French Astérix, comes from astérisque, meaning "asterisk", which is the typographical symbol * indicating a footnote, from the Greek word αστήρ (aster), meaning a "star". His name is usually left unchanged in translations, aside from accents and the use of local alphabets. For example, in Esperanto, Polish, Slovene, Latvian, and Turkish it is Asteriks (in Turkish he was first named Bücür meaning "shorty", but the name was then standardised). Two exceptions include Icelandic, in which he is known as Ástríkur ("Rich of love"), and Sinhala, where he is known as සූර පප්පා (Soora Pappa), which can be interpreted as "Hero".
+
+For explanations of some of the other names, see List of Asterix characters.
+
+Many of the Asterix adventures take place in other countries away from their homeland in Gaul. In every album that takes place abroad, the characters meet (usually modern-day) stereotypes for each country, as seen by the French.
+
+When the Gauls see foreigners speaking their foreign languages, these have different representation in the cartoon speech bubbles:
+
+The various volumes have been translated into more than 100 languages and dialects. Besides the original French language, most albums are available in Estonian, English, Czech, Dutch, German, Galician, Danish, Icelandic, Norwegian, Swedish, Finnish, Spanish, Catalan, Basque, Portuguese, Italian, Greek, Hungarian, Polish, Romanian, Turkish, Slovene, Bulgarian, Serbian, Croatian, Latvian, Welsh,[26] as well as Latin.[27]
+
+Selected albums have also been translated into languages such as Esperanto, Scottish Gaelic, Irish, Scots, Indonesian, Persian, Mandarin, Korean, Japanese, Bengali, Afrikaans, Arabic, Hindi, Hebrew, Frisian, Romansch, Vietnamese, Sinhala, Ancient Greek, and Luxembourgish.[26]
+
+In Europe, several volumes were translated into a variety of regional languages and dialects, such as Alsatian, Breton, Chtimi (Picard), and Corsican in France; Bavarian, Swabian, and Low German in Germany; and Savo, Karelia, Rauma, and Helsinki slang dialects in Finland. Also, in Portugal, a special edition of the first volume, Asterix the Gaul, was translated into local language Mirandese.[28] In Greece, a number of volumes have appeared in the Cretan Greek, Cypriot Greek, and Pontic Greek dialects.[29] In the Italian version, while the Gauls speak standard Italian, the legionaries speak in the Romanesque dialect. In the former Yugoslavia, the "Forum" publishing house translated Corsican text in Asterix in Corsica into the Montenegrin dialect of Serbo-Croatian (today called Montenegrin).
+
+In the Netherlands, several volumes were translated into West Frisian, a Germanic language spoken in the province of Friesland; into Limburgish, a regional language spoken not only in Dutch Limburg but also in Belgian Limburg and North Rhine-Westphalia, Germany; and into Tweants, a dialect in the region of Twente in the eastern province of Overijssel. Hungarian-language books have been published in Yugoslavia for the Hungarian minority living in Serbia. Although not translated into a fully autonomous dialect, the books differ slightly from the language of the books issued in Hungary. In Sri Lanka, the cartoon series was adapted into Sinhala as Sura Pappa.[28]
+
+Most volumes have been translated into Latin and Ancient Greek, with accompanying teachers' guides, as a way of teaching these ancient languages.
+
+Before Asterix became famous, translations of some strips were published in British comics including Valiant, Ranger, and Look & Learn, under names Little Fred and Big Ed[30] and Beric the Bold, set in Roman-occupied Britain. These were included in an exhibition on Goscinny's life and career, and Asterix, in London's Jewish Museum in 2018.[31][32]
+
+The first 33 Asterix books were translated into English by Derek Hockridge and Anthea Bell, who were widely praised for maintaining the spirit and humour of the original French versions. Derek Hockridge died in 2013, so Anthea Bell translated books 34 to 36 by herself, before retiring in 2016 for health reasons. She died in 2018.[33] Adriana Hunter is the present translator.
+
+US publisher Papercutz in December 2019 announced it would begin publishing "all-new more American translations" of the Asterix books, starting on 19 May 2020.[34] The launch was postponed to 15 July 2020 as a result of the COVID-19 pandemic.[35] The new translator is Joe Johnson (Dr. Edward Joseph Johnson), a Professor of French and Spanish at Clayton State University.[36]
+
+The series has been adapted into various media. There are 14 films, 15 board games, 40 video games, and 1 theme park.
+
+Many gamebooks, board games and video games are based upon the Asterix series. In particular, many video games were released by various computer game publishers.
+
+Parc Astérix, a theme park 22 miles north of Paris, based upon the series, was opened in 1989. It is one of the most visited sites in France, with around 1.6 million visitors per year.

en/4150.html.txt

@@ -0,0 +1,35 @@
+
+
+The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus. In an uncharged atom, the atomic number is also equal to the number of electrons.
+
+The sum of the atomic number Z and the number of neutrons N gives the mass number A of an atom. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number A.
+
+Atoms with the same atomic number but different neutron numbers, and hence different mass numbers, are known as isotopes. A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth, determines the element's standard atomic weight. Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.
+
+The conventional symbol Z comes from the German word Zahl meaning number, which, before the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order is approximately, but not completely, consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge and a physical characteristic of atoms, did the word Atomzahl (and its English equivalent atomic number) come into common use in this context.
+
+Loosely speaking, the existence or construction of a periodic table of elements creates an ordering of the elements, and so they can be numbered in order.
+
+Dmitri Mendeleev claimed that he arranged his first periodic tables (first published on March 6, 1869) in order of atomic weight ("Atomgewicht").[1] However, in consideration of the elements' observed chemical properties, he changed the order slightly and placed tellurium (atomic weight 127.6) ahead of iodine (atomic weight 126.9).[1][2] This placement is consistent with the modern practice of ordering the elements by proton number, Z, but that number was not known or suspected at the time.
+
+A simple numbering based on periodic table position was never entirely satisfactory, however. Besides the case of iodine and tellurium, later several other pairs of elements (such as argon and potassium, cobalt and nickel) were known to have nearly identical or reversed atomic weights, thus requiring their placement in the periodic table to be determined by their chemical properties. However the gradual identification of more and more chemically similar lanthanide elements, whose atomic number was not obvious, led to inconsistency and uncertainty in the periodic numbering of elements at least from lutetium (element 71) onward (hafnium was not known at this time).
+
+In 1911, Ernest Rutherford gave a model of the atom in which a central nucleus held most of the atom's mass and a positive charge which, in units of the electron's charge, was to be approximately equal to half of the atom's atomic weight, expressed in numbers of hydrogen atoms. This central charge would thus be approximately half the atomic weight (though it was almost 25% different from the atomic number of gold (Z = 79, A = 197), the single element from which Rutherford made his guess). Nevertheless, in spite of Rutherford's estimation that gold had a central charge of about 100 (but was element Z = 79 on the periodic table), a month after Rutherford's paper appeared, Antonius van den Broek first formally suggested that the central charge and number of electrons in an atom was exactly equal to its place in the periodic table (also known as element number, atomic number, and symbolized Z). This proved eventually to be the case.
+
+The experimental position improved dramatically after research by Henry Moseley in 1913.[3] Moseley, after discussions with Bohr who was at the same lab (and who had used Van den Broek's hypothesis in his Bohr model of the atom), decided to test Van den Broek's and Bohr's hypothesis directly, by seeing if spectral lines emitted from excited atoms fitted the Bohr theory's postulation that the frequency of the spectral lines be proportional to the square of Z.
+
+To do this, Moseley measured the wavelengths of the innermost photon transitions (K and L lines) produced by the elements from aluminum (Z = 13) to gold (Z = 79) used as a series of movable anodic targets inside an x-ray tube.[4] The square root of the frequency of these photons (x-rays) increased from one target to the next in an arithmetic progression. This led to the conclusion (Moseley's law) that the atomic number does closely correspond (with an offset of one unit for K-lines, in Moseley's work) to the calculated electric charge of the nucleus, i.e. the element number Z. Among other things, Moseley demonstrated that the lanthanide series (from lanthanum to lutetium inclusive) must have 15 members—no fewer and no more—which was far from obvious from known chemistry at that time.
+
+After Moseley's death in 1915, the atomic numbers of all known elements from hydrogen to uranium (Z = 92) were examined by his method. There were seven elements (with Z < 92) which were not found and therefore identified as still undiscovered, corresponding to atomic numbers 43, 61, 72, 75, 85, 87 and 91.[5] From 1918 to 1947, all seven of these missing elements were discovered.[6] By this time, the first four transuranium elements had also been discovered, so that the periodic table was complete with no gaps as far as curium (Z = 96).
+
+In 1915, the reason for nuclear charge being quantized in units of Z, which were now recognized to be the same as the element number, was not understood. An old idea called Prout's hypothesis had postulated that the elements were all made of residues (or "protyles") of the lightest element hydrogen, which in the Bohr-Rutherford model had a single electron and a nuclear charge of one. However, as early as 1907, Rutherford and Thomas Royds had shown that alpha particles, which had a charge of +2, were the nuclei of helium atoms, which had a mass four times that of hydrogen, not two times. If Prout's hypothesis were true, something had to be neutralizing some of the charge of the hydrogen nuclei present in the nuclei of heavier atoms.
+
+In 1917, Rutherford succeeded in generating hydrogen nuclei from a nuclear reaction between alpha particles and nitrogen gas,[7] and believed he had proven Prout's law. He called the new heavy nuclear particles protons in 1920 (alternate names being proutons and protyles). It had been immediately apparent from the work of Moseley that the nuclei of heavy atoms have more than twice as much mass as would be expected from their being made of hydrogen nuclei, and thus there was required a hypothesis for the neutralization of the extra protons presumed present in all heavy nuclei. A helium nucleus was presumed to be composed of four protons plus two "nuclear electrons" (electrons bound inside the nucleus) to cancel two of the charges. At the other end of the periodic table, a nucleus of gold with a mass 197 times that of hydrogen was thought to contain 118 nuclear electrons in the nucleus to give it a residual charge of +79, consistent with its atomic number.
+
+All consideration of nuclear electrons ended with James Chadwick's discovery of the neutron in 1932. An atom of gold now was seen as containing 118 neutrons rather than 118 nuclear electrons, and its positive charge now was realized to come entirely from a content of 79 protons. After 1932, therefore, an element's atomic number Z was also realized to be identical to the proton number of its nuclei.
+
+The conventional symbol Z possibly comes from the German word Atomzahl (atomic number).[8] However, prior to 1915, the word Zahl (simply number) was used for an element's assigned number in the periodic table.
+
+Each element has a specific set of chemical properties as a consequence of the number of electrons present in the neutral atom, which is Z (the atomic number). The configuration of these electrons follows from the principles of quantum mechanics. The number of electrons in each element's electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. Hence, it is the atomic number alone that determines the chemical properties of an element; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number.
+
+The quest for new elements is usually described using atomic numbers. As of 2019, all elements with atomic numbers 1 to 118 have been observed. Synthesis of new elements is accomplished by bombarding target atoms of heavy elements with ions, such that the sum of the atomic numbers of the target and ion elements equals the atomic number of the element being created. In general, the half-life becomes shorter as atomic number increases, though an "island of stability" may exist for undiscovered isotopes with certain numbers of protons and neutrons.

en/4151.html.txt

@@ -0,0 +1,35 @@
+
+
+The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus. In an uncharged atom, the atomic number is also equal to the number of electrons.
+
+The sum of the atomic number Z and the number of neutrons N gives the mass number A of an atom. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number A.
+
+Atoms with the same atomic number but different neutron numbers, and hence different mass numbers, are known as isotopes. A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth, determines the element's standard atomic weight. Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.
+
+The conventional symbol Z comes from the German word Zahl meaning number, which, before the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order is approximately, but not completely, consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge and a physical characteristic of atoms, did the word Atomzahl (and its English equivalent atomic number) come into common use in this context.
+
+Loosely speaking, the existence or construction of a periodic table of elements creates an ordering of the elements, and so they can be numbered in order.
+
+Dmitri Mendeleev claimed that he arranged his first periodic tables (first published on March 6, 1869) in order of atomic weight ("Atomgewicht").[1] However, in consideration of the elements' observed chemical properties, he changed the order slightly and placed tellurium (atomic weight 127.6) ahead of iodine (atomic weight 126.9).[1][2] This placement is consistent with the modern practice of ordering the elements by proton number, Z, but that number was not known or suspected at the time.
+
+A simple numbering based on periodic table position was never entirely satisfactory, however. Besides the case of iodine and tellurium, later several other pairs of elements (such as argon and potassium, cobalt and nickel) were known to have nearly identical or reversed atomic weights, thus requiring their placement in the periodic table to be determined by their chemical properties. However the gradual identification of more and more chemically similar lanthanide elements, whose atomic number was not obvious, led to inconsistency and uncertainty in the periodic numbering of elements at least from lutetium (element 71) onward (hafnium was not known at this time).
+
+In 1911, Ernest Rutherford gave a model of the atom in which a central nucleus held most of the atom's mass and a positive charge which, in units of the electron's charge, was to be approximately equal to half of the atom's atomic weight, expressed in numbers of hydrogen atoms. This central charge would thus be approximately half the atomic weight (though it was almost 25% different from the atomic number of gold (Z = 79, A = 197), the single element from which Rutherford made his guess). Nevertheless, in spite of Rutherford's estimation that gold had a central charge of about 100 (but was element Z = 79 on the periodic table), a month after Rutherford's paper appeared, Antonius van den Broek first formally suggested that the central charge and number of electrons in an atom was exactly equal to its place in the periodic table (also known as element number, atomic number, and symbolized Z). This proved eventually to be the case.
+
+The experimental position improved dramatically after research by Henry Moseley in 1913.[3] Moseley, after discussions with Bohr who was at the same lab (and who had used Van den Broek's hypothesis in his Bohr model of the atom), decided to test Van den Broek's and Bohr's hypothesis directly, by seeing if spectral lines emitted from excited atoms fitted the Bohr theory's postulation that the frequency of the spectral lines be proportional to the square of Z.
+
+To do this, Moseley measured the wavelengths of the innermost photon transitions (K and L lines) produced by the elements from aluminum (Z = 13) to gold (Z = 79) used as a series of movable anodic targets inside an x-ray tube.[4] The square root of the frequency of these photons (x-rays) increased from one target to the next in an arithmetic progression. This led to the conclusion (Moseley's law) that the atomic number does closely correspond (with an offset of one unit for K-lines, in Moseley's work) to the calculated electric charge of the nucleus, i.e. the element number Z. Among other things, Moseley demonstrated that the lanthanide series (from lanthanum to lutetium inclusive) must have 15 members—no fewer and no more—which was far from obvious from known chemistry at that time.
+
+After Moseley's death in 1915, the atomic numbers of all known elements from hydrogen to uranium (Z = 92) were examined by his method. There were seven elements (with Z < 92) which were not found and therefore identified as still undiscovered, corresponding to atomic numbers 43, 61, 72, 75, 85, 87 and 91.[5] From 1918 to 1947, all seven of these missing elements were discovered.[6] By this time, the first four transuranium elements had also been discovered, so that the periodic table was complete with no gaps as far as curium (Z = 96).
+
+In 1915, the reason for nuclear charge being quantized in units of Z, which were now recognized to be the same as the element number, was not understood. An old idea called Prout's hypothesis had postulated that the elements were all made of residues (or "protyles") of the lightest element hydrogen, which in the Bohr-Rutherford model had a single electron and a nuclear charge of one. However, as early as 1907, Rutherford and Thomas Royds had shown that alpha particles, which had a charge of +2, were the nuclei of helium atoms, which had a mass four times that of hydrogen, not two times. If Prout's hypothesis were true, something had to be neutralizing some of the charge of the hydrogen nuclei present in the nuclei of heavier atoms.
+
+In 1917, Rutherford succeeded in generating hydrogen nuclei from a nuclear reaction between alpha particles and nitrogen gas,[7] and believed he had proven Prout's law. He called the new heavy nuclear particles protons in 1920 (alternate names being proutons and protyles). It had been immediately apparent from the work of Moseley that the nuclei of heavy atoms have more than twice as much mass as would be expected from their being made of hydrogen nuclei, and thus there was required a hypothesis for the neutralization of the extra protons presumed present in all heavy nuclei. A helium nucleus was presumed to be composed of four protons plus two "nuclear electrons" (electrons bound inside the nucleus) to cancel two of the charges. At the other end of the periodic table, a nucleus of gold with a mass 197 times that of hydrogen was thought to contain 118 nuclear electrons in the nucleus to give it a residual charge of +79, consistent with its atomic number.
+
+All consideration of nuclear electrons ended with James Chadwick's discovery of the neutron in 1932. An atom of gold now was seen as containing 118 neutrons rather than 118 nuclear electrons, and its positive charge now was realized to come entirely from a content of 79 protons. After 1932, therefore, an element's atomic number Z was also realized to be identical to the proton number of its nuclei.
+
+The conventional symbol Z possibly comes from the German word Atomzahl (atomic number).[8] However, prior to 1915, the word Zahl (simply number) was used for an element's assigned number in the periodic table.
+
+Each element has a specific set of chemical properties as a consequence of the number of electrons present in the neutral atom, which is Z (the atomic number). The configuration of these electrons follows from the principles of quantum mechanics. The number of electrons in each element's electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. Hence, it is the atomic number alone that determines the chemical properties of an element; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number.
+
+The quest for new elements is usually described using atomic numbers. As of 2019, all elements with atomic numbers 1 to 118 have been observed. Synthesis of new elements is accomplished by bombarding target atoms of heavy elements with ions, such that the sum of the atomic numbers of the target and ion elements equals the atomic number of the element being created. In general, the half-life becomes shorter as atomic number increases, though an "island of stability" may exist for undiscovered isotopes with certain numbers of protons and neutrons.

en/4152.html.txt

@@ -0,0 +1,181 @@
+
+
+Coordinates: 51°N 9°E / 51°N 9°E / 51; 9
+
+– in Europe (light green & dark grey)– in the European Union (light green)
+
+Germany (German: Deutschland, German pronunciation: [ˈdɔʏtʃlant]), officially the Federal Republic of Germany (German: Bundesrepublik Deutschland, listen),[e] is a country in Central and Western Europe. Covering an area of 357,022 square kilometres (137,847 sq mi), it lies between the Baltic and North seas to the north, and the Alps to the south. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west.
+
+Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity. A region named Germania was documented before AD 100. Beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation. Following the Napoleonic Wars and the dissolution of the Holy Roman Empire in 1806, the German Confederation was formed in 1815. In 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the German Revolution of 1918–1919, the Empire was replaced by the parliamentary Weimar Republic. The Nazi seizure of power in 1933 led to the establishment of a dictatorship, World War II, and the Holocaust. After the end of World War II in Europe and a period of Allied occupation, two new German states were founded: West Germany and East Germany. The Federal Republic of Germany was a founding member of the European Economic Community and the European Union. The country was reunified on 3 October 1990.
+
+Today, Germany is a federal parliamentary republic led by a chancellor. With 83 million inhabitants of its 16 constituent states, it is the second-most populous country in Europe after Russia, as well as the most populous member state of the European Union. Its capital and largest city is Berlin, and its financial centre is Frankfurt; the largest urban area is the Ruhr.
+
+Germany is a great power with a strong economy; it has the largest economy in Europe, the world's fourth-largest economy by nominal GDP, and the fifth-largest by PPP. As a global leader in several industrial and technological sectors, it is both the world's third-largest exporter and importer of goods. A highly developed country with a very high standard of living, it offers social security and a universal health care system, environmental protections, and a tuition-free university education. Germany is also a member of the United Nations, NATO, the G7, the G20, and the OECD. Known for its long and rich cultural history, Germany has many World Heritage sites and is among the top tourism destinations in the world.
+
+The English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine.[10] The German term Deutschland, originally diutisciu land ("the German lands") is derived from deutsch, descended from Old High German diutisc "of the people" (from diot or diota "people"), originally used to distinguish the language of the common people from Latin and its Romance descendants. This in turn descends from Proto-Germanic *þiudiskaz "of the people" (see also the Latinised form Theodiscus), derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- "people", from which the word Teutons also originates.[11]
+
+Ancient humans were present in Germany at least 600,000 years ago.[12] The first non-modern human fossil (the Neanderthal) was discovered in the Neander Valley.[13] Similarly dated evidence of modern humans has been found in the Swabian Jura, including 42,000-year-old flutes which are the oldest musical instruments ever found,[14] the 40,000-year-old Lion Man,[15] and the 35,000-year-old Venus of Hohle Fels.[16] The Nebra sky disk, created during the European Bronze Age, is attributed to a German site.[17]
+
+The Germanic tribes are thought to date from the Nordic Bronze Age or the Pre-Roman Iron Age.[18] From southern Scandinavia and north Germany, they expanded south, east, and west, coming into contact with the Celtic, Iranian, Baltic, and Slavic tribes.[19]
+
+Under Augustus, Rome began to invade Germania. In 9 AD, three Roman legions were defeated by Arminius.[20] By 100 AD, when Tacitus wrote Germania, Germanic tribes had settled along the Rhine and the Danube (the Limes Germanicus), occupying most of modern Germany. However, Baden Württemberg, southern Bavaria, southern Hesse and the western Rhineland had been incorporated into Roman provinces.[21][22][23] Around 260, Germanic peoples broke into Roman-controlled lands.[24] After the invasion of the Huns in 375, and with the decline of Rome from 395, Germanic tribes moved farther southwest: the Franks established the Frankish Kingdom and pushed east to subjugate Saxony and Bavaria, and areas of what is today eastern Germany were inhabited by Western Slavic tribes.[21]
+
+Charlemagne founded the Carolingian Empire in 800; it was divided in 843[25] and the Holy Roman Empire emerged from the eastern portion. The territory initially known as East Francia stretched from the Rhine in the west to the Elbe River in the east and from the North Sea to the Alps.[25] The Ottonian rulers (919–1024) consolidated several major duchies.[26] In 996 Gregory V became the first German Pope, appointed by his cousin Otto III, whom he shortly after crowned Holy Roman Emperor. The Holy Roman Empire absorbed northern Italy and Burgundy under the Salian emperors (1024–1125), although the emperors lost power through the Investiture controversy.[27]
+
+Under the Hohenstaufen emperors (1138–1254), German princes encouraged German settlement to the south and east (Ostsiedlung). Members of the Hanseatic League, mostly north German towns, prospered in the expansion of trade.[28] Population declined starting with the Great Famine in 1315, followed by the Black Death of 1348–50.[29] The Golden Bull issued in 1356 provided the constitutional structure of the Empire and codified the election of the emperor by seven prince-electors.[30]
+
+Johannes Gutenberg introduced moveable-type printing to Europe, laying the basis for the democratization of knowledge.[31] In 1517, Martin Luther incited the Protestant Reformation; the 1555 Peace of Augsburg tolerated the "Evangelical" faith (Lutheranism), but also decreed that the faith of the prince was to be the faith of his subjects (cuius regio, eius religio).[32] From the Cologne War through the Thirty Years' Wars (1618–1648), religious conflict devastated German lands and significantly reduced the population.[33][34]
+
+The Peace of Westphalia ended religious warfare among the Imperial Estates;[33] their mostly German-speaking rulers were able to choose Roman Catholicism, Lutheranism, or the Reformed faith as their official religion.[35] The legal system initiated by a series of Imperial Reforms (approximately 1495–1555) provided for considerable local autonomy and a stronger Imperial Diet.[36] The House of Habsburg held the imperial crown from 1438 until the death of Charles VI in 1740. Following the War of Austrian Succession and the Treaty of Aix-la-Chapelle, Charles VI's daughter Maria Theresa ruled as Empress Consort when her husband, Francis I, became Emperor.[37][38]
+
+From 1740, dualism between the Austrian Habsburg Monarchy and the Kingdom of Prussia dominated German history. In 1772, 1793, and 1795, Prussia and Austria, along with the Russian Empire, agreed to the Partitions of Poland.[39][40] During the period of the French Revolutionary Wars, the Napoleonic era and the subsequent final meeting of the Imperial Diet, most of the Free Imperial Cities were annexed by dynastic territories; the ecclesiastical territories were secularised and annexed. In 1806 the Imperium was dissolved; France, Russia, Prussia and the Habsburgs (Austria) competed for hegemony in the German states during the Napoleonic Wars.[41]
+
+Following the fall of Napoleon, the Congress of Vienna founded the German Confederation, a loose league of 39 sovereign states. The appointment of the Emperor of Austria as the permanent president reflected the Congress's rejection of Prussia's rising influence. Disagreement within restoration politics partly led to the rise of liberal movements, followed by new measures of repression by Austrian statesman Klemens von Metternich.[42][43] The Zollverein, a tariff union, furthered economic unity.[44] In light of revolutionary movements in Europe, intellectuals and commoners started the revolutions of 1848 in the German states. King Frederick William IV of Prussia was offered the title of Emperor, but with a loss of power; he rejected the crown and the proposed constitution, a temporary setback for the movement.[45]
+
+King William I appointed Otto von Bismarck as the Minister President of Prussia in 1862. Bismarck successfully concluded the war with Denmark in 1864; the subsequent decisive Prussian victory in the Austro-Prussian War of 1866 enabled him to create the North German Confederation which excluded Austria. After the defeat of France in the Franco-Prussian War, the German princes proclaimed the founding of the German Empire in 1871. Prussia was the dominant constituent state of the new empire; the King of Prussia ruled as its Kaiser, and Berlin became its capital.[46][47]
+
+In the Gründerzeit period following the unification of Germany, Bismarck's foreign policy as Chancellor of Germany secured Germany's position as a great nation by forging alliances and avoiding war.[47] However, under Wilhelm II, Germany took an imperialistic course, leading to friction with neighbouring countries.[48] A dual alliance was created with the multinational realm of Austria-Hungary; the Triple Alliance of 1882 included Italy. Britain, France and Russia also concluded alliances to protect against Habsburg interference with Russian interests in the Balkans or German interference against France.[49] At the Berlin Conference in 1884, Germany claimed several colonies including German East Africa, German South West Africa, Togoland, and Kamerun.[50] Later, Germany further expanded its colonial empire to include holdings in the Pacific and China.[51] The colonial government in South West Africa (present-day Namibia), from 1904 to 1907, carried out the annihilation of the local Herero and Namaqua peoples as punishment for an uprising;[52][53] this was the 20th century's first genocide.[53]
+
+The assassination of Austria's crown prince on 28 June 1914 provided the pretext for Austria-Hungary to attack Serbia and trigger World War I. After four years of warfare, in which approximately two million German soldiers were killed,[54] a general armistice ended the fighting. In the German Revolution (November 1918), Emperor Wilhelm II and the ruling princes abdicated their positions and Germany was declared a federal republic. Germany's new leadership signed the Treaty of Versailles in 1919, accepting defeat by the Allies. Germans perceived the treaty as humiliating, which was seen by historians as influential in the rise of Adolf Hitler.[55] Germany lost around 13% of its European territory and ceded all of its colonial possessions in Africa and the South Sea.[56]
+
+On 11 August 1919, President Friedrich Ebert signed the democratic Weimar Constitution.[57] In the subsequent struggle for power, communists seized power in Bavaria, but conservative elements elsewhere attempted to overthrow the Republic in the Kapp Putsch. Street fighting in the major industrial centres, the occupation of the Ruhr by Belgian and French troops, and a period of hyperinflation followed. A debt restructuring plan and the creation of a new currency in 1924 ushered in the Golden Twenties, an era of artistic innovation and liberal cultural life.[58][59][60]
+
+The worldwide Great Depression hit Germany in 1929. Chancellor Heinrich Brüning's government pursued a policy of fiscal austerity and deflation which caused unemployment of nearly 30% by 1932.[61] The Nazi Party led by Adolf Hitler won a special election in 1932 and Hindenburg appointed Hitler as Chancellor of Germany on 30 January 1933.[62] After the Reichstag fire, a decree abrogated basic civil rights and the first Nazi concentration camp opened.[63][64] The Enabling Act gave Hitler unrestricted legislative power, overriding the constitution;[65] his government established a centralised totalitarian state, withdrew from the League of Nations, and dramatically increased the country's rearmament.[66] A government-sponsored programme for economic renewal focused on public works, the most famous of which was the autobahn.[67]
+
+In 1935, the regime withdrew from the Treaty of Versailles and introduced the Nuremberg Laws which targeted Jews and other minorities.[68] Germany also reacquired control of the Saarland in 1935,[69] remilitarised the Rhineland in 1936, annexed Austria in 1938, annexed the Sudetenland in 1938 with the Munich Agreement, and in violation of the agreement occupied Czechoslovakia in March 1939.[70] Kristallnacht saw the burning of synagogues, the destruction of Jewish businesses, and mass arrests of Jewish people.[71]
+
+In August 1939, Hitler's government negotiated the Molotov–Ribbentrop pact that divided Eastern Europe into German and Soviet spheres of influence.[72] On 1 September 1939, Germany invaded Poland, beginning World War II in Europe;[73] Britain and France declared war on Germany on 3 September.[74] In the spring of 1940, Germany conquered Denmark and Norway, the Netherlands, Belgium, Luxembourg, and France, forcing the French government to sign an armistice. The British repelled German air attacks in the Battle of Britain in the same year. In 1941, German troops invaded Yugoslavia, Greece and the Soviet Union. By 1942, Germany and her allies controlled most of continental Europe and North Africa, but following the Soviet victory at the Battle of Stalingrad, the allies' reconquest of North Africa and invasion of Italy in 1943, German forces suffered repeated military defeats. In 1944, the Soviets pushed into Eastern Europe; the Western allies landed in France and entered Germany despite a final German counteroffensive. Following Hitler's suicide during the Battle of Berlin, Germany surrendered on 8 May 1945, ending World War II in Europe.[73][75] Following the end of the war, surviving Nazi officials were tried for war crimes at the Nuremberg trials.[76][77]
+
+In what later became known as the Holocaust, the German government persecuted minorities, including interning them in concentration and death camps across Europe. In total 17 million people were systematically murdered, including 6 million Jews, at least 130,000 Romani, 275,000 persons with disabilities, thousands of Jehovah's Witnesses, thousands of homosexuals, and hundreds of thousands of political and religious opponents.[78] Nazi policies in German-occupied countries resulted in the deaths of 2.7 million Poles,[79] 1.3 million Ukrainians, 1 million Belarusians[80] and 3.5 million Soviet prisoners of war.[80][76] German military casualties have been estimated at 5.3 million,[81] and around 900,000 German civilians died.[82] Around 12 million ethnic Germans were expelled from across Eastern Europe, and Germany lost roughly one-quarter of its pre-war territory.[83]
+
+After Nazi Germany surrendered, the Allies partitioned Berlin and Germany's remaining territory into four occupation zones. The western sectors, controlled by France, the United Kingdom, and the United States, were merged on 23 May 1949 to form the Federal Republic of Germany (Bundesrepublik Deutschland (BRD)); on 7 October 1949, the Soviet Zone became the German Democratic Republic (Deutsche Demokratische Republik (DDR)). They were informally known as West Germany and East Germany.[85] East Germany selected East Berlin as its capital, while West Germany chose Bonn as a provisional capital, to emphasise its stance that the two-state solution was temporary.[86]
+
+West Germany was established as a federal parliamentary republic with a "social market economy". Starting in 1948 West Germany became a major recipient of reconstruction aid under the Marshall Plan.[87] Konrad Adenauer was elected the first Federal Chancellor of Germany in 1949. The country enjoyed prolonged economic growth (Wirtschaftswunder) beginning in the early 1950s.[88] West Germany joined NATO in 1955 and was a founding member of the European Economic Community.[89]
+
+East Germany was an Eastern Bloc state under political and military control by the USSR via occupation forces and the Warsaw Pact. Although East Germany claimed to be a democracy, political power was exercised solely by leading members (Politbüro) of the communist-controlled Socialist Unity Party of Germany, supported by the Stasi, an immense secret service.[90] While East German propaganda was based on the benefits of the GDR's social programmes and the alleged threat of a West German invasion, many of its citizens looked to the West for freedom and prosperity.[91] The Berlin Wall, built in 1961, prevented East German citizens from escaping to West Germany, becoming a symbol of the Cold War.[92]
+
+Tensions between East and West Germany were reduced in the late 1960s by Chancellor Willy Brandt's Ostpolitik.[93] In 1989, Hungary decided to dismantle the Iron Curtain and open its border with Austria, causing the emigration of thousands of East Germans to West Germany via Hungary and Austria. This had devastating effects on the GDR, where regular mass demonstrations received increasing support. In an effort to help retain East Germany as a state, the East German authorities eased border restrictions, but this actually led to an acceleration of the Wende reform process culminating in the Two Plus Four Treaty under which Germany regained full sovereignty. This permitted German reunification on 3 October 1990, with the accession of the five re-established states of the former GDR.[94] The fall of the Wall in 1989 became a symbol of the Fall of Communism, the Dissolution of the Soviet Union, German Reunification and Die Wende.[95]
+
+United Germany was considered the enlarged continuation of West Germany so it retained its memberships in international organisations.[96] Based on the Berlin/Bonn Act (1994), Berlin again became the capital of Germany, while Bonn obtained the unique status of a Bundesstadt (federal city) retaining some federal ministries.[97] The relocation of the government was completed in 1999, and modernisation of the east German economy was scheduled to last until 2019.[98][99]
+
+Since reunification, Germany has taken a more active role in the European Union, signing the Maastricht Treaty in 1992 and the Lisbon Treaty in 2007,[100] and co-founding the Eurozone.[101] Germany sent a peacekeeping force to secure stability in the Balkans and sent German troops to Afghanistan as part of a NATO effort to provide security in that country after the ousting of the Taliban.[102][103]
+
+In the 2005 elections, Angela Merkel became the first female chancellor. In 2009 the German government approved a €50 billion stimulus plan.[104] Among the major German political projects of the early 21st century are the advancement of European integration, the energy transition (Energiewende) for a sustainable energy supply, the "Debt Brake" for balanced budgets, measures to increase the fertility rate (pronatalism), and high-tech strategies for the transition of the German economy, summarised as Industry 4.0.[105] Germany was affected by the European migrant crisis in 2015: the country took in over a million migrants and developed a quota system which redistributed migrants around its federal states.[106]
+
+Germany is in Western and Central Europe, bordering Denmark to the north, Poland and the Czech Republic to the east, Austria to the southeast, and Switzerland to the south-southwest. France, Luxembourg and Belgium are situated to the west, with the Netherlands to the northwest. Germany is also bordered by the North Sea and, at the north-northeast, by the Baltic Sea. German territory covers 357,022 km2 (137,847 sq mi), consisting of 348,672 km2 (134,623 sq mi) of land and 8,350 km2 (3,224 sq mi) of water. It is the seventh largest country by area in Europe and the 62nd largest in the world.[4]
+
+Elevation ranges from the mountains of the Alps (highest point: the Zugspitze at 2,963 metres or 9,721 feet) in the south to the shores of the North Sea (Nordsee) in the northwest and the Baltic Sea (Ostsee) in the northeast. The forested uplands of central Germany and the lowlands of northern Germany (lowest point: Wilstermarsch at 3.54 metres or 11.6 feet below sea level) are traversed by such major rivers as the Rhine, Danube and Elbe. Significant natural resources include iron ore, coal, potash, timber, lignite, uranium, copper, natural gas, salt, and nickel.[4]
+
+Most of Germany has a temperate climate, ranging from oceanic in the north to continental in the east and southeast. Winters range from cold in the southern Alps to mild and are generally overcast with limited precipitation, while summers can vary from hot and dry to cool and rainy. The northern regions have prevailing westerly winds that bring in moist air from the North Sea, moderating the temperature and increasing precipitation. Conversely, the southeast regions have more extreme temperatures.[107]
+
+From February 2019–2020, average monthly temperatures in Germany ranged from a low of 3.3 °C (37.9 °F) in January 2020 to a high of 19.8 °C (67.6 °F) in June 2019.[108] Average monthly precipitation ranged from 30 litres per square metre in February and April 2019 to 125 litres per square metre in February 2020.[109] Average monthly hours of sunshine ranged from 45 in November 2019 to 300 in June 2019.[110]
+
+The territory of Germany can be divided into two ecoregions: European-Mediterranean montane mixed forests and Northeast-Atlantic shelf marine.[111] As of 2016[update] 51% of Germany's land area is devoted to agriculture, while 30% is forested and 14% is covered by settlements or infrastructure.[112]
+
+Plants and animals include those generally common to Central Europe. According to the National Forest Inventory, beeches, oaks, and other deciduous trees constitute just over 40% of the forests; roughly 60% are conifers, particularly spruce and pine.[113] There are many species of ferns, flowers, fungi, and mosses. Wild animals include roe deer, wild boar, mouflon (a subspecies of wild sheep), fox, badger, hare, and small numbers of the Eurasian beaver.[114] The blue cornflower was once a German national symbol.[115]
+
+The 16 national parks in Germany include the Jasmund National Park, the Vorpommern Lagoon Area National Park, the Müritz National Park, the Wadden Sea National Parks, the Harz National Park, the Hainich National Park, the Black Forest National Park, the Saxon Switzerland National Park, the Bavarian Forest National Park and the Berchtesgaden National Park.[116] In addition, there are 17 Biosphere Reserves[117] and 105 nature parks.[118] More than 400 zoos and animal parks operate in Germany.[119] The Berlin Zoo, which opened in 1844, is the oldest in Germany, and claims the most comprehensive collection of species in the world.[120]
+
+Germany is a federal, parliamentary, representative democratic republic. Federal legislative power is vested in the parliament consisting of the Bundestag (Federal Diet) and Bundesrat (Federal Council), which together form the legislative body. The Bundestag is elected through direct elections: half by majority vote and half by proportional representation. The members of the Bundesrat represent and are appointed by the governments of the sixteen federated states.[4] The German political system operates under a framework laid out in the 1949 constitution known as the Grundgesetz (Basic Law). Amendments generally require a two-thirds majority of both the Bundestag and the Bundesrat; the fundamental principles of the constitution, as expressed in the articles guaranteeing human dignity, the separation of powers, the federal structure, and the rule of law, are valid in perpetuity.[121]
+
+The president, currently Frank-Walter Steinmeier, is the head of state and invested primarily with representative responsibilities and powers. He is elected by the Bundesversammlung (federal convention), an institution consisting of the members of the Bundestag and an equal number of state delegates.[4] The second-highest official in the German order of precedence is the Bundestagspräsident (president of the Bundestag), who is elected by the Bundestag and responsible for overseeing the daily sessions of the body.[122] The third-highest official and the head of government is the chancellor, who is appointed by the Bundespräsident after being elected by the party or coalition with the most seats in the Bundestag.[4] The chancellor, currently Angela Merkel, is the head of government and exercises executive power through their Cabinet.[4]
+
+Since 1949, the party system has been dominated by the Christian Democratic Union and the Social Democratic Party of Germany. So far every chancellor has been a member of one of these parties. However, the smaller liberal Free Democratic Party and the Alliance '90/The Greens have also achieved some success. Since 2007, the left-wing populist party The Left has been a staple in the German Bundestag, though they have never been part of the federal government. In the 2017 German federal election, the right-wing populist Alternative for Germany gained enough votes to attain representation in the parliament for the first time.[123][124]
+
+Germany comprises sixteen federal states which are collectively referred to as Bundesländer.[125] Each state has its own state constitution,[126] and is largely autonomous in regard to its internal organisation. As of 2017[update] Germany is divided into 401 districts (Kreise) at a municipal level; these consist of 294 rural districts and 107 urban districts.[127]
+
+Germany has a civil law system based on Roman law with some references to Germanic law.[131] The Bundesverfassungsgericht (Federal Constitutional Court) is the German Supreme Court responsible for constitutional matters, with power of judicial review.[132] Germany's supreme court system is specialised: for civil and criminal cases, the highest court of appeal is the inquisitorial Federal Court of Justice, and for other affairs the courts are the Federal Labour Court, the Federal Social Court, the Federal Finance Court and the Federal Administrative Court.[133]
+
+Criminal and private laws are codified on the national level in the Strafgesetzbuch and the Bürgerliches Gesetzbuch respectively. The German penal system seeks the rehabilitation of the criminal and the protection of the public.[134] Except for petty crimes, which are tried before a single professional judge, and serious political crimes, all charges are tried before mixed tribunals on which lay judges (Schöffen) sit side by side with professional judges.[135][136]
+
+Germany has a low murder rate with 1.18 murders per 100,000 as of 2016[update].[137] In 2018, the overall crime rate fell to its lowest since 1992.[138]
+
+Germany has a network of 227 diplomatic missions abroad[140] and maintains relations with more than 190 countries.[141]  Germany is a member of NATO, the OECD, the G8, the G20, the World Bank and the IMF. It has played an influential role in the European Union since its inception and has maintained a strong alliance with France and all neighbouring countries since 1990. Germany promotes the creation of a more unified European political, economic and security apparatus.[142][143][144] The governments of Germany and the United States are close political allies.[145] Cultural ties and economic interests have crafted a bond between the two countries resulting in Atlanticism.[146]
+
+The development policy of Germany is an independent area of foreign policy. It is formulated by the Federal Ministry for Economic Cooperation and Development and carried out by the implementing organisations. The German government sees development policy as a joint responsibility of the international community.[147] It was the world's second biggest aid donor in 2019 after the United States.[148]
+
+Germany's military, the Bundeswehr, is organised into the Heer (Army and special forces KSK), Marine (Navy), Luftwaffe (Air Force), Zentraler Sanitätsdienst der Bundeswehr (Joint Medical Service) and Streitkräftebasis (Joint Support Service) branches. In absolute terms, German military expenditure is the 8th highest in the world.[149] In 2018, military spending was at $49.5 billion, about 1.2% of the country's GDP, well below the NATO target of 2%.[150]
+
+As of January 2020[update], the Bundeswehr has a strength of 184,001 active soldiers and 80,947 civilians.[151] Reservists are available to the armed forces and participate in defence exercises and deployments abroad.[152] Until 2011, military service was compulsory for men at age 18, but this has been officially suspended and replaced with a voluntary service.[153][154] Since 2001 women may serve in all functions of service without restriction.[155] According to SIPRI, Germany was the fourth largest exporter of major arms in the world from 2014 to 2018.[156]
+
+In peacetime, the Bundeswehr is commanded by the Minister of Defence. In state of defence, the Chancellor would become commander-in-chief of the Bundeswehr.[157] The role of the Bundeswehr is described in the Constitution of Germany as defensive only. But after a ruling of the Federal Constitutional Court in 1994 the term "defence" has been defined to not only include protection of the borders of Germany, but also crisis reaction and conflict prevention, or more broadly as guarding the security of Germany anywhere in the world. As of 2017[update], the German military has about 3,600 troops stationed in foreign countries as part of international peacekeeping forces, including about 1,200 supporting operations against Daesh, 980 in the NATO-led Resolute Support Mission in Afghanistan, and 800 in Kosovo.[158]
+
+Germany has a social market economy with a highly skilled labour force, a low level of corruption, and a high level of innovation.[4][160][161] It is the world's third largest exporter of goods,[4] and has the largest national economy in Europe which is also the world's fourth largest by nominal GDP[162] and the fifth by PPP.[163] Its GDP per capita measured in purchasing power standards amounts to 121% of the EU27 average (100%).[164] The service sector contributes approximately 69% of the total GDP, industry 31%, and agriculture 1% as of 2017[update].[4] The unemployment rate published by Eurostat amounts to 3.2% as of January 2020[update], which is the fourth-lowest in the EU.[165]
+
+Germany is part of the European single market which represents more than 450 million consumers.[166] In 2017, the country accounted for 28% of the Eurozone economy according to the International Monetary Fund.[167] Germany introduced the common European currency, the Euro, in 2002.[168] Its monetary policy is set by the European Central Bank, which is headquartered in Frankfurt.[169][159]
+
+Being home to the modern car, the automotive industry in Germany is regarded as one of the most competitive and innovative in the world,[170] and is the fourth largest by production.[171] The top 10 exports of Germany are vehicles, machinery, chemical goods, electronic products, electrical equipments, pharmaceuticals, transport equipments, basic metals, food products, and rubber and plastics.[172] Germany is one of the largest exporters globally.[173]
+
+Of the world's 500 largest stock-market-listed companies measured by revenue in 2019, the Fortune Global 500, 29 are headquartered in Germany.[174] 30 major Germany-based companies are included in the DAX, the German stock market index which is operated by Frankfurt Stock Exchange.[175] Well-known international brands include Mercedes-Benz, BMW, Volkswagen, Audi, Siemens, Allianz, Adidas, Porsche, Bosch and Deutsche Telekom.[176] Berlin is a hub for startup companies and has become the leading location for venture capital funded firms in the European Union.[177] Germany is recognised for its large portion of specialised small and medium enterprises, known as the Mittelstand model.[178] These companies represent 48% global market leaders in their segments, labelled Hidden Champions.[179]
+
+Research and development efforts form an integral part of the German economy.[180] In 2018 Germany ranked fourth globally in terms of number of science and engineering research papers published.[181] Research institutions in Germany include the Max Planck Society, the Helmholtz Association, and the Fraunhofer Society and the Leibniz Association.[182] Germany is the largest contributor to the European Space Agency.[183]
+
+With its central position in Europe, Germany is a transport hub for the continent.[184] Its road network is among the densest in Europe.[185] The motorway (Autobahn) is widely known for having no federally mandated speed limit for some classes of vehicles.[186] The InterCityExpress or ICE train network serves major German cities as well as destinations in neighbouring countries with speeds up to 300 km/h (190 mph).[187] The largest German airports are Frankfurt Airport and Munich Airport.[188] The Port of Hamburg is one of the top twenty largest container ports in the world.[189]
+
+In 2015[update], Germany was the world's seventh-largest consumer of energy.[190] The government and the nuclear power industry agreed to phase out all nuclear power plants by 2021.[191] It meets the country's power demands using 40% renewable sources.[192] Germany is committed to the Paris Agreement and several other treaties promoting biodiversity, low emission standards, and water management.[193][194][195] The country's household recycling rate is among the highest in the world—at around 65%.[196] Nevertheless, the country's total greenhouse gas emissions were the highest in the EU in 2017[update].[197] The German energy transition (Energiewende) is the recognised move to a sustainable economy by means of energy efficiency and renewable energy.[198]
+
+Germany is the ninth most visited country in the world as of 2017[update], with 37.4 million visits.[199] Berlin has become the third most visited city destination in Europe.[200] Domestic and international travel and tourism combined directly contribute over €105.3 billion to German GDP. Including indirect and induced impacts, the industry supports 4.2 million jobs.[201]
+
+Germany's most visited and popular landmarks include Cologne Cathedral, the Brandenburg Gate, the Reichstag, the Dresden Frauenkirche, Neuschwanstein Castle, Heidelberg Castle, the Wartburg, and Sanssouci Palace.[202] The Europa-Park near Freiburg is Europe's second most popular theme park resort.[203]
+
+With a population of 80.2 million according to the 2011 census,[204] rising to 83.1 million as of 2019[update],[5] Germany is the most populous country in the European Union, the second most populous country in Europe after Russia, and the 19th most populous country in the world. Its population density stands at 227 inhabitants per square kilometre (588 per square mile). The overall life expectancy in Germany at birth is 80.19 years (77.93 years for males and 82.58 years for females).[4] The fertility rate of 1.41 children born per woman (2011 estimates) is below the replacement rate of 2.1 and is one of the lowest fertility rates in the world.[4] Since the 1970s, Germany's death rate has exceeded its birth rate. However, Germany is witnessing increased birth rates and migration rates since the beginning of the 2010s, particularly a rise in the number of well-educated migrants. Germany has the third oldest population in the world, with the average age of 47.4 years.[4]
+
+Four sizeable groups of people are referred to as "national minorities" because their ancestors have lived in their respective regions for centuries:[205] There is a Danish minority in the northernmost state of Schleswig-Holstein;[205] the Sorbs, a Slavic population, are in the Lusatia region of Saxony and Brandenburg.; the Roma and Sinti live throughout the country; and the Frisians are concentrated in Schleswig-Holstein's western coast and in the north-western part of Lower Saxony.[205]
+
+After the United States, Germany is the second most popular immigration destination in the world. The majority of migrants live in western Germany, in particular in urban areas. Of the country's residents, 18.6 million people (22.5%) were of immigrant or partially immigrant descent in 2016 (including persons descending or partially descending from ethnic German repatriates).[206] In 2015, the Population Division of the United Nations Department of Economic and Social Affairs listed Germany as host to the second-highest number of international migrants worldwide, about 5% or 12 million of all 244 million migrants.[207] As of 2018[update], Germany ranks fifth amongst EU countries in terms of the percentage of migrants in the country's population, at 12.9%.[208]
+
+Germany has a number of large cities. There are 11 officially recognised metropolitan regions. The country's largest city is Berlin, while its largest urban area is the Ruhr.[209]
+
+The 2011 German Census showed Christianity as the largest religion in Germany, with 66.8% identified themselves as Christian, with 3.8% of those not being church members.[210] 31.7% declared themselves as Protestants, including members of the Evangelical Church in Germany (which encompasses Lutheran, Reformed and administrative or confessional unions of both traditions) and the free churches (German: Evangelische Freikirchen); 31.2% declared themselves as Roman Catholics, and Orthodox believers constituted 1.3%. According to data from 2016, the Catholic Church and the Evangelical Church claimed 28.5% and 27.5%, respectively, of the population.[211][212] Islam is the second largest religion in the country.[213] In the 2011 census, 1.9% of the census population (1.52 million people) gave their religion as Islam, but this figure is deemed unreliable because a disproportionate number of adherents of this religion (and other religions, such as Judaism) are likely to have made use of their right not to answer the question.[214] Most of the Muslims are Sunnis and Alevites from Turkey, but there are a small number of Shi'ites, Ahmadiyyas and other denominations. Other religions comprise less than one percent of Germany's population.[213]
+
+A study in 2018 estimated that 38% of the population are not members of any religious organization or denomination,[215] though up to a third may still consider themselves religious. Irreligion in Germany is strongest in the former East Germany, which used to be predominantly Protestant before state atheism, and in major metropolitan areas.[216][217]
+
+German is the official and predominant spoken language in Germany.[218] It is one of 24 official and working languages of the European Union, and one of the three procedural languages of the European Commission.[219] German is the most widely spoken first language in the European Union, with around 100 million native speakers.[220]
+
+Recognised native minority languages in Germany are Danish, Low German, Low Rhenish, Sorbian, Romany, North Frisian and Saterland Frisian; they are officially protected by the European Charter for Regional or Minority Languages. The most used immigrant languages are Turkish, Arabic, Kurdish, Polish, the Balkan languages and Russian. Germans are typically multilingual: 67% of German citizens claim to be able to communicate in at least one foreign language and 27% in at least two.[218]
+
+Responsibility for educational supervision in Germany is primarily organised within the individual federal states. Optional kindergarten education is provided for all children between three and six years old, after which school attendance is compulsory for at least nine years. Primary education usually lasts for four to six years.[221] Secondary schooling is divided into tracks based on whether students pursue academic or vocational education.[222] A system of apprenticeship called Duale Ausbildung leads to a skilled qualification which is almost comparable to an academic degree. It allows students in vocational training to learn in a company as well as in a state-run trade school.[221] This model is well regarded and reproduced all around the world.[223]
+
+Most of the German universities are public institutions, and students traditionally study without fee payment.[224] The general requirement for university is the Abitur. According to an OECD report in 2014, Germany is the world's third leading destination for international study.[225] The established universities in Germany include some of the oldest in the world, with Heidelberg University (established in 1386) being the oldest.[226] The Humboldt University of Berlin, founded in 1810 by the liberal educational reformer Wilhelm von Humboldt, became the academic model for many Western universities.[227][228] In the contemporary era Germany has developed eleven Universities of Excellence.
+
+Germany's system of hospitals, called Krankenhäuser, dates from medieval times, and today, Germany has the world's oldest universal health care system, dating from Bismarck's social legislation of the 1880s.[230] Since the 1880s, reforms and provisions have ensured a balanced health care system. The population is covered by a health insurance plan provided by statute, with criteria allowing some groups to opt for a private health insurance contract. According to the World Health Organization, Germany's health care system was 77% government-funded and 23% privately funded as of 2013[update].[231] In 2014, Germany spent 11.3% of its GDP on health care.[232]
+
+Germany ranked 20th in the world in 2013 in life expectancy with 77 years for men and 82 years for women, and it had a very low infant mortality rate (4 per 1,000 live births). In 2019[update], the principal cause of death was cardiovascular disease, at 37%.[233] Obesity in Germany has been increasingly cited as a major health issue. A 2014 study showed that 52 percent of the adult German population was overweight or obese.[234]
+
+Culture in German states has been shaped by major intellectual and popular currents in Europe, both religious and secular. Historically, Germany has been called Das Land der Dichter und Denker ("the land of poets and thinkers"),[235] because of the major role its writers and philosophers have played in the development of Western thought.[236] A global opinion poll for the BBC revealed that Germany is recognised for having the most positive influence in the world in 2013 and 2014.[237][238]
+
+Germany is well known for such folk festival traditions as Oktoberfest and Christmas customs, which include Advent wreaths, Christmas pageants, Christmas trees, Stollen cakes, and other practices.[239][240] As of 2016[update] UNESCO inscribed 41 properties in Germany on the World Heritage List.[241] There are a number of public holidays in Germany determined by each state; 3 October has been a national day of Germany since 1990, celebrated as the Tag der Deutschen Einheit (German Unity Day).[242]
+
+German classical music includes works by some of the world's most well-known composers. Dieterich Buxtehude, Johann Sebastian Bach and Georg Friedrich Händel were influential composers of the Baroque period. Ludwig van Beethoven was a crucial figure in the transition between the Classical and Romantic eras. Carl Maria von Weber, Felix Mendelssohn, Robert Schumann and Johannes Brahms were significant Romantic composers. Richard Wagner was known for his operas. Richard Strauss was a leading composer of the late Romantic and early modern eras. Karlheinz Stockhausen and Wolfgang Rihm are important composers of the 20th and early 21st centuries.[243]
+
+As of 2013, Germany was the second largest music market in Europe, and fourth largest in the world.[244] German popular music of the 20th and 21st centuries includes the movements of Neue Deutsche Welle, pop, Ostrock, heavy metal/rock, punk, pop rock, indie and schlager pop. German electronic music gained global influence, with Kraftwerk and Tangerine Dream pioneering in this genre.[245] DJs and artists of the techno and house music scenes of Germany have become well known (e.g. Paul van Dyk, Paul Kalkbrenner, and Scooter).[246]
+
+German painters have influenced western art. Albrecht Dürer, Hans Holbein the Younger, Matthias Grünewald and Lucas Cranach the Elder were important German artists of the Renaissance, Peter Paul Rubens and Johann Baptist Zimmermann of the Baroque, Caspar David Friedrich and Carl Spitzweg of Romanticism, Max Liebermann of Impressionism and Max Ernst of Surrealism. Several German art groups formed in the 20th century; Die Brücke (The Bridge) and Der Blaue Reiter (The Blue Rider) influenced the development of expressionism in Munich and Berlin. The New Objectivity arose in response to expressionism during the Weimar Republic. After World War II, broad trends in German art include neo-expressionism and the New Leipzig School.[247]
+
+Architectural contributions from Germany include the Carolingian and Ottonian styles, which were precursors of Romanesque. Brick Gothic is a distinctive medieval style that evolved in Germany. Also in Renaissance and Baroque art, regional and typically German elements evolved (e.g. Weser Renaissance).[247] Vernacular architecture in Germany is often identified by its timber framing (Fachwerk) traditions and varies across regions, and among carpentry styles.[248] When industrialisation spread across Europe, Classicism and a distinctive style of historism developed in Germany, sometimes referred to as Gründerzeit style. Expressionist architecture developed in the 1910s in Germany and influenced Art Deco and other modern styles. Germany was particularly important in the early modernist movement: it is the home of Werkbund initiated by Hermann Muthesius (New Objectivity), and of the Bauhaus movement founded by Walter Gropius.[247] Ludwig Mies van der Rohe became one of the world's most renowned architects in the second half of the 20th century; he conceived of the glass façade skyscraper.[249] Renowned contemporary architects and offices include Pritzker Prize winners Gottfried Böhm and Frei Otto.[250]
+
+German designers became early leaders of modern product design.[251] The Berlin Fashion Week and the fashion trade fair Bread & Butter are held twice a year.[252]
+
+German literature can be traced back to the Middle Ages and the works of writers such as Walther von der Vogelweide and Wolfram von Eschenbach. Well-known German authors include Johann Wolfgang von Goethe, Friedrich Schiller, Gotthold Ephraim Lessing and Theodor Fontane. The collections of folk tales published by the Brothers Grimm popularised German folklore on an international level.[253] The Grimms also gathered and codified regional variants of the German language, grounding their work in historical principles; their Deutsches Wörterbuch, or German Dictionary, sometimes called the Grimm dictionary, was begun in 1838 and the first volumes published in 1854.[254]
+
+Influential authors of the 20th century include Gerhart Hauptmann, Thomas Mann, Hermann Hesse, Heinrich Böll and Günter Grass.[255] The German book market is the third largest in the world, after the United States and China.[256] The Frankfurt Book Fair is the most important in the world for international deals and trading, with a tradition spanning over 500 years.[257] The Leipzig Book Fair also retains a major position in Europe.[258]
+
+German philosophy is historically significant: Gottfried Leibniz's contributions to rationalism; the enlightenment philosophy by Immanuel Kant; the establishment of classical German idealism by Johann Gottlieb Fichte, Georg Wilhelm Friedrich Hegel and Friedrich Wilhelm Joseph Schelling; Arthur Schopenhauer's composition of metaphysical pessimism; the formulation of communist theory by Karl Marx and Friedrich Engels; Friedrich Nietzsche's development of perspectivism; Gottlob Frege's contributions to the dawn of analytic philosophy; Martin Heidegger's works on Being; Oswald Spengler's historical philosophy; the development of the Frankfurt School has been particularly influential.[259]
+
+The largest internationally operating media companies in Germany are the Bertelsmann enterprise, Axel Springer SE and ProSiebenSat.1 Media. Germany's television market is the largest in Europe, with some 38 million TV households.[260] Around 90% of German households have cable or satellite TV, with a variety of free-to-view public and commercial channels.[261] There are more than 300 public and private radio stations in Germany; Germany's national radio network is the Deutschlandradio and the public Deutsche Welle is the main German radio and television broadcaster in foreign languages.[261]  Germany's print market of newspapers and magazines is the largest in Europe.[261] The papers with the highest circulation are Bild, Süddeutsche Zeitung, Frankfurter Allgemeine Zeitung and Die Welt.[261] The largest magazines include ADAC Motorwelt and Der Spiegel.[261] Germany has a large video gaming market, with over 34 million players nationwide.[262]
+
+German cinema has made major technical and artistic contributions to film. The first works of the Skladanowsky Brothers were shown to an audience in 1895. The renowned Babelsberg Studio in Potsdam was established in 1912, thus being the first large-scale film studio in the world. Early German cinema was particularly influential with German expressionists such as Robert Wiene and Friedrich Wilhelm Murnau. Director Fritz Lang's Metropolis (1927) is referred to as the first major science-fiction film. After 1945, many of the films of the immediate post-war period can be characterised as Trümmerfilm (rubble film). East German film was dominated by state-owned film studio DEFA, while the dominant genre in West Germany was the Heimatfilm ("homeland film").[263] During the 1970s and 1980s, New German Cinema directors such as Volker Schlöndorff, Werner Herzog, Wim Wenders, and Rainer Werner Fassbinder brought West German auteur cinema to critical acclaim.
+
+The Academy Award for Best Foreign Language Film ("Oscar") went to the German production Die Blechtrommel (The Tin Drum) in 1979, to Nirgendwo in Afrika (Nowhere in Africa) in 2002, and to Das Leben der Anderen (The Lives of Others) in 2007. Various Germans won an Oscar for their performances in other films. The annual European Film Awards ceremony is held every other year in Berlin, home of the European Film Academy. The Berlin International Film Festival, known as "Berlinale", awarding the "Golden Bear" and held annually since 1951, is one of the world's leading film festivals. The "Lolas" are annually awarded in Berlin, at the German Film Awards.[264]
+
+German cuisine varies from region to region and often neighbouring regions share some culinary similarities (e.g. the southern regions of Bavaria and Swabia share some traditions with Switzerland and Austria). International varieties such as pizza, sushi, Chinese food, Greek food, Indian cuisine and doner kebab are also popular.
+
+Bread is a significant part of German cuisine and German bakeries produce about 600 main types of bread and 1,200 types of pastries and rolls (Brötchen).[265] German cheeses account for about 22% of all cheese produced in Europe.[266] In 2012 over 99% of all meat produced in Germany was either pork, chicken or beef. Germans produce their ubiquitous sausages in almost 1,500 varieties, including Bratwursts and Weisswursts.[267] Although wine is becoming more popular in many parts of Germany, especially close to German wine regions,[268] the national alcoholic drink is beer. German beer consumption per person stands at 110 litres (24 imp gal; 29 US gal) in 2013 and remains among the highest in the world.[269] German beer purity regulations date back to the 16th century.[270]
+
+The 2018 Michelin Guide awarded eleven restaurants in Germany three stars, giving the country a cumulative total of 300 stars.[271]
+
+Football is the most popular sport in Germany. With more than 7 million official members, the German Football Association (Deutscher Fußball-Bund) is the largest single-sport organisation worldwide,[272] and the German top league, the Bundesliga, attracts the second highest average attendance of all professional sports leagues in the world.[273] The German men's national football team won the FIFA World Cup in 1954, 1974, 1990, and 2014,[274] the UEFA European Championship in 1972, 1980 and 1996,[275] and the FIFA Confederations Cup in 2017.[276]
+
+Germany is one of the leading motor sports countries in the world. Constructors like BMW and Mercedes are prominent manufacturers in motor sport. Porsche has won the 24 Hours of Le Mans race 19 times, and Audi 13 times (as of 2017[update]). The driver Michael Schumacher has set many motor sport records during his career, having won seven Formula One World Drivers' Championships.[277] Sebastian Vettel is also among the top five most successful Formula One drivers of all time.[278]
+
+Historically, German athletes have been successful contenders in the Olympic Games, ranking third in an all-time Olympic Games medal count (when combining East and West German medals). Germany was the last country to host both the summer and winter games in the same year, in 1936: the Berlin Summer Games and the Winter Games in Garmisch-Partenkirchen.[279] Munich hosted the Summer Games of 1972.[280]

en/4153.html.txt

@@ -0,0 +1,162 @@
+
+
+An integer (from the Latin integer meaning "whole")[a] is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
+
+The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers,[2][3] and their additive inverses (the negative integers, i.e., −1, −2, −3, ...). The set of integers is often denoted by a boldface letter ‘Z’ ("Z") or blackboard bold 
+
+
+
+
+Z
+
+
+
+{\displaystyle \mathbb {Z} }
+
+ (Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").[4][5]
+
+ℤ is a subset of the set of all rational numbers ℚ, in turn a subset of the real numbers ℝ.  Like the natural numbers, ℤ is countably infinite.
+
+The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers.
+
+The symbol ℤ can be annotated to denote various sets, with varying usage amongst different authors: ℤ+, ℤ+ or ℤ> for the positive integers, ℤ0+ or ℤ≥ for non-negative integers, ℤ≠ for non-zero integers. Some authors use ℤ* for non-zero integers, others use it for non-negative integers, or for {–1, 1}. Additionally, ℤp is used to denote either the set of integers modulo p, i.e., a set of congruence classes of integers, or the set of p-adic integers.[6][7][8]
+
+Ring homomorphisms
+
+Algebraic structures
+
+Related structures
+
+Algebraic number theory
+
+p-adic number theory and decimals
+
+Algebraic geometry
+
+Noncommutative algebraic geometry
+
+Free algebra
+
+Clifford algebra
+
+Like the natural numbers, ℤ is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly, 0, ℤ (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring ℤ.
+
+ℤ is not closed under division, since the quotient of two integers (e.g., 1 divided by 2), need not be an integer. Although the natural numbers are closed under exponentiation, the integers are not (since the result can be a fraction when the exponent is negative).
+
+The following table lists some of the basic properties of addition and multiplication for any integers a, b and c.
+
+In the language of abstract algebra, the first five properties listed above for addition say that ℤ under addition is an abelian group. It is also a cyclic group, since every non-zero integer can be written as a finite sum 1 + 1 + … + 1 or (−1) + (−1) + … + (−1). In fact, ℤ under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to ℤ.
+
+The first four properties listed above for multiplication say that ℤ under multiplication is a commutative monoid. However, not every integer has a multiplicative inverse; e.g., there is no integer x such that 2x = 1. This means that ℤ under multiplication is not a group.
+
+All the rules from the above property table, except for the last, taken together say that ℤ together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of such algebraic structure. Only those equalities of expressions are true in ℤ for all values of variables, which are true in any unital commutative ring. Certain non-zero integers map to zero in certain rings.
+
+The lack of zero divisors in the integers (last property in the table) means that the commutative ring ℤ is an integral domain.
+
+The lack of multiplicative inverses, which is equivalent to the fact that ℤ is not closed under division, means that ℤ is not a field. The smallest field containing the integers as a subring is the field of rational numbers. The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain. And back, starting from an algebraic number field (an extension of rational numbers), its ring of integers can be extracted, which includes ℤ as its subring.
+
+Although ordinary division is not defined on ℤ, the division "with remainder" is defined on them. It is called Euclidean division and possesses the following important property: that is, given two integers a and b with b ≠ 0, there exist unique integers q and r such that a = q × b + r and 0 ≤ r <  | b |, where | b | denotes the absolute value of b. The integer q is called the quotient and r is called the remainder of the division of a by b. The Euclidean algorithm for computing greatest common divisors works by a sequence of Euclidean divisions.
+
+Again, in the language of abstract algebra, the above says that ℤ is a Euclidean domain. This implies that ℤ is a principal ideal domain and any positive integer can be written as the products of primes in an essentially unique way.[9] This is the fundamental theorem of arithmetic.
+
+ℤ is a totally ordered set without upper or lower bound. The ordering of ℤ is given by:
+:... −3 < −2 < −1 < 0 < 1 < 2 < 3 < ...
+An integer is positive if it is greater than zero and negative if it is less than zero. Zero is defined as neither negative nor positive.
+
+The ordering of integers is compatible with the algebraic operations in the following way:
+
+It follows that ℤ together with the above ordering is an ordered ring.
+
+The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.[10] This is equivalent to the statement that any Noetherian valuation ring is either a field or a discrete valuation ring.
+
+In elementary school teaching, integers are often intuitively defined as the (positive) natural numbers, zero, and the negations of the natural numbers. However, this style of definition leads to many different cases (each arithmetic operation needs to be defined on each combination of types of integer) and makes it tedious to prove that these operations obey the laws of arithmetic.[11] Therefore, in modern set-theoretic mathematics a more abstract construction,[12] which allows one to define the arithmetical operations without any case distinction, is often used instead.[13] The integers can thus be formally constructed as the equivalence classes of ordered pairs of natural numbers (a,b).[14]
+
+The intuition is that (a,b) stands for the result of subtracting b from a.[14] To confirm our expectation that 1 − 2 and 4 − 5 denote the same number, we define an equivalence relation ~ on these pairs with the following rule:
+
+precisely when
+
+Addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers;[14] denoting by [(a,b)] the equivalence class having (a,b) as a member, one has:
+
+The negation (or additive inverse) of an integer is obtained by reversing the order of the pair:
+
+Hence subtraction can be defined as the addition of the additive inverse:
+
+The standard ordering on the integers is given by:
+
+It is easily verified that these definitions are independent of the choice of representatives of the equivalence classes.
+
+Every equivalence class has a unique member that is of the form (n,0) or (0,n) (or both at once). The natural number n is identified with the class [(n,0)] (in other words the natural numbers are embedded into the integers by map sending n to [(n,0)]), and the class [(0,n)] is denoted −n (this covers all remaining classes, and gives the class [(0,0)] a second time since −0 = 0.
+
+Thus, [(a,b)] is denoted by
+
+If the natural numbers are identified with the corresponding integers (using the embedding mentioned above), this convention creates no ambiguity.
+
+This notation recovers the familiar representation of the integers as  {…, −2, −1, 0, 1, 2, …}.
+
+Some examples are:
+
+In theoretical computer science, other approaches for the construction of integers are used by automated theorem provers and term rewrite engines.
+Integers are represented as algebraic terms built using a few basic operations  (such as zero, succ, pred, etc.) and, possibly, using natural numbers, which are assumed to be already constructed (e.g., using the Peano approach).
+
+There exist at least ten such constructions of signed integers.[15] These constructions differ in several ways: the number of basic operations used for the construction, the number (usually, between 0 and 2) and the types of arguments accepted by these operations; the presence or absence of natural numbers as arguments of some of these operations, and the fact that these operations are free constructors or not, i.e., that the same integer can be represented using only one or many algebraic terms.
+
+The technique for the construction of integers presented above in this section corresponds to the particular case where there is a single basic operation pair
+
+
+
+(
+x
+,
+y
+)
+
+
+{\displaystyle (x,y)}
+
+ that takes as arguments two natural numbers 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+, and returns an integer (equal to 
+
+
+
+x
+−
+y
+
+
+{\displaystyle x-y}
+
+). This operation is not free since the integer 0 can be written pair(0,0), or pair(1,1), or pair(2,2), etc. This technique of construction is used by the proof assistant Isabelle; however, many other tools use alternative construction techniques, notable those based upon free constructors, which are simpler and can be implemented more efficiently in computers.
+
+An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in the common two's complement representation, the inherent definition of sign distinguishes between "negative" and "non-negative" rather than "negative, positive, and 0". (It is, however, certainly possible for a computer to determine whether an integer value is truly positive.) Fixed length integer approximation data types (or subsets) are denoted int or Integer in several programming languages (such as Algol68, C, Java, Delphi, etc.).
+
+Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10).
+
+The cardinality of the set of integers is equal to ℵ0 (aleph-null). This is readily demonstrated by the construction of a bijection, that is, a function that is injective and surjective from ℤ to ℕ.
+If ℕ₀ ≡ {0, 1, 2, ...} then consider the function:
+
+{… (−4,8) (−3,6) (−2,4) (−1,2) (0,0) (1,1) (2,3) (3,5) ...}
+
+If ℕ ≡ {1, 2, 3, ...} then consider the function:
+
+{... (−4,8) (−3,6) (−2,4) (−1,2) (0,1) (1,3) (2,5) (3,7) ...}
+
+If the domain is restricted to ℤ then each and every member of ℤ has one and only one corresponding member of ℕ and by the definition of cardinal equality the two sets have equal cardinality.
+
+This article incorporates material from Integer on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

en/4154.html.txt

@@ -0,0 +1,162 @@
+
+
+An integer (from the Latin integer meaning "whole")[a] is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
+
+The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers,[2][3] and their additive inverses (the negative integers, i.e., −1, −2, −3, ...). The set of integers is often denoted by a boldface letter ‘Z’ ("Z") or blackboard bold 
+
+
+
+
+Z
+
+
+
+{\displaystyle \mathbb {Z} }
+
+ (Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").[4][5]
+
+ℤ is a subset of the set of all rational numbers ℚ, in turn a subset of the real numbers ℝ.  Like the natural numbers, ℤ is countably infinite.
+
+The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers.
+
+The symbol ℤ can be annotated to denote various sets, with varying usage amongst different authors: ℤ+, ℤ+ or ℤ> for the positive integers, ℤ0+ or ℤ≥ for non-negative integers, ℤ≠ for non-zero integers. Some authors use ℤ* for non-zero integers, others use it for non-negative integers, or for {–1, 1}. Additionally, ℤp is used to denote either the set of integers modulo p, i.e., a set of congruence classes of integers, or the set of p-adic integers.[6][7][8]
+
+Ring homomorphisms
+
+Algebraic structures
+
+Related structures
+
+Algebraic number theory
+
+p-adic number theory and decimals
+
+Algebraic geometry
+
+Noncommutative algebraic geometry
+
+Free algebra
+
+Clifford algebra
+
+Like the natural numbers, ℤ is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly, 0, ℤ (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring ℤ.
+
+ℤ is not closed under division, since the quotient of two integers (e.g., 1 divided by 2), need not be an integer. Although the natural numbers are closed under exponentiation, the integers are not (since the result can be a fraction when the exponent is negative).
+
+The following table lists some of the basic properties of addition and multiplication for any integers a, b and c.
+
+In the language of abstract algebra, the first five properties listed above for addition say that ℤ under addition is an abelian group. It is also a cyclic group, since every non-zero integer can be written as a finite sum 1 + 1 + … + 1 or (−1) + (−1) + … + (−1). In fact, ℤ under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to ℤ.
+
+The first four properties listed above for multiplication say that ℤ under multiplication is a commutative monoid. However, not every integer has a multiplicative inverse; e.g., there is no integer x such that 2x = 1. This means that ℤ under multiplication is not a group.
+
+All the rules from the above property table, except for the last, taken together say that ℤ together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of such algebraic structure. Only those equalities of expressions are true in ℤ for all values of variables, which are true in any unital commutative ring. Certain non-zero integers map to zero in certain rings.
+
+The lack of zero divisors in the integers (last property in the table) means that the commutative ring ℤ is an integral domain.
+
+The lack of multiplicative inverses, which is equivalent to the fact that ℤ is not closed under division, means that ℤ is not a field. The smallest field containing the integers as a subring is the field of rational numbers. The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain. And back, starting from an algebraic number field (an extension of rational numbers), its ring of integers can be extracted, which includes ℤ as its subring.
+
+Although ordinary division is not defined on ℤ, the division "with remainder" is defined on them. It is called Euclidean division and possesses the following important property: that is, given two integers a and b with b ≠ 0, there exist unique integers q and r such that a = q × b + r and 0 ≤ r <  | b |, where | b | denotes the absolute value of b. The integer q is called the quotient and r is called the remainder of the division of a by b. The Euclidean algorithm for computing greatest common divisors works by a sequence of Euclidean divisions.
+
+Again, in the language of abstract algebra, the above says that ℤ is a Euclidean domain. This implies that ℤ is a principal ideal domain and any positive integer can be written as the products of primes in an essentially unique way.[9] This is the fundamental theorem of arithmetic.
+
+ℤ is a totally ordered set without upper or lower bound. The ordering of ℤ is given by:
+:... −3 < −2 < −1 < 0 < 1 < 2 < 3 < ...
+An integer is positive if it is greater than zero and negative if it is less than zero. Zero is defined as neither negative nor positive.
+
+The ordering of integers is compatible with the algebraic operations in the following way:
+
+It follows that ℤ together with the above ordering is an ordered ring.
+
+The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.[10] This is equivalent to the statement that any Noetherian valuation ring is either a field or a discrete valuation ring.
+
+In elementary school teaching, integers are often intuitively defined as the (positive) natural numbers, zero, and the negations of the natural numbers. However, this style of definition leads to many different cases (each arithmetic operation needs to be defined on each combination of types of integer) and makes it tedious to prove that these operations obey the laws of arithmetic.[11] Therefore, in modern set-theoretic mathematics a more abstract construction,[12] which allows one to define the arithmetical operations without any case distinction, is often used instead.[13] The integers can thus be formally constructed as the equivalence classes of ordered pairs of natural numbers (a,b).[14]
+
+The intuition is that (a,b) stands for the result of subtracting b from a.[14] To confirm our expectation that 1 − 2 and 4 − 5 denote the same number, we define an equivalence relation ~ on these pairs with the following rule:
+
+precisely when
+
+Addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers;[14] denoting by [(a,b)] the equivalence class having (a,b) as a member, one has:
+
+The negation (or additive inverse) of an integer is obtained by reversing the order of the pair:
+
+Hence subtraction can be defined as the addition of the additive inverse:
+
+The standard ordering on the integers is given by:
+
+It is easily verified that these definitions are independent of the choice of representatives of the equivalence classes.
+
+Every equivalence class has a unique member that is of the form (n,0) or (0,n) (or both at once). The natural number n is identified with the class [(n,0)] (in other words the natural numbers are embedded into the integers by map sending n to [(n,0)]), and the class [(0,n)] is denoted −n (this covers all remaining classes, and gives the class [(0,0)] a second time since −0 = 0.
+
+Thus, [(a,b)] is denoted by
+
+If the natural numbers are identified with the corresponding integers (using the embedding mentioned above), this convention creates no ambiguity.
+
+This notation recovers the familiar representation of the integers as  {…, −2, −1, 0, 1, 2, …}.
+
+Some examples are:
+
+In theoretical computer science, other approaches for the construction of integers are used by automated theorem provers and term rewrite engines.
+Integers are represented as algebraic terms built using a few basic operations  (such as zero, succ, pred, etc.) and, possibly, using natural numbers, which are assumed to be already constructed (e.g., using the Peano approach).
+
+There exist at least ten such constructions of signed integers.[15] These constructions differ in several ways: the number of basic operations used for the construction, the number (usually, between 0 and 2) and the types of arguments accepted by these operations; the presence or absence of natural numbers as arguments of some of these operations, and the fact that these operations are free constructors or not, i.e., that the same integer can be represented using only one or many algebraic terms.
+
+The technique for the construction of integers presented above in this section corresponds to the particular case where there is a single basic operation pair
+
+
+
+(
+x
+,
+y
+)
+
+
+{\displaystyle (x,y)}
+
+ that takes as arguments two natural numbers 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+, and returns an integer (equal to 
+
+
+
+x
+−
+y
+
+
+{\displaystyle x-y}
+
+). This operation is not free since the integer 0 can be written pair(0,0), or pair(1,1), or pair(2,2), etc. This technique of construction is used by the proof assistant Isabelle; however, many other tools use alternative construction techniques, notable those based upon free constructors, which are simpler and can be implemented more efficiently in computers.
+
+An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in the common two's complement representation, the inherent definition of sign distinguishes between "negative" and "non-negative" rather than "negative, positive, and 0". (It is, however, certainly possible for a computer to determine whether an integer value is truly positive.) Fixed length integer approximation data types (or subsets) are denoted int or Integer in several programming languages (such as Algol68, C, Java, Delphi, etc.).
+
+Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10).
+
+The cardinality of the set of integers is equal to ℵ0 (aleph-null). This is readily demonstrated by the construction of a bijection, that is, a function that is injective and surjective from ℤ to ℕ.
+If ℕ₀ ≡ {0, 1, 2, ...} then consider the function:
+
+{… (−4,8) (−3,6) (−2,4) (−1,2) (0,0) (1,1) (2,3) (3,5) ...}
+
+If ℕ ≡ {1, 2, 3, ...} then consider the function:
+
+{... (−4,8) (−3,6) (−2,4) (−1,2) (0,1) (1,3) (2,5) (3,7) ...}
+
+If the domain is restricted to ℤ then each and every member of ℤ has one and only one corresponding member of ℕ and by the definition of cardinal equality the two sets have equal cardinality.
+
+This article incorporates material from Integer on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

en/4155.html.txt

@@ -0,0 +1,162 @@
+
+
+An integer (from the Latin integer meaning "whole")[a] is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
+
+The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers,[2][3] and their additive inverses (the negative integers, i.e., −1, −2, −3, ...). The set of integers is often denoted by a boldface letter ‘Z’ ("Z") or blackboard bold 
+
+
+
+
+Z
+
+
+
+{\displaystyle \mathbb {Z} }
+
+ (Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").[4][5]
+
+ℤ is a subset of the set of all rational numbers ℚ, in turn a subset of the real numbers ℝ.  Like the natural numbers, ℤ is countably infinite.
+
+The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers.
+
+The symbol ℤ can be annotated to denote various sets, with varying usage amongst different authors: ℤ+, ℤ+ or ℤ> for the positive integers, ℤ0+ or ℤ≥ for non-negative integers, ℤ≠ for non-zero integers. Some authors use ℤ* for non-zero integers, others use it for non-negative integers, or for {–1, 1}. Additionally, ℤp is used to denote either the set of integers modulo p, i.e., a set of congruence classes of integers, or the set of p-adic integers.[6][7][8]
+
+Ring homomorphisms
+
+Algebraic structures
+
+Related structures
+
+Algebraic number theory
+
+p-adic number theory and decimals
+
+Algebraic geometry
+
+Noncommutative algebraic geometry
+
+Free algebra
+
+Clifford algebra
+
+Like the natural numbers, ℤ is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly, 0, ℤ (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring ℤ.
+
+ℤ is not closed under division, since the quotient of two integers (e.g., 1 divided by 2), need not be an integer. Although the natural numbers are closed under exponentiation, the integers are not (since the result can be a fraction when the exponent is negative).
+
+The following table lists some of the basic properties of addition and multiplication for any integers a, b and c.
+
+In the language of abstract algebra, the first five properties listed above for addition say that ℤ under addition is an abelian group. It is also a cyclic group, since every non-zero integer can be written as a finite sum 1 + 1 + … + 1 or (−1) + (−1) + … + (−1). In fact, ℤ under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to ℤ.
+
+The first four properties listed above for multiplication say that ℤ under multiplication is a commutative monoid. However, not every integer has a multiplicative inverse; e.g., there is no integer x such that 2x = 1. This means that ℤ under multiplication is not a group.
+
+All the rules from the above property table, except for the last, taken together say that ℤ together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of such algebraic structure. Only those equalities of expressions are true in ℤ for all values of variables, which are true in any unital commutative ring. Certain non-zero integers map to zero in certain rings.
+
+The lack of zero divisors in the integers (last property in the table) means that the commutative ring ℤ is an integral domain.
+
+The lack of multiplicative inverses, which is equivalent to the fact that ℤ is not closed under division, means that ℤ is not a field. The smallest field containing the integers as a subring is the field of rational numbers. The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain. And back, starting from an algebraic number field (an extension of rational numbers), its ring of integers can be extracted, which includes ℤ as its subring.
+
+Although ordinary division is not defined on ℤ, the division "with remainder" is defined on them. It is called Euclidean division and possesses the following important property: that is, given two integers a and b with b ≠ 0, there exist unique integers q and r such that a = q × b + r and 0 ≤ r <  | b |, where | b | denotes the absolute value of b. The integer q is called the quotient and r is called the remainder of the division of a by b. The Euclidean algorithm for computing greatest common divisors works by a sequence of Euclidean divisions.
+
+Again, in the language of abstract algebra, the above says that ℤ is a Euclidean domain. This implies that ℤ is a principal ideal domain and any positive integer can be written as the products of primes in an essentially unique way.[9] This is the fundamental theorem of arithmetic.
+
+ℤ is a totally ordered set without upper or lower bound. The ordering of ℤ is given by:
+:... −3 < −2 < −1 < 0 < 1 < 2 < 3 < ...
+An integer is positive if it is greater than zero and negative if it is less than zero. Zero is defined as neither negative nor positive.
+
+The ordering of integers is compatible with the algebraic operations in the following way:
+
+It follows that ℤ together with the above ordering is an ordered ring.
+
+The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.[10] This is equivalent to the statement that any Noetherian valuation ring is either a field or a discrete valuation ring.
+
+In elementary school teaching, integers are often intuitively defined as the (positive) natural numbers, zero, and the negations of the natural numbers. However, this style of definition leads to many different cases (each arithmetic operation needs to be defined on each combination of types of integer) and makes it tedious to prove that these operations obey the laws of arithmetic.[11] Therefore, in modern set-theoretic mathematics a more abstract construction,[12] which allows one to define the arithmetical operations without any case distinction, is often used instead.[13] The integers can thus be formally constructed as the equivalence classes of ordered pairs of natural numbers (a,b).[14]
+
+The intuition is that (a,b) stands for the result of subtracting b from a.[14] To confirm our expectation that 1 − 2 and 4 − 5 denote the same number, we define an equivalence relation ~ on these pairs with the following rule:
+
+precisely when
+
+Addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers;[14] denoting by [(a,b)] the equivalence class having (a,b) as a member, one has:
+
+The negation (or additive inverse) of an integer is obtained by reversing the order of the pair:
+
+Hence subtraction can be defined as the addition of the additive inverse:
+
+The standard ordering on the integers is given by:
+
+It is easily verified that these definitions are independent of the choice of representatives of the equivalence classes.
+
+Every equivalence class has a unique member that is of the form (n,0) or (0,n) (or both at once). The natural number n is identified with the class [(n,0)] (in other words the natural numbers are embedded into the integers by map sending n to [(n,0)]), and the class [(0,n)] is denoted −n (this covers all remaining classes, and gives the class [(0,0)] a second time since −0 = 0.
+
+Thus, [(a,b)] is denoted by
+
+If the natural numbers are identified with the corresponding integers (using the embedding mentioned above), this convention creates no ambiguity.
+
+This notation recovers the familiar representation of the integers as  {…, −2, −1, 0, 1, 2, …}.
+
+Some examples are:
+
+In theoretical computer science, other approaches for the construction of integers are used by automated theorem provers and term rewrite engines.
+Integers are represented as algebraic terms built using a few basic operations  (such as zero, succ, pred, etc.) and, possibly, using natural numbers, which are assumed to be already constructed (e.g., using the Peano approach).
+
+There exist at least ten such constructions of signed integers.[15] These constructions differ in several ways: the number of basic operations used for the construction, the number (usually, between 0 and 2) and the types of arguments accepted by these operations; the presence or absence of natural numbers as arguments of some of these operations, and the fact that these operations are free constructors or not, i.e., that the same integer can be represented using only one or many algebraic terms.
+
+The technique for the construction of integers presented above in this section corresponds to the particular case where there is a single basic operation pair
+
+
+
+(
+x
+,
+y
+)
+
+
+{\displaystyle (x,y)}
+
+ that takes as arguments two natural numbers 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+, and returns an integer (equal to 
+
+
+
+x
+−
+y
+
+
+{\displaystyle x-y}
+
+). This operation is not free since the integer 0 can be written pair(0,0), or pair(1,1), or pair(2,2), etc. This technique of construction is used by the proof assistant Isabelle; however, many other tools use alternative construction techniques, notable those based upon free constructors, which are simpler and can be implemented more efficiently in computers.
+
+An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in the common two's complement representation, the inherent definition of sign distinguishes between "negative" and "non-negative" rather than "negative, positive, and 0". (It is, however, certainly possible for a computer to determine whether an integer value is truly positive.) Fixed length integer approximation data types (or subsets) are denoted int or Integer in several programming languages (such as Algol68, C, Java, Delphi, etc.).
+
+Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10).
+
+The cardinality of the set of integers is equal to ℵ0 (aleph-null). This is readily demonstrated by the construction of a bijection, that is, a function that is injective and surjective from ℤ to ℕ.
+If ℕ₀ ≡ {0, 1, 2, ...} then consider the function:
+
+{… (−4,8) (−3,6) (−2,4) (−1,2) (0,0) (1,1) (2,3) (3,5) ...}
+
+If ℕ ≡ {1, 2, 3, ...} then consider the function:
+
+{... (−4,8) (−3,6) (−2,4) (−1,2) (0,1) (1,3) (2,5) (3,7) ...}
+
+If the domain is restricted to ℤ then each and every member of ℤ has one and only one corresponding member of ℕ and by the definition of cardinal equality the two sets have equal cardinality.
+
+This article incorporates material from Integer on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

en/4156.html.txt

@@ -0,0 +1,311 @@
+A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.[1] For being manipulated, individual numbers need to be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows representing any number by a combination of ten basic numerals called digits.[2][3] In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
+
+In mathematics, the notion of number has been extended over the centuries to include 0,[4] negative numbers,[5] rational numbers such as 1/2 and −2/3, real numbers[6] such as √2 and π, and complex numbers,[7] which extend the real numbers with a square root of −1 (and its combinations with real numbers by addition and multiplication).[5] Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers.
+
+Besides their practical uses, numbers have cultural significance throughout the world.[8][9] For example, in Western society, the number 13 is regarded as unlucky, and "a million" may signify "a lot."[8] Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought.[10] Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.[10]
+
+During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Today, number systems are considered important special examples of much more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.[11]
+
+Numbers should be distinguished from numerals, the symbols used to represent numbers. The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets.[12] Roman numerals, a system that used combinations of letters from the Roman alphabet, remained dominant in Europe until the spread of the superior Hindu–Arabic numeral system around the late 14th century, and the Hindu–Arabic numeral system remains the most common system for representing numbers in the world today.[13] The key to the effectiveness of the system was the symbol for zero, which was developed by ancient Indian mathematicians around 500 AD.[13]
+
+Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks.[14] These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals.
+
+A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless tallying systems are considered the first kind of abstract numeral system.
+
+The first known system with place value was the Mesopotamian base 60 system (ca. 3400 BC) and the earliest known base 10 system dates to 3100 BC in Egypt.[15]
+
+The first known documented use of zero dates to AD 628, and appeared in the Brāhmasphuṭasiddhānta, the main work of the Indian mathematician Brahmagupta.  He treated 0 as a number and discussed operations involving it, including division. By this time (the 7th century) the concept had clearly reached Cambodia as Khmer numerals, and documentation shows the idea later spreading to China and the Islamic world.
+
+Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, hence Brahmagupta is usually considered the first to formulate the concept of zero. He gave rules of using zero with negative and positive numbers, such as "zero plus a positive number is a positive number, and a negative number plus zero is the negative number." The Brāhmasphuṭasiddhānta is the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit in representing another number as was done by the Babylonians or as a symbol for a lack of quantity as was done by Ptolemy and the Romans.
+
+The use of 0 as a number should be distinguished from its use as a placeholder numeral in place-value systems. Many ancient texts used 0. Babylonian and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting. Indian texts used a Sanskrit word Shunye or shunya to refer to the concept of void. In mathematics texts this word often refers to the number zero.[16] In a similar vein, Pāṇini (5th century BC) used the null (zero) operator in the Ashtadhyayi, an early example of an algebraic grammar for the Sanskrit language (also see Pingala).
+
+There are other uses of zero before Brahmagupta, though the documentation is not as complete as it is in the Brāhmasphuṭasiddhānta.
+
+Records show that the Ancient Greeks seemed unsure about the status of 0 as a number: they asked themselves "how can 'nothing' be something?" leading to interesting philosophical and, by the Medieval period, religious arguments about the nature and existence of 0 and the vacuum. The paradoxes of Zeno of Elea depend in part on the uncertain interpretation of 0. (The ancient Greeks even questioned whether 1 was a number.)
+
+The late Olmec people of south-central Mexico began to use a symbol for zero, a shell glyph, in the New World, possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar. Mayan arithmetic used base 4 and base 5 written as base 20. Sanchez in 1961 reported a base 4, base 5 "finger" abacus.
+
+By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for 0 (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not as just a placeholder, this Hellenistic zero was the first documented use of a true zero in the Old World. In later Byzantine manuscripts of his Syntaxis Mathematica (Almagest), the Hellenistic zero had morphed into the Greek letter Omicron (otherwise meaning 70).
+
+Another true zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning nothing, not as a symbol. When division produced 0 as a remainder, nihil, also meaning nothing, was used. These medieval zeros were used by all future medieval computists (calculators of Easter). An isolated use of their initial, N, was used in a table of Roman numerals by Bede or a colleague about 725, a true zero symbol.
+
+The abstract concept of negative numbers was recognized as early as 100–50 BC in China.  The Nine Chapters on the Mathematical Art contains methods for finding the areas of figures; red rods were used to denote positive coefficients, black for negative.[17] The first reference in a Western work was in the 3rd century AD in Greece. Diophantus referred to the equation equivalent to 4x + 20 = 0 (the solution is negative) in Arithmetica, saying that the equation gave an absurd result.
+
+During the 600s, negative numbers were in use in India to represent debts. Diophantus' previous reference was discussed more explicitly by Indian mathematician Brahmagupta, in Brāhmasphuṭasiddhānta in 628, who used negative numbers to produce the general form quadratic formula that remains in use today. However, in the 12th century in India, Bhaskara gives negative roots for quadratic equations but says the negative value "is in this case not to be taken, for it is inadequate; people do not approve of negative roots."
+
+European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debts (chapter 13 of Liber Abaci, 1202) and later as losses (in Flos). At the same time, the Chinese were indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit of the corresponding positive number's numeral.[18] The first use of negative numbers in a European work was by Nicolas Chuquet during the 15th century. He used them as exponents, but referred to them as "absurd numbers".
+
+As recently as the 18th century, it was common practice to ignore any negative results returned by equations on the assumption that they were meaningless, just as René Descartes did with negative solutions in a Cartesian coordinate system.
+
+It is likely that the concept of fractional numbers dates to prehistoric times. The Ancient Egyptians used their Egyptian fraction notation for rational numbers in mathematical texts such as the Rhind Mathematical Papyrus and the Kahun Papyrus. Classical Greek and Indian mathematicians made studies of the theory of rational numbers, as part of the general study of number theory. The best known of these is Euclid's Elements, dating to roughly 300 BC. Of the Indian texts, the most relevant is the Sthananga Sutra, which also covers number theory as part of a general study of mathematics.
+
+The concept of decimal fractions is closely linked with decimal place-value notation; the two seem to have developed in tandem. For example, it is common for the Jain math sutra to include calculations of decimal-fraction approximations to pi or the square root of 2. Similarly, Babylonian math texts used sexagesimal (base 60) fractions with great frequency.
+
+The earliest known use of irrational numbers was in the Indian Sulba Sutras composed between 800 and 500 BC.[19] The first existence proofs of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2. The story goes that Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. However, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. He could not disprove their existence through logic, but he could not accept irrational numbers, and so, allegedly and frequently reported, he sentenced Hippasus to death by drowning, to impede spreading of this disconcerting news.[20]
+
+The 16th century brought final European acceptance of negative integral and fractional numbers. By the 17th  century, mathematicians generally used decimal fractions with modern notation. It was not, however, until the 19th century that mathematicians separated irrationals into algebraic and transcendental parts, and once more undertook the scientific study of irrationals. It had remained almost dormant since Euclid. In 1872, the publication of the theories of Karl Weierstrass (by his pupil E. Kossak), Eduard Heine (Crelle, 74), Georg Cantor (Annalen, 5), and Richard Dedekind was brought about. In 1869, Charles Méray had taken the same point of departure as Heine, but the theory is generally referred to the year 1872. Weierstrass's method was completely set forth by Salvatore Pincherle (1880), and Dedekind's has received additional prominence through the author's later work (1888) and endorsement by Paul Tannery (1894). Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on the idea of a cut (Schnitt) in the system of real numbers, separating all rational numbers into two groups having certain characteristic properties. The subject has received later contributions at the hands of Weierstrass, Kronecker (Crelle, 101), and Méray.
+
+The search for roots of quintic and higher degree equations was an important development, the Abel–Ruffini theorem (Ruffini 1799, Abel 1824) showed that they could not be solved by radicals (formulas involving only arithmetical operations and roots). Hence it was necessary to consider the wider set of algebraic numbers (all solutions to polynomial equations). Galois (1832) linked polynomial equations to group theory giving rise to the field of Galois theory.
+
+Continued fractions, closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler, and at the opening of the 19th century were brought into prominence through the writings of Joseph Louis Lagrange. Other noteworthy contributions have been made by Druckenmüller (1837), Kunze (1857), Lemke (1870), and Günther (1872). Ramus (1855) first connected the subject with determinants, resulting, with the subsequent contributions of Heine, Möbius, and Günther, in the theory of Kettenbruchdeterminantencode: deu promoted to code: de .
+
+The existence of transcendental numbers[21] was first established by Liouville (1844, 1851). Hermite proved in 1873 that e is transcendental and Lindemann proved in 1882 that π is transcendental. Finally, Cantor showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite, so there is an uncountably infinite number of transcendental numbers.
+
+The earliest known conception of mathematical infinity appears in the Yajur Veda, an ancient Indian script, which at one point states, "If you remove a part from infinity or add a part to infinity, still what remains is infinity." Infinity was a popular topic of philosophical study among the Jain mathematicians c. 400 BC. They distinguished between five types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
+
+Aristotle defined the traditional Western notion of mathematical infinity. He distinguished between actual infinity and potential infinity—the general consensus being that only the latter had true value. Galileo Galilei's Two New Sciences discussed the idea of one-to-one correspondences between infinite sets. But the next major advance in the theory was made by Georg Cantor; in 1895 he published a book about his new set theory, introducing, among other things, transfinite numbers and formulating the continuum hypothesis.
+
+In the 1960s, Abraham Robinson showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis. The system of hyperreal numbers represents a rigorous method of treating the ideas about infinite and infinitesimal numbers that had been used casually by mathematicians, scientists, and engineers ever since the invention of infinitesimal calculus by Newton and Leibniz.
+
+A modern geometrical version of infinity is given by projective geometry, which introduces "ideal points at infinity", one for each spatial direction. Each family of parallel lines in a given direction is postulated to converge to the corresponding ideal point. This is closely related to the idea of vanishing points in perspective drawing.
+
+The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid. They became more prominent when in the 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians such as Niccolò Fontana Tartaglia and Gerolamo Cardano. It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers.
+
+This was doubly unsettling since they did not even consider negative numbers to be on firm ground at the time. When René Descartes coined the term "imaginary" for these quantities in 1637, he intended it as derogatory. (See imaginary number for a discussion of the "reality" of complex numbers.) A further source of confusion was that the equation
+
+seemed capriciously inconsistent with the algebraic identity
+
+which is valid for positive real numbers a and b, and was also used in complex number calculations with one of a, b positive and the other negative. The incorrect use of this identity, and the related identity
+
+in the case when both a and b are negative even bedeviled Euler. This difficulty eventually led him to the convention of using the special symbol i in place of 
+
+
+
+
+
+−
+1
+
+
+
+
+{\displaystyle {\sqrt {-1}}}
+
+ to guard against this mistake.
+
+The 18th century saw the work of Abraham de Moivre and Leonhard Euler. De Moivre's formula (1730) states:
+
+while Euler's formula of complex analysis (1748) gave us:
+
+The existence of complex numbers was not completely accepted until Caspar Wessel described the geometrical interpretation in 1799. Carl Friedrich Gauss rediscovered and popularized it several years later, and as a result the theory of complex numbers received a notable expansion. The idea of the graphic representation of complex numbers had appeared, however, as early as 1685, in Wallis's De Algebra tractatus.
+
+Also in 1799, Gauss provided the first generally accepted proof of the fundamental theorem of algebra, showing that every polynomial over the complex numbers has a full set of solutions in that realm. The general acceptance of the theory of complex numbers is due to the labors of Augustin Louis Cauchy and Niels Henrik Abel, and especially the latter, who was the first to boldly use complex numbers with a success that is well known.
+
+Gauss studied complex numbers of the form a + bi, where a and b are integral, or rational (and i is one of the two roots of x2 + 1 = 0). His student, Gotthold Eisenstein, studied the type a + bω, where ω is a complex root of x3 − 1 = 0. Other such classes (called cyclotomic fields) of complex numbers derive from the roots of unity xk − 1 = 0 for higher values of k. This generalization is largely due to Ernst Kummer, who also invented ideal numbers, which were expressed as geometrical entities by Felix Klein in 1893.
+
+In 1850 Victor Alexandre Puiseux took the key step of distinguishing between poles and branch points, and introduced the concept of essential singular points. This eventually led to the concept of the extended complex plane.
+
+Prime numbers have been studied throughout recorded history. Euclid devoted one book of the Elements to the theory of primes; in it he proved the infinitude of the primes and the fundamental theorem of arithmetic, and presented the Euclidean algorithm for finding the greatest common divisor of two numbers.
+
+In 240 BC, Eratosthenes used the Sieve of Eratosthenes to quickly isolate prime numbers. But most further development of the theory of primes in Europe dates to the Renaissance and later eras.
+
+In 1796, Adrien-Marie Legendre conjectured the prime number theorem, describing the asymptotic distribution of primes. Other results concerning the distribution of the primes include Euler's proof that the sum of the reciprocals of the primes diverges, and the Goldbach conjecture, which claims that any sufficiently large even number is the sum of two primes. Yet another conjecture related to the distribution of prime numbers is the Riemann hypothesis, formulated by Bernhard Riemann in 1859. The prime number theorem was finally proved by Jacques Hadamard and Charles de la Vallée-Poussin in 1896. Goldbach and Riemann's conjectures remain unproven and unrefuted.
+
+Numbers can be classified into sets, called number systems, such as the natural numbers and the real numbers.[22] The major categories of numbers are as follows:
+
+N
+
+
+0
+
+
+
+
+{\displaystyle \mathbb {N} _{0}}
+
+ or 
+
+
+
+
+
+N
+
+
+1
+
+
+
+
+{\displaystyle \mathbb {N} _{1}}
+
+ are sometimes used.
+
+There is generally no problem in identifying each number system with a proper subset of the next one (by abuse of notation), because each of these number systems is canonically isomorphic to a proper subset of the next one.[citation needed] The resulting hierarchy allows, for example, to talk, formally correctly, about real numbers that are rational numbers, and is expressed symbolically by writing
+
+The most familiar numbers are the natural numbers (sometimes called whole numbers or counting numbers): 1, 2, 3, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.) However, in the 19th century, set theorists and other mathematicians started including 0 (cardinality of the empty set, i.e. 0 elements, where 0 is thus the smallest cardinal number) in the set of natural numbers.[23][24]  Today, different mathematicians use the term to describe both sets, including 0 or not. The mathematical symbol for the set of all natural numbers is N, also written 
+
+
+
+
+N
+
+
+
+{\displaystyle \mathbb {N} }
+
+, and sometimes 
+
+
+
+
+
+N
+
+
+0
+
+
+
+
+{\displaystyle \mathbb {N} _{0}}
+
+ or 
+
+
+
+
+
+N
+
+
+1
+
+
+
+
+{\displaystyle \mathbb {N} _{1}}
+
+ when it is necessary to indicate whether the set should start with 0 or 1, respectively.
+
+In the base 10 numeral system, in almost universal use today for mathematical operations, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The radix or base is the number of unique numerical digits, including zero, that a numeral system uses to represent numbers (for the decimal system, the radix is 10). In this base 10 system, the rightmost digit of a natural number has a place value of 1, and every other digit has a place value ten times that of the place value of the digit to its right.
+
+In set theory, which is capable of acting as an axiomatic foundation for modern mathematics,[25] natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three elements. Alternatively, in Peano Arithmetic, the number 3 is represented as sss0, where s is the "successor" function (i.e., 3 is the third successor of 0). Many different representations are possible; all that is needed to formally represent 3 is to inscribe a certain symbol or pattern of symbols three times.
+
+The negative of a positive integer is defined as a number that produces 0 when it is added to the corresponding positive integer. Negative numbers are usually written with a negative sign (a minus sign). As an example, the negative of 7 is written −7, and 7 + (−7) = 0. When the set of negative numbers is combined with the set of natural numbers (including 0), the result is defined as the set of integers, Z also written 
+
+
+
+
+Z
+
+
+
+{\displaystyle \mathbb {Z} }
+
+. Here the letter Z comes from German  Zahl, meaning 'number'. The set of integers forms a ring with the operations addition and multiplication.[26]
+
+The natural numbers form a subset of the integers. As there is no common standard for the inclusion or not of zero in the natural numbers, the natural numbers without zero are commonly referred to as positive integers, and the natural numbers with zero are referred to as non-negative integers.
+
+A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator. Fractions are written as two integers, the numerator and the denominator, with a dividing bar between them. The fraction m/n represents m parts of a whole divided into n equal parts. Two different fractions may correspond to the same rational number; for example 1/2 and 2/4 are equal, that is:
+
+In general,
+
+If the absolute value of m is greater than n (supposed to be positive), then the absolute value of the fraction is greater than 1. Fractions can be greater than, less than, or equal to 1 and can also be positive, negative, or 0. The set of all rational numbers includes the integers since every integer can be written as a fraction with denominator 1. For example −7 can be written −7/1. The symbol for the rational numbers is Q (for quotient), also written 
+
+
+
+
+Q
+
+
+
+{\displaystyle \mathbb {Q} }
+
+.
+
+The symbol for the real numbers is R, also written as 
+
+
+
+
+R
+
+.
+
+
+{\displaystyle \mathbb {R} .}
+
+ They include all the measuring numbers. Every real number corresponds to a point on the number line. The following paragraph will focus primarily on positive real numbers. The treatment of negative real numbers is according to the general rules of arithmetic and their denotation is simply prefixing the corresponding positive numeral by a minus sign, e.g. −123.456.
+
+Most real numbers can only be approximated by decimal numerals, in which a decimal point is placed to the right of the digit with place value 1. Each digit to the right of the decimal point has a place value one-tenth of the place value of the digit to its left. For example, 123.456 represents 123456/1000, or, in words, one hundred, two tens, three ones, four tenths, five hundredths, and six thousandths. A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.  Representing other real numbers as decimals would require an infinite sequence of digits to the right of the decimal point. If this infinite sequence of digits follows a pattern, it can be written with an ellipsis or another notation that indicates the repeating pattern.  Such a decimal is called a repeating decimal. Thus 1/3 can be written as 0.333..., with an ellipsis to indicate that the pattern continues. Forever repeating 3s are also written as 0.3.[27]
+
+It turns out that these repeating decimals (including the repetition of zeroes) denote exactly the rational numbers, i.e., all rational numbers are also real numbers, but it is not the case that every real number is rational. A real number that is not rational is called irrational. A famous irrational real number is the number π, the ratio of the circumference of any circle to its diameter. When pi is written as
+
+as it sometimes is, the ellipsis does not mean that the decimals repeat (they do not), but rather that there is no end to them. It has been proved that π is irrational. Another well-known number, proven to be an irrational real number, is
+
+the square root of 2, that is, the unique positive real number whose square is 2. Both these numbers have been approximated (by computer) to trillions ( 1 trillion =  1012 = 1,000,000,000,000 ) of digits.
+
+Not only these prominent examples but almost all real numbers are irrational and therefore have no repeating patterns and hence no corresponding decimal numeral. They can only be approximated by decimal numerals, denoting rounded or truncated real numbers. Any rounded or truncated number is necessarily a rational number, of which there are only countably many. All measurements are, by their nature, approximations, and always have a margin of error. Thus 123.456 is considered an approximation of any real number greater or equal to 1234555/10000 and strictly less than 1234565/10000 (rounding to 3 decimals), or of any real number  greater or equal to 123456/1000 and strictly less than 123457/1000 (truncation after the 3. decimal). Digits that suggest a greater accuracy than the measurement itself does, should be removed. The remaining digits are then called significant digits. For example, measurements with a ruler can seldom be made without a margin of error of at least 0.001  meters. If the sides of a rectangle are measured as 1.23 meters and 4.56 meters, then multiplication gives an area for the rectangle between 5.614591 square meters and 5.603011 square meters. Since not even the second digit after the decimal place is preserved, the following digits are not significant. Therefore, the result is usually rounded to 5.61.
+
+Just as the same fraction can be written in more than one way, the same real number may have more than one decimal representation. For example, 0.999..., 1.0, 1.00, 1.000, ..., all represent the natural number 1. A given real number has only the following decimal representations: an approximation to some finite number of decimal places, an approximation in which a pattern is established that continues for an unlimited number of decimal places or an exact value with only finitely many decimal places.  In this last case, the last non-zero digit may be replaced by the digit one smaller followed by an unlimited number of 9's, or the last non-zero digit may be followed by an unlimited number of zeros.  Thus the exact real number 3.74 can also be written 3.7399999999... and 3.74000000000.... Similarly, a decimal numeral with an unlimited number of 0's can be rewritten by dropping the 0's to the right of the decimal place, and a decimal numeral with an unlimited number of 9's can be rewritten by increasing the rightmost -9 digit by one, changing all the 9's to the right of that digit to 0's. Finally, an unlimited sequence of 0's to the right of the decimal place can be dropped. For example, 6.849999999999... = 6.85 and 6.850000000000... = 6.85.  Finally, if all of the digits in a numeral are 0, the number is 0, and if all of the digits in a numeral are an unending string of 9's, you can drop the nines to the right of the decimal place, and add one to the string of 9s to the left of the decimal place.  For example, 99.999... = 100.
+
+The real numbers also have an important but highly technical property called the least upper bound property.
+
+It can be shown that any ordered field, which is also complete, is isomorphic to the real numbers. The real numbers are not, however, an algebraically closed field, because they do not include a solution (often called a square root of minus one) to the algebraic equation 
+
+
+
+
+x
+
+2
+
+
++
+1
+=
+0
+
+
+{\displaystyle x^{2}+1=0}
+
+.
+
+Moving to a greater level of abstraction, the real numbers can be extended to the complex numbers. This set of numbers arose historically from trying to find closed formulas for the roots of cubic and quadratic polynomials. This led to expressions involving the square roots of negative numbers, and eventually to the definition of a new number: a square root of −1, denoted by i, a symbol assigned by Leonhard Euler, and called the imaginary unit. The complex numbers consist of all numbers of the form
+
+where a and b are real numbers. Because of this, complex numbers correspond to points on the complex plane, a vector space of two real dimensions. In the expression a + bi, the real number a is called the real part and b is called the imaginary part. If the real part of a complex number is 0, then the number is called an imaginary number or is referred to as purely imaginary; if the imaginary part is 0, then the number is a real number. Thus the real numbers are a subset of the complex numbers. If the real and imaginary parts of a complex number are both integers, then the number is called a Gaussian integer. The symbol for the complex numbers is C or 
+
+
+
+
+C
+
+
+
+{\displaystyle \mathbb {C} }
+
+.
+
+The fundamental theorem of algebra asserts that the complex numbers form an algebraically closed field, meaning that every polynomial with complex coefficients has a root in the complex numbers. Like the reals, the complex numbers form a field, which is complete, but unlike the real numbers, it is not ordered. That is, there is no consistent meaning assignable to saying that  I is greater than 1, nor is there any meaning in saying that  I is less than 1. In technical terms, the complex numbers lack a total order that is compatible with field operations.
+
+An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula n = 2k + 1, for a suitable integer k. Starting with k = 0, the first non-negative odd numbers are {1, 3, 5, 7, ...}. Any even number m has the form m = 2k where k is again an integer. Similarly, the first non-negative even numbers are {0, 2, 4, 6, ...}.
+
+A prime number is an integer greater than 1 that is not the product of two smaller positive integers. The first few prime numbers are 2, 3, 5, 7, and 11. There is no such simple formula as for odd and even numbers to generate the prime numbers. The primes have been widely studied for more than 2000 years and have led to many questions, only some of which have been answered.  The study of these questions belongs to number theory.  An example of a still unanswered question is, whether every even number is the sum of two primes.  This is called Goldbach's conjecture.
+
+The question, whether every integer greater than one is a product of primes in only one way, except for a rearrangement of the primes, has been answered to the positive: this proven claim is called fundamental theorem of arithmetic. A proof appears in Euclid's Elements.
+
+Many subsets of the natural numbers have been the subject of specific studies and have been named, often after the first mathematician that has studied them. Example of such sets of integers are Fibonacci numbers and perfect numbers. For more examples, see Integer sequence.
+
+Algebraic numbers are those that are a solution to a polynomial equation with integer coefficients. Real numbers that are not rational numbers are called irrational numbers. Complex numbers which are not algebraic are called transcendental numbers. The algebraic numbers that are solutions of a monic polynomial equation with integer coefficients are called algebraic integers.
+
+Motivated by the classical problems of constructions with straightedge and compass, the constructible numbers are those complex numbers whose real and imaginary parts can be constructed using straightedge and compass, starting from a given segment of unit length, in a finite number of steps.
+
+A computable number, also known as recursive number, is a real number such that there exists an algorithm which, given a positive number n as input, produces the first n digits of the computable number's decimal representation. Equivalent definitions can be given using μ-recursive functions, Turing machines or λ-calculus. The computable numbers are stable for all usual arithmetic operations, including the computation of the roots of a polynomial, and thus form a real closed field that contains the real algebraic numbers.
+
+The computable numbers may be viewed as the real numbers that may be exactly represented in a computer: a computable number is exactly represented by its first digits and a program for computing further digits. However, the computable numbers are rarely used in practice. One reason is that there is no algorithm for testing the equality of two computable numbers. More precisely, there cannot exist any algorithm which takes any computable number as an input, and decides in every case if this number is equal to zero or not.
+
+The set of computable numbers has the same cardinality as the natural numbers. Therefore, almost all real numbers are non-computable. However, it is very difficult to produce explicitly a real number that is not computable.
+
+The p-adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right. The number system that results depends on what base is used for the digits: any base is possible, but a prime number base provides the best mathematical properties. The set of the p-adic numbers contains the rational numbers, but is not contained in the complex numbers.
+
+The elements of an algebraic function field over a finite field and algebraic numbers have many similar properties (see Function field analogy). Therefore, they are often regarded as numbers by number theorists. The p-adic numbers play an important role in this analogy.
+
+Some number systems that are not included in the complex numbers may be constructed from the real numbers in a way that generalize the construction of the complex numbers. They are sometimes called hypercomplex numbers. They include the quaternions H, introduced by Sir William Rowan Hamilton, in which multiplication is not commutative, the octonions, in which multiplication is not associative in addition to not being commutative, and the sedenions, in which multiplication is not alternative, neither associative nor commutative.
+
+For dealing with infinite sets, the natural numbers have been generalized to the ordinal numbers and to the cardinal numbers. The former gives the ordering of the set, while the latter gives its size. For finite sets, both ordinal and cardinal numbers are identified with the natural numbers. In the infinite case, many ordinal numbers correspond to the same cardinal number.
+
+Hyperreal numbers are used in non-standard analysis. The hyperreals, or nonstandard reals (usually denoted as *R), denote an ordered field that is a proper extension of the ordered field of real numbers R and satisfies the transfer principle. This principle allows true first-order statements about R to be reinterpreted as true first-order statements about *R.
+
+Superreal and surreal numbers extend the real numbers by adding infinitesimally small numbers and infinitely large numbers, but still form fields.

en/4157.html.txt

@@ -0,0 +1,1238 @@
+In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a (possibly infinite) collection of objects in order, one after another.  Any finite collection of objects can be put in order just by the process of counting: labeling the objects with distinct natural numbers.  Ordinal numbers are thus the "labels" needed to arrange collections of objects in order.
+
+An ordinal number is used to describe the order type of a well-ordered set (though this does not work for a well-ordered proper class). A well-ordered set is a set with a relation > such that
+
+Two well-ordered sets have the same order type if and only if there is a bijection from one set to the other that converts the relation in the first set to the relation in the second set.
+
+Whereas ordinals are useful for ordering the objects in a collection, they are distinct from cardinal numbers, which are useful for saying how many objects are in a collection. Although the distinction between ordinals and cardinals is not always apparent in finite sets (one can go from one to the other just by counting labels), different infinite ordinals can correspond to the same cardinal.  Like other kinds of numbers, ordinals can be added, multiplied, and exponentiated, although none of these operations are commutative.
+
+Ordinals were introduced by Georg Cantor in 1883[1] in order to accommodate infinite sequences and classify derived sets, which he had previously introduced in 1872 while studying the uniqueness of trigonometric series.[2]
+
+A natural number (which, in this context, includes the number 0) can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence.  When restricted to finite sets these two concepts coincide, there is only one way to put a finite set into a linear sequence, up to isomorphism.  When dealing with infinite sets one has to distinguish between the notion of size, which leads to cardinal numbers, and the notion of position, which is generalized by the ordinal numbers described here.  This is because while any set has only one size (its cardinality), there are many nonisomorphic well-orderings of any infinite set, as explained below.
+
+Whereas the notion of cardinal number is associated with a set with no particular structure on it, the ordinals are intimately linked with the special kind of sets that are called well-ordered (so intimately linked, in fact, that some mathematicians make no distinction between the two concepts). A well-ordered set is a totally ordered set (given any two elements one defines a smaller and a larger one in a coherent way) in which there is no infinite decreasing sequence (however, there may be infinite increasing sequences); equivalently, every non-empty subset of the set has a least element. Ordinals may be used to label the elements of any given well-ordered set (the smallest element being labelled 0, the one after that 1, the next one 2, "and so on") and to measure the "length" of the whole set by the least ordinal that is not a label for an element of the set.  This "length" is called the order type of the set.
+
+Any ordinal is defined by the set of ordinals that precede it: in fact, the most common definition of ordinals identifies each ordinal as the set of ordinals that precede it.  For example, the ordinal 42 is the order type of the ordinals less than it, i.e., the ordinals from 0 (the smallest of all ordinals) to 41 (the immediate predecessor of 42), and it is generally identified as the set {0,1,2,…,41}.  Conversely, any set S of ordinals that is downward-closed — meaning that for any ordinal α in S and any ordinal β < α, β is also in S — is (or can be identified with) an ordinal.
+
+There are infinite ordinals as well: the smallest infinite ordinal is ω, which is the order type of the natural numbers (finite ordinals) and that can even be identified with the set of natural numbers (indeed, the set of natural numbers is well-ordered—as is any set of ordinals—and since it is downward closed it can be identified with the ordinal associated with it, which is exactly how ω is defined).
+
+Perhaps a clearer intuition of ordinals can be formed by examining a first few of them: as mentioned above, they start with the natural numbers, 0, 1, 2, 3, 4, 5, …  After all natural numbers comes the first infinite ordinal, ω, and after that come ω+1, ω+2, ω+3, and so on.  (Exactly what addition means will be defined later on: just consider them as names.)  After all of these come ω·2 (which is ω+ω), ω·2+1, ω·2+2, and so on, then ω·3, and then later on ω·4.  Now the set of ordinals formed in this way (the ω·m+n, where m and n are natural numbers) must itself have an ordinal associated with it: and that is ω2.  Further on, there will be ω3, then ω4, and so on, and ωω, then ωωω, then later ωωωω, and even later ε0 (epsilon nought) (to give a few examples of relatively small—countable—ordinals).  This can be continued indefinitely far ("indefinitely far" is exactly what ordinals are good at: every time one says "and so on" when enumerating ordinals, it defines a larger ordinal). The smallest uncountable ordinal is the set of all countable ordinals, expressed as ω1.
+
+In a well-ordered set, every non-empty subset contains a distinct smallest element.  Given the axiom of dependent choice, this is equivalent to just saying that the set is totally ordered and there is no infinite decreasing sequence, something perhaps easier to visualize. In practice, the importance of well-ordering is justified by the possibility of applying transfinite induction, which says, essentially, that any property that passes on from the predecessors of an element to that element itself must be true of all elements (of the given well-ordered set).  If the states of a computation (computer program or game) can be well-ordered in such a way that each step is followed by a "lower" step, then the computation will terminate.
+
+It is inappropriate to distinguish between two well-ordered sets if they only differ in the "labeling of their elements", or more formally: if the elements of the first set can be paired off with the elements of the second set such that if one element is smaller than another in the first set, then the partner of the first element is smaller than the partner of the second element in the second set, and vice versa.  Such a one-to-one correspondence is called an order isomorphism and the two well-ordered sets are said to be order-isomorphic, or similar (obviously this is an equivalence relation).  Formally, if a partial order ≤ is defined on the set S, and a partial order ≤' is defined on the set S' , then the posets (S,≤) and (S' ,≤') are order isomorphic if there is a bijection f that preserves the ordering. That is, f(a) ≤' f(b) if and only if a ≤ b.  Provided there exists an order isomorphism between two well-ordered sets, the order isomorphism is unique: this makes it quite justifiable to consider the two sets as essentially identical, and to seek a "canonical" representative of the isomorphism type (class).  This is exactly what the ordinals provide, and it also provides a canonical labeling of the elements of any well-ordered set. Every well-ordered set (S,<) is order-isomorphic to the set of ordinals less than one specific ordinal number under their natural ordering. This canonical set is the order type of (S,<).
+
+Essentially, an ordinal is intended to be defined as an isomorphism class of well-ordered sets: that is, as an equivalence class for the equivalence relation of "being order-isomorphic".  There is a technical difficulty involved, however, in the fact that the equivalence class is too large to be a set in the usual Zermelo–Fraenkel (ZF) formalization of set theory.  But this is not a serious difficulty.  The ordinal can be said to be the order type of any set in the class.
+
+The original definition of ordinal numbers, found for example in the Principia Mathematica, defines the order type of a well-ordering as the set of all well-orderings similar (order-isomorphic) to that well-ordering: in other words, an ordinal number is genuinely an equivalence class of well-ordered sets.  This definition must be abandoned in ZF and related systems of axiomatic set theory because these equivalence classes are too large to form a set.  However, this definition still can be used in type theory and in Quine's axiomatic set theory New Foundations and related systems (where it affords a rather surprising alternative solution to the Burali-Forti paradox of the largest ordinal).
+
+Rather than defining an ordinal as an equivalence class of well-ordered sets, it will be defined as a particular well-ordered set that (canonically) represents the class.  Thus, an ordinal number will be a well-ordered set; and every well-ordered set will be order-isomorphic to exactly one ordinal number.
+
+For each well-ordered set 
+
+
+
+T
+
+
+{\displaystyle T}
+
+, 
+
+
+
+a
+↦
+
+T
+
+<
+a
+
+
+
+
+{\displaystyle a\mapsto T_{<a}}
+
+ defines an order isomorphism between 
+
+
+
+T
+
+
+{\displaystyle T}
+
+ and the set of all subsets of 
+
+
+
+T
+
+
+{\displaystyle T}
+
+ having the form 
+
+
+
+
+T
+
+<
+a
+
+
+:=
+{
+x
+∈
+T
+∣
+x
+<
+a
+}
+
+
+{\displaystyle T_{<a}:=\{x\in T\mid x<a\}}
+
+ ordered by inclusion. This motivates the standard definition, suggested by John von Neumann, now called definition of von Neumann ordinals: "each ordinal is the well-ordered set of all smaller ordinals." In symbols, λ = [0,λ).[3][4] Formally:
+
+The natural numbers are thus ordinals by this definition. For instance, 2 is an element of 4 = {0, 1, 2, 3}, and 2 is equal to {0, 1} and so it is a subset of {0, 1, 2, 3}.
+
+It can be shown by transfinite induction that every well-ordered set is order-isomorphic to exactly one of these ordinals, that is, there is an order preserving bijective function between them.
+
+Furthermore, the elements of every ordinal are ordinals themselves. Given two ordinals S and T, S is an element of T if and only if S is a proper subset of T. Moreover, either S is an element of T, or T is an element of S, or they are equal. So every set of ordinals is totally ordered. Further, every set of ordinals is well-ordered. This generalizes the fact that every set of natural numbers is well-ordered.
+
+Consequently, every ordinal S is a set having as elements precisely the ordinals smaller than S. For example, every set of ordinals has a supremum, the ordinal obtained by taking the union of all the ordinals in the set. This union exists regardless of the set's size, by the axiom of union.
+
+The class of all ordinals is not a set. If it were a set, one could show that it was an ordinal and thus a member of itself, which would contradict its strict ordering by membership. This is the Burali-Forti paradox. The class of all ordinals is variously called "Ord", "ON", or "∞".
+
+An ordinal is finite if and only if the opposite order is also well-ordered, which is the case if and only if each of its non-empty subsets has a maximum.
+
+There are other modern formulations of the definition of ordinal. For example, assuming the axiom of regularity, the following are equivalent for a set x:
+
+These definitions cannot be used in non-well-founded set theories. In set theories with urelements, one has to further make sure that the definition excludes urelements from appearing in ordinals.
+
+If α is any ordinal and X is a set, an α-indexed sequence of elements of X is a function from α to X.  This concept, a transfinite sequence (if α is infinite) or ordinal-indexed sequence, is a generalization of the concept of a sequence. An ordinary sequence corresponds to the case α = ω, while a finite α corresponds to a tuple (mathematics), a.k.a. string (computer science).
+
+Transfinite induction holds in any well-ordered set, but it is so important in relation to ordinals that it is worth restating here.
+
+That is, if P(α) is true whenever P(β) is true for all β < α, then P(α) is true for all α.  Or, more practically: in order to prove a property P for all ordinals α, one can assume that it is already known for all smaller β < α.
+
+Transfinite induction can be used not only to prove things, but also to define them. Such a definition is normally said to be by transfinite recursion – the proof that the result is well-defined uses transfinite induction. Let F denote a (class) function F to be defined on the ordinals. The idea now is that, in defining F(α) for an unspecified ordinal α, one may assume that F(β) is already defined for all β < α and thus give a formula for F(α) in terms of these F(β). It then follows by transfinite induction that there is one and only one function satisfying the recursion formula up to and including α.
+
+Here is an example of definition by transfinite recursion on the ordinals (more will be given later): define function F by letting F(α) be the smallest ordinal not in the set {F(β) | β < α}, that is, the set consisting of all F(β) for β < α. This definition assumes the F(β) known in the very process of defining F; this apparent vicious circle is exactly what definition by transfinite recursion permits. In fact, F(0) makes sense since there is no ordinal β < 0, and the set {F(β) | β < 0} is empty. So F(0) is equal to 0 (the smallest ordinal of all). Now that F(0) is known, the definition applied to F(1) makes sense (it is the smallest ordinal not in the singleton set {F(0)} = {0}), and so on (the and so on is exactly transfinite induction). It turns out that this example is not very exciting, since provably F(α) = α for all ordinals α, which can be shown, precisely, by transfinite induction.
+
+Any nonzero ordinal has the minimum element, zero. It may or may not have a maximum element. For example, 42 has maximum 41 and ω+6 has maximum ω+5. On the other hand, ω does not have a maximum since there is no largest natural number. If an ordinal has a maximum α, then it is the next ordinal after α, and it is called a successor ordinal, namely the successor of α, written α+1.  In the von Neumann definition of ordinals, the successor of α is 
+
+
+
+α
+∪
+{
+α
+}
+
+
+{\displaystyle \alpha \cup \{\alpha \}}
+
+ since its elements are those of α and α itself.[3]
+
+A nonzero ordinal that is not a successor is called a limit ordinal.  One justification for this term is that a limit ordinal is the limit in a topological sense of all smaller ordinals (under the order topology).
+
+When 
+
+
+
+⟨
+
+α
+
+ι
+
+
+
+|
+
+ι
+<
+γ
+⟩
+
+
+{\displaystyle \langle \alpha _{\iota }|\iota <\gamma \rangle }
+
+ is an ordinal-indexed sequence, indexed by a limit γ and the sequence is increasing, i.e. 
+
+
+
+
+α
+
+ι
+
+
+<
+
+α
+
+ρ
+
+
+
+
+
+{\displaystyle \alpha _{\iota }<\alpha _{\rho }\!}
+
+ whenever 
+
+
+
+ι
+<
+ρ
+,
+
+
+
+{\displaystyle \iota <\rho ,\!}
+
+ its limit is defined as the least upper bound of the set 
+
+
+
+{
+
+α
+
+ι
+
+
+
+|
+
+ι
+<
+γ
+}
+,
+
+
+
+{\displaystyle \{\alpha _{\iota }|\iota <\gamma \},\!}
+
+ that is, the smallest ordinal (it always exists) greater than any term of the sequence.  In this sense, a limit ordinal is the limit of all smaller ordinals (indexed by itself). Put more directly, it is the supremum of the set of smaller ordinals.
+
+Another way of defining a limit ordinal is to say that α is a limit ordinal if and only if:
+
+So in the following sequence:
+
+ω is a limit ordinal because for any smaller ordinal (in this example, a natural number) there is another ordinal (natural number) larger than it, but still less than ω.
+
+Thus, every ordinal is either zero, or a successor (of a well-defined predecessor), or a limit.  This distinction is important, because many definitions by transfinite induction rely upon it.  Very often, when defining a function F by transfinite induction on all ordinals, one defines F(0), and F(α+1) assuming F(α) is defined, and then, for limit ordinals δ one defines F(δ) as the limit of the F(β) for all β<δ (either in the sense of ordinal limits, as previously explained, or for some other notion of limit if F does not take ordinal values).  Thus, the interesting step in the definition is the successor step, not the limit ordinals.  Such functions (especially for F nondecreasing and taking ordinal values) are called continuous.  Ordinal addition, multiplication and exponentiation are continuous as functions of their second argument.
+
+Any well-ordered set is similar (order-isomorphic) to a unique ordinal number 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+; in other words, its elements can be indexed in increasing fashion by the ordinals less than 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+.  This applies, in particular, to any set of ordinals: any set of ordinals is naturally indexed by the ordinals less than some 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+.  The same holds, with a slight modification, for classes of ordinals (a collection of ordinals, possibly too large to form a set, defined by some property): any class of ordinals can be indexed by ordinals (and, when the class is unbounded in the class of all ordinals, this puts it in class-bijection with the class of all ordinals).  So the 
+
+
+
+γ
+
+
+{\displaystyle \gamma }
+
+-th element in the class (with the convention that the "0-th" is the smallest, the "1-st" is the next smallest, and so on) can be freely spoken of.  Formally, the definition is by transfinite induction: the 
+
+
+
+γ
+
+
+{\displaystyle \gamma }
+
+-th element of the class is defined (provided it has already been defined for all 
+
+
+
+β
+<
+γ
+
+
+{\displaystyle \beta <\gamma }
+
+), as the smallest element greater than the 
+
+
+
+β
+
+
+{\displaystyle \beta }
+
+-th element for all 
+
+
+
+β
+<
+γ
+
+
+{\displaystyle \beta <\gamma }
+
+.
+
+This could be applied, for example, to the class of limit ordinals: the 
+
+
+
+γ
+
+
+{\displaystyle \gamma }
+
+-th ordinal, which is either a limit or zero is 
+
+
+
+ω
+⋅
+γ
+
+
+{\displaystyle \omega \cdot \gamma }
+
+ (see ordinal arithmetic for the definition of multiplication of ordinals).  Similarly, one can consider additively indecomposable ordinals (meaning a nonzero ordinal that is not the sum of two strictly smaller ordinals): the 
+
+
+
+γ
+
+
+{\displaystyle \gamma }
+
+-th additively indecomposable ordinal is indexed as 
+
+
+
+
+ω
+
+γ
+
+
+
+
+{\displaystyle \omega ^{\gamma }}
+
+.  The technique of indexing classes of ordinals is often useful in the context of fixed points: for example, the 
+
+
+
+γ
+
+
+{\displaystyle \gamma }
+
+-th ordinal 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ such that 
+
+
+
+
+ω
+
+α
+
+
+=
+α
+
+
+{\displaystyle \omega ^{\alpha }=\alpha }
+
+ is written 
+
+
+
+
+ε
+
+γ
+
+
+
+
+{\displaystyle \varepsilon _{\gamma }}
+
+. These are called the "epsilon numbers".
+
+A class 
+
+
+
+C
+
+
+{\displaystyle C}
+
+ of ordinals is said to be unbounded, or cofinal, when given any ordinal 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+, there is a 
+
+
+
+β
+
+
+{\displaystyle \beta }
+
+ in 
+
+
+
+C
+
+
+{\displaystyle C}
+
+ such that 
+
+
+
+α
+<
+β
+
+
+{\displaystyle \alpha <\beta }
+
+ (then the class must be a proper class, i.e., it cannot be a set).  It is said to be closed when the limit of a sequence of ordinals in the class is again in the class: or, equivalently, when the indexing (class-)function 
+
+
+
+F
+
+
+{\displaystyle F}
+
+ is continuous in the sense that, for 
+
+
+
+δ
+
+
+{\displaystyle \delta }
+
+ a limit ordinal, 
+
+
+
+F
+(
+δ
+)
+
+
+{\displaystyle F(\delta )}
+
+ (the 
+
+
+
+δ
+
+
+{\displaystyle \delta }
+
+-th ordinal in the class) is the limit of all 
+
+
+
+F
+(
+γ
+)
+
+
+{\displaystyle F(\gamma )}
+
+ for 
+
+
+
+γ
+<
+δ
+
+
+{\displaystyle \gamma <\delta }
+
+; this is also the same as being closed, in the topological sense, for the order topology (to avoid talking of topology on proper classes, one can demand that the intersection of the class with any given ordinal is closed for the order topology on that ordinal, this is again equivalent).
+
+Of particular importance are those classes of ordinals that are closed and unbounded, sometimes called clubs.  For example, the class of all limit ordinals is closed and unbounded: this translates the fact that there is always a limit ordinal greater than a given ordinal, and that a limit of limit ordinals is a limit ordinal (a fortunate fact if the terminology is to make any sense at all!).  The class of additively indecomposable ordinals, or the class of 
+
+
+
+
+ε
+
+⋅
+
+
+
+
+{\displaystyle \varepsilon _{\cdot }}
+
+ ordinals, or the class of cardinals, are all closed unbounded; the set of regular cardinals, however, is unbounded but not closed, and any finite set of ordinals is closed but not unbounded.
+
+A class is stationary if it has a nonempty intersection with every closed unbounded class.  All superclasses of closed unbounded classes are stationary, and stationary classes are unbounded, but there are stationary classes that are not closed and stationary classes that have no closed unbounded subclass (such as the class of all limit ordinals with countable cofinality).  Since the intersection of two closed unbounded classes is closed and unbounded, the intersection of a stationary class and a closed unbounded class is stationary.  But the intersection of two stationary classes may be empty, e.g. the class of ordinals with cofinality ω with the class of ordinals with uncountable cofinality.
+
+Rather than formulating these definitions for (proper) classes of ordinals, one can formulate them for sets of ordinals below a given ordinal 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+:  A subset of a limit ordinal 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ is said to be unbounded (or cofinal) under 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ provided any ordinal less than 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ is less than some ordinal in the set.  More generally, one can call a subset of any ordinal 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ cofinal in 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ provided every ordinal less than 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ is less than or equal to some ordinal in the set. The subset is said to be closed under 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ provided it is closed for the order topology in 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+, i.e. a limit of ordinals in the set is either in the set or equal to 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ itself.
+
+There are three usual operations on ordinals: addition, multiplication, and (ordinal) exponentiation.  Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the operation or by using transfinite recursion.  The Cantor normal form provides a standardized way of writing ordinals.  It uniquely represents each ordinal as a finite sum of ordinal powers of ω. However, this cannot form the basis of a universal ordinal notation due to such self-referential representations as ε0 = ωε0. The so-called "natural" arithmetical operations retain commutativity at the expense of continuity.
+
+Interpreted as nimbers, ordinals are also subject to nimber arithmetic operations.
+
+Each ordinal associates with one cardinal, its cardinality. If there is a bijection between two ordinals (e.g. ω = 1 + ω and ω + 1 > ω), then they associate with the same cardinal. Any well-ordered set having an ordinal as its order-type has the same cardinality as that ordinal. The least ordinal associated with a given cardinal is called the initial ordinal of that cardinal. Every finite ordinal (natural number) is initial, and no other ordinal associates with its cardinal. But most infinite ordinals are not initial, as many infinite ordinals associate with the same cardinal. The axiom of choice is equivalent to the statement that every set can be well-ordered, i.e. that every cardinal has an initial ordinal. In theories with the axiom of choice, the cardinal number of any set has an initial ordinal, and one may employ the Von Neumann cardinal assignment as the cardinal's representation. In set theories without the axiom of choice, a cardinal may be represented by the set of sets with that cardinality having minimal rank (see Scott's trick).
+
+The α-th infinite initial ordinal is written 
+
+
+
+
+ω
+
+α
+
+
+
+
+{\displaystyle \omega _{\alpha }}
+
+, it is always a limit ordinal. Its cardinality is written 
+
+
+
+
+ℵ
+
+α
+
+
+
+
+{\displaystyle \aleph _{\alpha }}
+
+.  For example, the cardinality of ω0 = ω is 
+
+
+
+
+ℵ
+
+0
+
+
+
+
+{\displaystyle \aleph _{0}}
+
+, which is also the cardinality of ω2 or ε0 (all are countable ordinals).  So ω can be identified with 
+
+
+
+
+ℵ
+
+0
+
+
+
+
+{\displaystyle \aleph _{0}}
+
+, except that the notation 
+
+
+
+
+ℵ
+
+0
+
+
+
+
+{\displaystyle \aleph _{0}}
+
+ is used when writing cardinals, and ω when writing ordinals (this is important since, for example, 
+
+
+
+
+ℵ
+
+0
+
+
+2
+
+
+
+
+{\displaystyle \aleph _{0}^{2}}
+
+ = 
+
+
+
+
+ℵ
+
+0
+
+
+
+
+{\displaystyle \aleph _{0}}
+
+ whereas 
+
+
+
+
+ω
+
+2
+
+
+>
+ω
+
+
+{\displaystyle \omega ^{2}>\omega }
+
+).  Also, 
+
+
+
+
+ω
+
+1
+
+
+
+
+{\displaystyle \omega _{1}}
+
+ is the smallest uncountable ordinal (to see that it exists, consider the set of equivalence classes of well-orderings of the natural numbers: each such well-ordering defines a countable ordinal, and 
+
+
+
+
+ω
+
+1
+
+
+
+
+{\displaystyle \omega _{1}}
+
+ is the order type of that set), 
+
+
+
+
+ω
+
+2
+
+
+
+
+{\displaystyle \omega _{2}}
+
+ is the smallest ordinal whose cardinality is greater than 
+
+
+
+
+ℵ
+
+1
+
+
+
+
+{\displaystyle \aleph _{1}}
+
+, and so on, and 
+
+
+
+
+ω
+
+ω
+
+
+
+
+{\displaystyle \omega _{\omega }}
+
+ is the limit of the 
+
+
+
+
+ω
+
+n
+
+
+
+
+{\displaystyle \omega _{n}}
+
+ for natural numbers n (any limit of cardinals is a cardinal, so this limit is indeed the first cardinal after all the 
+
+
+
+
+ω
+
+n
+
+
+
+
+{\displaystyle \omega _{n}}
+
+).
+
+The cofinality of an ordinal 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+ is the smallest ordinal 
+
+
+
+δ
+
+
+{\displaystyle \delta }
+
+ that is the order type of a cofinal subset of 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+.  Notice that a number of authors define cofinality or use it only for limit ordinals.  The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set.
+
+Thus for a limit ordinal, there exists a 
+
+
+
+δ
+
+
+{\displaystyle \delta }
+
+-indexed strictly increasing sequence with limit 
+
+
+
+α
+
+
+{\displaystyle \alpha }
+
+.  For example, the cofinality of ω² is ω, because the sequence ω·m (where m ranges over the natural numbers) tends to ω²; but, more generally, any countable limit ordinal has cofinality ω.  An uncountable limit ordinal may have either cofinality ω as does 
+
+
+
+
+ω
+
+ω
+
+
+
+
+{\displaystyle \omega _{\omega }}
+
+ or an uncountable cofinality.
+
+The cofinality of 0 is 0.  And the cofinality of any successor ordinal is 1.  The cofinality of any limit ordinal is at least 
+
+
+
+ω
+
+
+{\displaystyle \omega }
+
+.
+
+An ordinal that is equal to its cofinality is called regular and it is always an initial ordinal.  Any limit of regular ordinals is a limit of initial ordinals and thus is also initial even if it is not regular, which it usually is not.  If the Axiom of Choice, then 
+
+
+
+
+ω
+
+α
++
+1
+
+
+
+
+{\displaystyle \omega _{\alpha +1}}
+
+ is regular for each α.  In this case, the ordinals 0, 1, 
+
+
+
+ω
+
+
+{\displaystyle \omega }
+
+, 
+
+
+
+
+ω
+
+1
+
+
+
+
+{\displaystyle \omega _{1}}
+
+, and 
+
+
+
+
+ω
+
+2
+
+
+
+
+{\displaystyle \omega _{2}}
+
+ are regular, whereas 2, 3, 
+
+
+
+
+ω
+
+ω
+
+
+
+
+{\displaystyle \omega _{\omega }}
+
+, and ωω·2 are initial ordinals that are not regular.
+
+The cofinality of any ordinal α is a regular ordinal, i.e. the cofinality of the cofinality of α is the same as the cofinality of α.  So the cofinality operation is idempotent.
+
+As mentioned above (see Cantor normal form) the ordinal ε0, which is the smallest satisfying the equation 
+
+
+
+
+ω
+
+α
+
+
+=
+α
+
+
+{\displaystyle \omega ^{\alpha }=\alpha }
+
+, so it is the limit of the sequence 0, 1, 
+
+
+
+ω
+
+
+{\displaystyle \omega }
+
+, 
+
+
+
+
+ω
+
+ω
+
+
+
+
+{\displaystyle \omega ^{\omega }}
+
+, 
+
+
+
+
+ω
+
+
+ω
+
+ω
+
+
+
+
+
+
+{\displaystyle \omega ^{\omega ^{\omega }}}
+
+, etc.  Many ordinals can be defined in such a manner as fixed points of certain ordinal functions (the 
+
+
+
+ι
+
+
+{\displaystyle \iota }
+
+-th ordinal such that 
+
+
+
+
+ω
+
+α
+
+
+=
+α
+
+
+{\displaystyle \omega ^{\alpha }=\alpha }
+
+ is called 
+
+
+
+
+ε
+
+ι
+
+
+
+
+{\displaystyle \varepsilon _{\iota }}
+
+, then one could go on trying to find the 
+
+
+
+ι
+
+
+{\displaystyle \iota }
+
+-th ordinal such that 
+
+
+
+
+ε
+
+α
+
+
+=
+α
+
+
+{\displaystyle \varepsilon _{\alpha }=\alpha }
+
+, "and so on", but all the subtlety lies in the "and so on").  One could try to do this systematically, but no matter what system is used to define and construct ordinals, there is always an ordinal that lies just above all the ordinals constructed by the system.  Perhaps the most important ordinal that limits a system of construction in this manner is the Church–Kleene ordinal, 
+
+
+
+
+ω
+
+1
+
+
+
+C
+K
+
+
+
+
+
+{\displaystyle \omega _{1}^{\mathrm {CK} }}
+
+ (despite the 
+
+
+
+
+ω
+
+1
+
+
+
+
+{\displaystyle \omega _{1}}
+
+ in the name, this ordinal is countable), which is the smallest ordinal that cannot in any way be represented by a computable function (this can be made rigorous, of course).  Considerably large ordinals can be defined below 
+
+
+
+
+ω
+
+1
+
+
+
+C
+K
+
+
+
+
+
+{\displaystyle \omega _{1}^{\mathrm {CK} }}
+
+, however, which measure the "proof-theoretic strength" of certain formal systems (for example, 
+
+
+
+
+ε
+
+0
+
+
+
+
+{\displaystyle \varepsilon _{0}}
+
+ measures the strength of Peano arithmetic).  Large countable ordinals such as countable admissible ordinals can also be defined above the Church-Kleene ordinal, which are of interest in various parts of logic.[citation needed]
+
+Any ordinal number can be made into a topological space by endowing it with the order topology; this topology is discrete if and only if the ordinal is a countable cardinal, i.e. at most ω. A subset of ω + 1 is open in the order topology if and only if either it is cofinite or it does not contain ω as an element.
+
+See the Topology and ordinals section of the "Order topology" article.
+
+A set is downward closed if anything less than an element of the set is also in the set. If a set of ordinals is downward closed, then that set is an ordinal—the least ordinal not in the set.
+
+Examples:
+
+The transfinite ordinal numbers, which first appeared in 1883,[5] originated in Cantor's work with derived sets. If P is a set of real numbers, the derived set P'  is the set of limit points of P. In 1872, Cantor generated the sets P(n) by applying the derived set operation n times to P. In 1880, he pointed out that these sets form the sequence P' ⊇ ··· ⊇ P(n) ⊇ P(n + 1) ⊇ ···, and he continued the derivation process by defining P(∞) as the intersection of these sets. Then he iterated the derived set operation and intersections to extend his sequence of sets into the infinite: P(∞) ⊇ P(∞ + 1) ⊇ P(∞ + 2) ⊇ ··· ⊇ P(2∞) ⊇ ··· ⊇ P(∞2) ⊇ ···.[6] The superscripts containing ∞ are just indices defined by the derivation process.[7]
+
+Cantor used these sets in the theorems: (1) If P(α) = ∅ for some index α, then P'  is countable; (2) Conversely, if P'  is countable, then there is an index α such that P(α) = ∅. These theorems are proved by partitioning P'  into pairwise disjoint sets: P' = (P' ∖ P(2)) ∪ (P(2) ∖ P(3)) ∪ ··· ∪ (P(∞) ∖ P(∞ + 1)) ∪ ··· ∪ P(α). For β < α: since P(β + 1) contains the limit points of P(β), the sets P(β) ∖ P(β + 1) have no limit points. Hence, they are discrete sets, so they are countable. Proof of first theorem: If P(α) = ∅ for some index α, then P'  is the countable union of countable sets. Therefore, P'  is countable.[8]
+
+The second theorem requires proving the existence of an α such that P(α) = ∅. To prove this, Cantor considered the set of all α having countably many predecessors. To define this set, he defined the transfinite ordinal numbers and transformed the infinite indices into ordinals by replacing ∞ with ω, the first transfinite ordinal number. Cantor called the set of finite ordinals the first number class. The second number class is the set of ordinals whose predecessors form a countably infinite set. The set of all α having countably many predecessors—that is, the set of countable ordinals—is the union of these two number classes. Cantor proved that the cardinality of the second number class is the first uncountable cardinality.[9]
+
+Cantor's second theorem becomes: If P'  is countable, then there is a countable ordinal α such that P(α) = ∅. Its proof uses proof by contradiction. Let P'  be countable, and assume there is no such α. This assumption produces two cases.
+
+In both cases, P'  is uncountable, which contradicts P'  being countable. Therefore, there is a countable ordinal α such that P(α) = ∅. Cantor's work with derived sets and ordinal numbers led to the Cantor-Bendixson theorem.[11]
+
+Using successors, limits, and cardinality, Cantor generated an unbounded sequence of ordinal numbers and number classes.[12] The (α + 1)-th number class is the set of ordinals whose predecessors form a set of the same cardinality as the α-th number class. The cardinality of the (α + 1)-th number class is the cardinality immediately following that of the α-th number class.[13] For a limit ordinal α, the α-th number class is the union of the β-th number classes for β < α.[14] Its cardinality is the limit of the cardinalities of these number classes.
+
+If n is finite, the n-th number class has cardinality 
+
+
+
+
+ℵ
+
+n
+−
+1
+
+
+
+
+{\displaystyle \aleph _{n-1}}
+
+. If α ≥ ω, the α-th number class has cardinality 
+
+
+
+
+ℵ
+
+α
+
+
+
+
+{\displaystyle \aleph _{\alpha }}
+
+.[15] Therefore, the cardinalities of the number classes correspond one-to-one with the aleph numbers. Also, the α-th number class consists of ordinals different from those in the preceding number classes if and only if α is a non-limit ordinal. Therefore, the non-limit number classes partition the ordinals into pairwise disjoint sets.

en/4158.html.txt

@@ -0,0 +1,896 @@
+
+
+
+
+The number π (/paɪ/) is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics.  It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, and is spelled out as "pi". It is also referred to as Archimedes' constant.
+
+Being an irrational number, π cannot be expressed as a common fraction, although fractions such as 22/7 are commonly used to approximate it. Equivalently its decimal representation never ends and never settles into a permanently repeating pattern. Its decimal (or other base) digits appear to be randomly distributed, and are conjectured to satisfy a specific kind of statistical randomness. It is known that π is a transcendental number: it is not the root of any polynomial with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
+
+Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations to π for practical computations. Around 250 BC the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematics approximated π to seven digits, while Indian mathematics made a five-digit approximation, both using geometrical techniques. The first exact formula for π, based on infinite series, was discovered a millennium later, when in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics.[1][2] The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits.[3][4] The primary motivation for these computations is as a test case to develop efficient algorithms to calculate numeric series, as well as the quest to break records.[5][6] The extensive calculations involved have also been used to test supercomputers and high-precision multiplication algorithms.
+
+Because its most elementary definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres. In more modern mathematical analysis, the number is instead defined using the spectral properties of the real number system, as an eigenvalue or a period, without any reference to geometry. It appears therefore in areas of mathematics and the sciences having little to do with the geometry of circles, such as number theory and statistics, as well as in almost all areas of physics. The ubiquity of π makes it one of the most widely known mathematical constants both inside and outside the scientific community. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines. Adepts have succeeded in memorizing the value of π to over 70,000 digits.
+
+The symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase Greek letter π, sometimes spelled out as pi, and derived from the first letter of the Greek word perimetros, meaning circumference.[7] In English, π is pronounced as "pie" (/paɪ/ PY).[8] In mathematical use, the lowercase letter π is distinguished from its capitalized and enlarged counterpart ∏, which denotes a product of a sequence, analogous to how ∑ denotes summation.
+
+The choice of the symbol π is discussed in the section Adoption of the symbol π.
+
+π is commonly defined as the ratio of a circle's circumference C to its diameter d:[9]
+
+The ratio C/d is constant, regardless of the circle's size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π implicitly makes use of flat (Euclidean) geometry; although the notion of a circle can be extended to any curved (non-Euclidean) geometry, these new circles will no longer satisfy the formula π = C/d.[9]
+
+Here, the circumference of a circle is the arc length around the perimeter of the circle, a quantity which can be formally defined independently of geometry using limits, a concept in calculus.[10]  For example, one may directly compute the arc length of the top half of the unit circle, given in Cartesian coordinates by the equation x2 + y2 = 1, as the integral:[11]
+
+An integral such as this was adopted as the definition of π by Karl Weierstrass, who defined it directly as an integral in 1841.[a]
+
+Definitions of π such as these that rely on concepts of the integral calculus are no longer common in the literature. Remmert 2012, Ch. 5 explains that this is because in many modern treatments of calculus, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to have a definition of π that does not rely on the latter.  One such definition, due to Richard Baltzer,[12] and popularized by Edmund Landau,[13] is the following: π is twice the smallest positive number at which the cosine function equals 0.[9][11][14]  The cosine can be defined independently of geometry as a power series,[15] or as the solution of a differential equation.[14]
+
+In a similar spirit, π can be defined instead using properties of the complex exponential, exp z, of a complex variable z.  Like the cosine, the complex exponential can be defined in one of several ways.  The set of complex numbers at which exp z is equal to one is then an (imaginary) arithmetic progression of the form:
+
+and there is a unique positive real number π with this property.[11][16]
+A more abstract variation on the same idea, making use of sophisticated mathematical concepts of topology and algebra, is the following theorem:[17] there is a unique (up to automorphism) continuous isomorphism from the group R/Z of real numbers under addition modulo integers (the circle group) onto the multiplicative group of complex numbers of absolute value one.  The number π is then defined as half the magnitude of the derivative of this homomorphism.[18]
+
+A circle encloses the largest area that can be attained within a given perimeter.  Thus the number π is also characterized as the best constant in the isoperimetric inequality (times one-fourth).  There are many other, closely related, ways in which π appears as an eigenvalue of some geometrical or physical process; see below.
+
+π is an irrational number, meaning that it cannot be written as the ratio of two integers. Fractions such as 22/7 and 355/113 are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value.[19] Because π is irrational, it has an infinite number of digits in its decimal representation, and it does not settle into an infinitely repeating pattern of digits. There are several proofs that π is irrational; they generally require calculus and rely on the reductio ad absurdum technique. The degree to which π can be approximated by rational numbers (called the irrationality measure) is not precisely known; estimates have established that the irrationality measure is larger than the measure of e or ln 2 but smaller than the measure of Liouville numbers.[20]
+
+The digits of π have no apparent pattern and have passed tests for statistical randomness, including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often.[21] The conjecture that π is normal has not been proven or disproven.[21]
+
+Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis. Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π and found them consistent with normality; for example, the frequencies of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found.[22] Any random sequence of digits contains arbitrarily long subsequences that appear non-random, by the infinite monkey theorem.  Thus, because the sequence of π's digits passes statistical tests for randomness, it contains some sequences of digits that may appear non-random, such as a sequence of six consecutive 9s that begins at the 762nd decimal place of the decimal representation of π.[23] This is also called the "Feynman point" in mathematical folklore, after Richard Feynman, although no connection to Feynman is known.
+
+In addition to being irrational, more strongly π is a transcendental number, which means that it is not the solution of any non-constant polynomial equation with rational coefficients, such as x5/120 − x3/6 + x = 0.[24][b]
+
+The transcendence of π has two important consequences: First, π cannot be expressed using any finite combination of rational numbers and square roots or n-th roots such as 3√31 or √10. Second, since no transcendental number can be constructed with compass and straightedge, it is not possible to "square the circle". In other words, it is impossible to construct, using compass and straightedge alone, a square whose area is exactly equal to the area of a given circle.[25] Squaring a circle was one of the important geometry problems of the classical antiquity.[26] Amateur mathematicians in modern times have sometimes attempted to square the circle and sometimes claim success despite the fact that it is mathematically impossible.[27]
+
+Like all irrational numbers, π cannot be represented as a common fraction (also known as a simple or vulgar fraction), by the very definition of "irrational number" (that is, "not a rational number"). But every irrational number, including π, can be represented by an infinite series of nested fractions, called a continued fraction:
+
+Truncating the continued fraction at any point yields a rational approximation for π; the first four of these are 3, 22/7, 333/106, and 355/113. These numbers are among the best-known and most widely used historical approximations of the constant. Each approximation generated in this way is a best rational approximation; that is, each is closer to π than any other fraction with the same or a smaller denominator.[28] Because π is known to be transcendental, it is by definition not algebraic and so cannot be a quadratic irrational. Therefore, π cannot have a periodic continued fraction. Although the simple continued fraction for π (shown above) also does not exhibit any other obvious pattern,[29] mathematicians have discovered several generalized continued fractions that do, such as:[30]
+
+Some approximations of pi include:
+
+Digits in other number systems
+
+Any complex number, say z, can be expressed using a pair of real numbers. In the polar coordinate system, one number (radius or r) is used to represent z's distance from the origin of the complex plane and the other (angle or φ) to represent a counter-clockwise rotation from the positive real line as follows:[34]
+
+where i is the imaginary unit satisfying i2 = −1. The frequent appearance of π in complex analysis can be related to the behaviour of the exponential function of a complex variable, described by Euler's formula:[35]
+
+where the constant e is the base of the natural logarithm. This formula establishes a correspondence between imaginary powers of e and points on the unit circle centered at the origin of the complex plane. Setting φ = π in Euler's formula results in Euler's identity, celebrated by mathematicians because it contains the five most important mathematical constants:[35][36]
+
+There are n different complex numbers z satisfying zn = 1, and these are called the "n-th roots of unity".[37] They are given by this formula:
+
+The best-known approximations to π dating before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places.
+After this, no further progress was made until the late medieval period.
+
+Based on the measurements of the Great Pyramid of Giza (c. 2560 BC) ,[c] some Egyptologists have claimed that the ancient Egyptians used an approximation of π as 22/7 from as early as the Old Kingdom.[38][39] This claim has met with scepticism.[40][41][42][43][44]
+The earliest written approximations of π are found in Babylon and Egypt, both within one per cent of the true value. In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25/8 = 3.125.[45] In Egypt, the Rhind Papyrus, dated around 1650 BC but copied from a document dated to 1850 BC, has a formula for the area of a circle that treats π as (16/9)2 ≈ 3.16.[45]
+
+Astronomical calculations in the Shatapatha Brahmana (ca. 4th century BC) use a fractional approximation of 339/108 ≈ 3.139 (an accuracy of 9×10−4).[46] Other Indian sources by about 150 BC treat π as √10 ≈ 3.1622.[47]
+
+The first recorded algorithm for rigorously calculating the value of π was a geometrical approach using polygons, devised around 250 BC by the Greek mathematician Archimedes.[48] This polygonal algorithm dominated for over 1,000 years, and as a result π is sometimes referred to as "Archimedes' constant".[49] Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that 223/71 < π < 22/7 (that is 3.1408 < π < 3.1429).[50] Archimedes' upper bound of 22/7 may have led to a widespread popular belief that π is equal to 22/7.[51] Around 150 AD, Greek-Roman scientist Ptolemy, in his Almagest, gave a value for π of 3.1416, which he may have obtained from Archimedes or from Apollonius of Perga.[52][53] Mathematicians using polygonal algorithms reached 39 digits of π in 1630, a record only broken in 1699 when infinite series were used to reach 71 digits.[54]
+
+In ancient China, values for π included 3.1547 (around 1 AD), √10 (100 AD, approximately 3.1623), and 142/45 (3rd century, approximately 3.1556).[55] Around 265 AD, the Wei Kingdom mathematician Liu Hui created a polygon-based iterative algorithm and used it with a 3,072-sided polygon to obtain a value of π of 3.1416.[56][57] Liu later invented a faster method of calculating π and obtained a value of 3.14 with a 96-sided polygon, by taking advantage of the fact that the differences in area of successive polygons form a geometric series with a factor of 4.[56] The Chinese mathematician Zu Chongzhi, around 480 AD, calculated that 3.1415926 < π < 3.1415927 and suggested the approximations π ≈ 355/113 = 3.14159292035... and π ≈ 22/7 = 3.142857142857..., which he termed the Milü (''close ratio") and Yuelü ("approximate ratio"), respectively, using Liu Hui's algorithm applied to a 12,288-sided polygon. With a correct value for its seven first decimal digits, this value of remained the most accurate approximation of π available for the next 800 years.[58]
+
+The Indian astronomer Aryabhata used a value of 3.1416 in his Āryabhaṭīya (499 AD).[59] Fibonacci in c. 1220 computed 3.1418 using a polygonal method, independent of Archimedes.[60] Italian author Dante apparently employed the value 3+√2/10 ≈ 3.14142.[60]
+
+The Persian astronomer Jamshīd al-Kāshī produced 9 sexagesimal digits, roughly the equivalent of 16 decimal digits, in 1424 using a polygon with 3×228 sides,[61][62] which stood as the world record for about 180 years.[63] French mathematician François Viète in 1579 achieved 9 digits with a polygon of 3×217 sides.[63] Flemish mathematician Adriaan van Roomen arrived at 15 decimal places in 1593.[63] In 1596, Dutch mathematician Ludolph van Ceulen reached 20 digits, a record he later increased to 35 digits (as a result, π was called the "Ludolphian number" in Germany until the early 20th century).[64] Dutch scientist Willebrord Snellius reached 34 digits in 1621,[65] and Austrian astronomer Christoph Grienberger arrived at 38 digits in 1630 using 1040 sides,[66] which remains the most accurate approximation manually achieved using polygonal algorithms.[65]
+
+The calculation of π was revolutionized by the development of infinite series techniques in the 16th and 17th centuries. An infinite series is the sum of the terms of an infinite sequence.[67] Infinite series allowed mathematicians to compute π with much greater precision than Archimedes and others who used geometrical techniques.[67] Although infinite series were exploited for π most notably by European mathematicians such as James Gregory and Gottfried Wilhelm Leibniz, the approach was first discovered in India sometime between 1400 and 1500 AD.[68][69] The first written description of an infinite series that could be used to compute π was laid out in Sanskrit verse by Indian astronomer Nilakantha Somayaji in his Tantrasamgraha, around 1500 AD.[70] The series are presented without proof, but proofs are presented in a later Indian work, Yuktibhāṣā, from around 1530 AD. Nilakantha attributes the series to an earlier Indian mathematician, Madhava of Sangamagrama, who lived c. 1350 – c. 1425.[70] Several infinite series are described, including series for sine, tangent, and cosine, which are now referred to as the Madhava series or Gregory–Leibniz series.[70] Madhava used infinite series to estimate π to 11 digits around 1400, but that value was improved on around 1430 by the Persian mathematician Jamshīd al-Kāshī, using a polygonal algorithm.[71]
+
+The first infinite sequence discovered in Europe was an infinite product (rather than an infinite sum, which are more typically used in π calculations) found by French mathematician François Viète in 1593:[73][74][75]
+
+The second infinite sequence found in Europe, by John Wallis in 1655, was also an infinite product:[73]
+
+The discovery of calculus, by English scientist Isaac Newton and German mathematician Gottfried Wilhelm Leibniz in the 1660s, led to the development of many infinite series for approximating π. Newton himself used an arcsin series to compute a 15 digit approximation of π in 1665 or 1666, later writing "I am ashamed to tell you to how many figures I carried these computations, having no other business at the time."[72]
+
+In Europe, Madhava's formula was rediscovered by Scottish mathematician James Gregory in 1671, and by Leibniz in 1674:[76][77]
+
+This formula, the Gregory–Leibniz series, equals π/4 when evaluated with z = 1.[77] In 1699, English mathematician Abraham Sharp used the Gregory–Leibniz series for 
+
+
+
+z
+=
+
+
+1
+
+3
+
+
+
+
+
+{\textstyle z={\frac {1}{\sqrt {3}}}}
+
+ to compute π to 71 digits, breaking the previous record of 39 digits, which was set with a polygonal algorithm.[78] The Gregory–Leibniz for 
+
+
+
+z
+=
+1
+
+
+{\displaystyle z=1}
+
+ series is simple, but converges very slowly (that is, approaches the answer gradually), so it is not used in modern π calculations.[79]
+
+In 1706 John Machin used the Gregory–Leibniz series to produce an algorithm that converged much faster:[80]
+
+Machin reached 100 digits of π with this formula.[81] Other mathematicians created variants, now known as Machin-like formulae, that were used to set several successive records for calculating digits of π.[81] Machin-like formulae remained the best-known method for calculating π well into the age of computers, and were used to set records for 250 years, culminating in a 620-digit approximation in 1946 by Daniel Ferguson – the best approximation achieved without the aid of a calculating device.[82]
+
+A record was set by the calculating prodigy Zacharias Dase, who in 1844 employed a Machin-like formula to calculate 200 decimals of π in his head at the behest of German mathematician Carl Friedrich Gauss.[83] British mathematician William Shanks famously took 15 years to calculate π to 707 digits, but made a mistake in the 528th digit, rendering all subsequent digits incorrect.[83]
+
+Some infinite series for π converge faster than others. Given the choice of two infinite series for π, mathematicians will generally use the one that converges more rapidly because faster convergence reduces the amount of computation needed to calculate π to any given accuracy.[84] A simple infinite series for π is the Gregory–Leibniz series:[85]
+
+As individual terms of this infinite series are added to the sum, the total gradually gets closer to π, and – with a sufficient number of terms – can get as close to π as desired. It converges quite slowly, though – after 500,000 terms, it produces only five correct decimal digits of π.[86]
+
+An infinite series for π (published by Nilakantha in the 15th century) that converges more rapidly than the Gregory–Leibniz series is:{{sfn|Arndt|Haenel|2006|p=223|ps=: (formula 16.10). Note that (n − 1)n(n + 1) = n3 − n.[87]
+
+The following table compares the convergence rates of these two series:
+
+After five terms, the sum of the Gregory–Leibniz series is within 0.2 of the correct value of π, whereas the sum of Nilakantha's series is within 0.002 of the correct value of π. Nilakantha's series converges faster and is more useful for computing digits of π. Series that converge even faster include Machin's series and Chudnovsky's series, the latter producing 14 correct decimal digits per term.[84]
+
+Not all mathematical advances relating to π were aimed at increasing the accuracy of approximations. When Euler solved the Basel problem in 1735, finding the exact value of the sum of the reciprocal squares, he established a connection between π and the prime numbers that later contributed to the development and study of the Riemann zeta function:[88]
+
+Swiss scientist Johann Heinrich Lambert in 1761 proved that π is irrational, meaning it is not equal to the quotient of any two whole numbers.[19] Lambert's proof exploited a continued-fraction representation of the tangent function.[89] French mathematician Adrien-Marie Legendre proved in 1794 that π2 is also irrational. In 1882, German mathematician Ferdinand von Lindemann proved that π is transcendental, confirming a conjecture made by both Legendre and Euler.[90][91] Hardy and Wright states that "the proofs were afterwards modified and simplified by Hilbert, Hurwitz, and other writers".[92]
+
+In the earliest usages, the Greek letter π was an abbreviation of the Greek word for periphery (περιφέρεια),[93] and was combined in ratios with δ (for diameter) or ρ (for radius) to form circle constants.[94][95][96] (Before then, mathematicians sometimes used letters such as c or p instead.[97]) The first recorded use is Oughtred's "
+
+
+
+δ
+.
+π
+
+
+{\displaystyle \delta .\pi }
+
+", to express the ratio of periphery and diameter in the 1647 and later editions of Clavis Mathematicae.[98][97] Barrow likewise used "
+
+
+
+
+
+π
+δ
+
+
+
+
+{\textstyle {\frac {\pi }{\delta }}}
+
+" to represent the constant 3.14...,[99] while Gregory instead used "
+
+
+
+
+
+π
+ρ
+
+
+
+
+{\textstyle {\frac {\pi }{\rho }}}
+
+" to represent 6.28... .[100][95]
+
+The earliest known use of the Greek letter π alone to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in his 1706 work Synopsis Palmariorum Matheseos; or, a New Introduction to the Mathematics.[101][102] The Greek letter first appears there in the phrase "1/2 Periphery (π)" in the discussion of a circle with radius one.[103] However, he writes that his equations for π are from the "ready pen of the truly ingenious Mr. John Machin", leading to speculation that Machin may have employed the Greek letter before Jones.[97] Jones' notation was not immediately adopted by other mathematicians, with the fraction notation still being used as late as 1767.[94][104]
+
+Euler started using the single-letter form beginning with his 1727 Essay Explaining the Properties of Air, though he used π = 6.28..., the ratio of radius to periphery, in this and some later writing.[105][106]   Euler first used π = 3.14... in his 1736 work Mechanica,[107] and continued in his widely-read 1748 work Introductio in analysin infinitorum (he wrote: "for the sake of brevity we will write this number as π; thus π is equal to half the circumference of a circle of radius 1").[108] Because Euler corresponded heavily with other mathematicians in Europe, the use of the Greek letter spread rapidly, and the practice was universally adopted thereafter in the Western world,[97] though the definition still varied between 3.14... and 6.28... as late as 1761.[109]
+
+Iterate
+
+Then an estimate for π is given by
+
+The development of computers in the mid-20th century again revolutionized the hunt for digits of π. Mathematicians John Wrench and Levi Smith reached 1,120 digits in 1949 using a desk calculator.[110] Using an inverse tangent (arctan) infinite series, a team led by George Reitwiesner and John von Neumann that same year achieved 2,037 digits with a calculation that took 70 hours of computer time on the ENIAC computer.[111][112] The record, always relying on an arctan series, was broken repeatedly (7,480 digits in 1957; 10,000 digits in 1958; 100,000 digits in 1961) until 1 million digits were reached in 1973.[111]
+
+Two additional developments around 1980 once again accelerated the ability to compute π. First, the discovery of new iterative algorithms for computing π, which were much faster than the infinite series; and second, the invention of fast multiplication algorithms that could multiply large numbers very rapidly.[113] Such algorithms are particularly important in modern π computations because most of the computer's time is devoted to multiplication.[114] They include the Karatsuba algorithm, Toom–Cook multiplication, and Fourier transform-based methods.[115]
+
+The iterative algorithms were independently published in 1975–1976 by physicist Eugene Salamin and scientist Richard Brent.[116] These avoid reliance on infinite series. An iterative algorithm repeats a specific calculation, each iteration using the outputs from prior steps as its inputs, and produces a result in each step that converges to the desired value. The approach was actually invented over 160 years earlier by Carl Friedrich Gauss, in what is now termed the arithmetic–geometric mean method (AGM method) or Gauss–Legendre algorithm.[116] As modified by Salamin and Brent, it is also referred to as the Brent–Salamin algorithm.
+
+The iterative algorithms were widely used after 1980 because they are faster than infinite series algorithms: whereas infinite series typically increase the number of correct digits additively in successive terms, iterative algorithms generally multiply the number of correct digits at each step. For example, the Brent-Salamin algorithm doubles the number of digits in each iteration. In 1984, brothers John and Peter Borwein produced an iterative algorithm that quadruples the number of digits in each step; and in 1987, one that increases the number of digits five times in each step.[117] Iterative methods were used by Japanese mathematician Yasumasa Kanada to set several records for computing π between 1995 and 2002.[118] This rapid convergence comes at a price: the iterative algorithms require significantly more memory than infinite series.[118]
+
+For most numerical calculations involving π, a handful of digits provide sufficient precision. According to Jörg Arndt and Christoph Haenel, thirty-nine digits are sufficient to perform most cosmological calculations, because that is the accuracy necessary to calculate the circumference of the observable universe with a precision of one atom.[119] Accounting for additional digits needed to compensate for computational round-off errors, Arndt concludes that a few hundred digits would suffice for any scientific application. Despite this, people have worked strenuously to compute π to thousands and millions of digits.[120] This effort may be partly ascribed to the human compulsion to break records, and such achievements with π often make headlines around the world.[121][122] They also have practical benefits, such as testing supercomputers, testing numerical analysis algorithms (including high-precision multiplication algorithms); and within pure mathematics itself, providing data for evaluating the randomness of the digits of π.[123]
+
+Modern π calculators do not use iterative algorithms exclusively. New infinite series were discovered in the 1980s and 1990s that are as fast as iterative algorithms, yet are simpler and less memory intensive.[118] The fast iterative algorithms were anticipated in 1914, when the Indian mathematician Srinivasa Ramanujan published dozens of innovative new formulae for π, remarkable for their elegance, mathematical depth, and rapid convergence.[124] One of his formulae, based on modular equations, is
+
+This series converges much more rapidly than most arctan series, including Machin's formula.[125] Bill Gosper was the first to use it for advances in the calculation of π, setting a record of 17 million digits in 1985.[126] Ramanujan's formulae anticipated the modern algorithms developed by the Borwein brothers and the Chudnovsky brothers.[127] The Chudnovsky formula developed in 1987 is
+
+It produces about 14 digits of π per term,[128] and has been used for several record-setting π calculations, including the first to surpass 1 billion (109) digits in 1989 by the Chudnovsky brothers, 2.7 trillion (2.7×1012) digits by Fabrice Bellard in 2009,[129] 10 trillion (1013) digits in 2011 by Alexander Yee and Shigeru Kondo,[130] and over 22 trillion digits in 2016 by Peter Trueb.[131][132] For similar formulas, see also the Ramanujan–Sato series.
+
+In 2006, mathematician Simon Plouffe used the PSLQ integer relation algorithm[133] to generate several new formulas for π, conforming to the following template:
+
+where q is eπ (Gelfond's constant), k is an odd number, and a, b, c are certain rational numbers that Plouffe computed.[134]
+
+Monte Carlo methods, which evaluate the results of multiple random trials, can be used to create approximations of π.[135] Buffon's needle is one such technique: If a needle of length ℓ is dropped n times on a surface on which parallel lines are drawn t units apart, and if x of those times it comes to rest crossing a line (x > 0), then one may approximate π based on the counts:[136]
+
+Another Monte Carlo method for computing π is to draw a circle inscribed in a square, and randomly place dots in the square. The ratio of dots inside the circle to the total number of dots will approximately equal π/4.[137]
+
+Another way to calculate π using probability is to start with a random walk, generated by a sequence of (fair) coin tosses: independent random variables Xk such that Xk ∈ {−1,1} with equal probabilities.  The associated random walk is
+
+so that, for each n, Wn is drawn from a shifted and scaled binomial distribution.  As n varies, Wn defines a (discrete) stochastic process.  Then π can be calculated by[138]
+
+This Monte Carlo method is independent of any relation to circles, and is a consequence of the central limit theorem, discussed below.
+
+These Monte Carlo methods for approximating π are very slow compared to other methods, and do not provide any information on the exact number of digits that are obtained. Thus they are never used to approximate π when speed or accuracy is desired.[139]
+
+Two algorithms were discovered in 1995 that opened up new avenues of research into π. They are called spigot algorithms because, like water dripping from a spigot, they produce single digits of π that are not reused after they are calculated.[140][141] This is in contrast to infinite series or iterative algorithms, which retain and use all intermediate digits until the final result is produced.[140]
+
+Mathematicians Stan Wagon and Stanley Rabinowitz produced a simple spigot algorithm in 1995.[141][142][143] Its speed is comparable to arctan algorithms, but not as fast as iterative algorithms.[142]
+
+Another spigot algorithm, the BBP digit extraction algorithm, was discovered in 1995 by Simon Plouffe:[144][145]
+
+This formula, unlike others before it, can produce any individual hexadecimal digit of π without calculating all the preceding digits.[144] Individual binary digits may be extracted from individual hexadecimal digits, and octal digits can be extracted from one or two hexadecimal digits. Variations of the algorithm have been discovered, but no digit extraction algorithm has yet been found that rapidly produces decimal digits.[146] An important application of digit extraction algorithms is to validate new claims of record π computations: After a new record is claimed, the decimal result is converted to hexadecimal, and then a digit extraction algorithm is used to calculate several random hexadecimal digits near the end; if they match, this provides a measure of confidence that the entire computation is correct.[130]
+
+Between 1998 and 2000, the distributed computing project PiHex used Bellard's formula (a modification of the BBP algorithm) to compute the quadrillionth (1015th) bit of π, which turned out to be 0.[147] In September 2010, a Yahoo! employee used the company's Hadoop application on one thousand computers over a 23-day period to compute 256 bits of π at the two-quadrillionth (2×1015th) bit, which also happens to be zero.[148]
+
+Because π is closely related to the circle, it is found in many formulae from the fields of geometry and trigonometry, particularly those concerning circles, spheres, or ellipses. Other branches of science, such as statistics, physics, Fourier analysis, and number theory, also include π in some of their important formulae.
+
+π appears in formulae for areas and volumes of geometrical shapes based on circles, such as ellipses, spheres, cones, and tori. Below are some of the more common formulae that involve π.[149]
+
+The formulae above are special cases of the volume of the n-dimensional ball and the surface area of its boundary, the (n−1)-dimensional sphere, given below.
+
+Definite integrals that describe circumference, area, or volume of shapes generated by circles typically have values that involve π. For example, an integral that specifies half the area of a circle of radius one is given by:[150]
+
+In that integral the function √1 − x2 represents the top half of a circle (the square root is a consequence of the Pythagorean theorem), and the integral ∫1−1 computes the area between that half of a circle and the x axis.
+
+The trigonometric functions rely on angles, and mathematicians generally use radians as units of measurement. π plays an important role in angles measured in radians, which are defined so that a complete circle spans an angle of 2π radians.[151] The angle measure of 180° is equal to π radians, and 1° = π/180 radians.[151]
+
+Common trigonometric functions have periods that are multiples of π; for example, sine and cosine have period 2π,[152] so for any angle θ and any integer k,
+
+Many of the appearances of π in the formulas of mathematics and the sciences have to do with its close relationship with geometry.  However, π also appears in many natural situations having apparently nothing to do with geometry.
+
+In many applications, it plays a distinguished role as an eigenvalue.  For example, an idealized vibrating string can be modelled as the graph of a function f on the unit interval [0,1], with fixed ends f(0) = f(1) = 0.  The modes of vibration of the string are solutions of the differential equation 
+
+
+
+
+f
+″
+
+(
+x
+)
++
+λ
+f
+(
+x
+)
+=
+0
+
+
+{\displaystyle f''(x)+\lambda f(x)=0}
+
+, or 
+
+
+
+
+f
+″
+
+(
+t
+)
+=
+−
+λ
+f
+(
+x
+)
+
+
+{\displaystyle f''(t)=-\lambda f(x)}
+
+.  Thus λ is an eigenvalue of the second derivative operator 
+
+
+
+f
+↦
+
+f
+″
+
+
+
+{\displaystyle f\mapsto f''}
+
+, and is constrained by Sturm–Liouville theory to take on only certain specific values. It must be positive, since the operator is negative definite, so it is convenient to write λ = ν2, where ν > 0 is called the wavenumber.  Then f(x) = sin(π x) satisfies the boundary conditions and the differential equation with ν = π.[153]
+
+The value π is, in fact, the least such value of the wavenumber, and is associated with the fundamental mode of vibration of the string.  One way to show this is by estimating the energy, which satisfies Wirtinger's inequality:[154] for a function f : [0, 1] → ℂ with f(0) = f(1) = 0 and f , f ' both square integrable, we have:
+
+with equality precisely when f is a multiple of sin(π x). Here π appears as an optimal constant in Wirtinger's inequality, and it follows that it is the smallest wavenumber, using the variational characterization of the eigenvalue. As a consequence, π is the smallest singular value of the derivative operator on the space of functions on [0,1] vanishing at both endpoints (the Sobolev space 
+
+
+
+
+H
+
+0
+
+
+1
+
+
+[
+0
+,
+1
+]
+
+
+{\displaystyle H_{0}^{1}[0,1]}
+
+).
+
+The number π serves appears in similar eigenvalue problems in higher-dimensional analysis.  As mentioned above, it can be characterized via its role as the best constant in the isoperimetric inequality: the area A enclosed by a plane Jordan curve of perimeter P satisfies the inequality
+
+and equality is clearly achieved for the circle, since in that case A = πr2 and P = 2πr.[155]
+
+Ultimately as a consequence of the isoperimetric inequality, π appears in the optimal constant for the critical Sobolev inequality in n dimensions, which thus characterizes the role of π in many physical phenomena as well, for example those of classical potential theory.[156][157][158]  In two dimensions, the critical Sobolev inequality is
+
+for f a smooth function with compact support in R2, 
+
+
+
+∇
+f
+
+
+{\displaystyle \nabla f}
+
+ is the gradient of f, and 
+
+
+
+‖
+f
+
+‖
+
+2
+
+
+
+
+{\displaystyle \|f\|_{2}}
+
+ and 
+
+
+
+‖
+∇
+f
+
+‖
+
+1
+
+
+
+
+{\displaystyle \|\nabla f\|_{1}}
+
+ refer respectively to the L2 and L1-norm.  The Sobolev inequality is equivalent to the isoperimetric inequality (in any dimension), with the same best constants.
+
+Wirtinger's inequality also generalizes to higher-dimensional Poincaré inequalities that provide best constants for the Dirichlet energy of an n-dimensional membrane.  Specifically, π is the greatest constant such that
+
+for all convex subsets G of Rn of diameter 1, and square-integrable functions u on G of mean zero.[159]  Just as Wirtinger's inequality is the variational form of the Dirichlet eigenvalue problem in one dimension, the Poincaré inequality is the variational form of the Neumann eigenvalue problem, in any dimension.
+
+The constant π also appears as a critical spectral parameter in the Fourier transform.  This is the integral transform, that takes a complex-valued integrable function f on the real line to the function defined as:
+
+Although there are several different conventions for the Fourier transform and its inverse, any such convention must involve π somewhere. The above is the most canonical definition, however, giving the unique unitary operator on L2 that is also an algebra homomorphism of L1 to L∞.[160]
+
+The Heisenberg uncertainty principle also contains the number π.  The uncertainty principle gives a sharp lower bound on the extent to which it is possible to localize a function both in space and in frequency: with our conventions for the Fourier transform,
+
+The physical consequence, about the uncertainty in simultaneous position and momentum observations of a quantum mechanical system, is discussed below.  The appearance of π in the formulae of Fourier analysis is ultimately a consequence of the Stone–von Neumann theorem, asserting the uniqueness of the Schrödinger representation of the Heisenberg group.[161]
+
+The fields of probability and statistics frequently use the normal distribution as a simple model for complex phenomena; for example, scientists generally assume that the observational error in most experiments follows a normal distribution.[162] The Gaussian function, which is the probability density function of the normal distribution with mean μ and standard deviation σ, naturally contains π:[163]
+
+The factor of 
+
+
+
+
+
+
+1
+
+2
+π
+
+
+
+
+
+
+{\displaystyle {\tfrac {1}{\sqrt {2\pi }}}}
+
+ makes the area under the graph of f  equal to one, as is required for a probability distribution. This follows from a change of variables in the Gaussian integral:[163]
+
+which says that the area under the basic bell curve in the figure is equal to the square root of π.
+
+The central limit theorem explains the central role of normal distributions, and thus of π, in probability and statistics. This theorem is ultimately connected with the spectral characterization of π as the eigenvalue associated with the Heisenberg uncertainty principle, and the fact that equality holds in the uncertainty principle only for the Gaussian function.[164] Equivalently, π is the unique constant making the Gaussian normal distribution e-πx2 equal to its own Fourier transform.[165] Indeed,  according to Howe (1980), the "whole business" of establishing the fundamental theorems of Fourier analysis reduces to the Gaussian integral.
+
+Let V be the set of all twice differentiable real functions 
+
+
+
+f
+:
+
+R
+
+→
+
+R
+
+
+
+{\displaystyle f:\mathbb {R} \to \mathbb {R} }
+
+ that satisfy the ordinary differential equation 
+
+
+
+
+f
+″
+
+(
+x
+)
++
+f
+(
+x
+)
+=
+0
+
+
+{\displaystyle f''(x)+f(x)=0}
+
+.  Then V is a two-dimensional real vector space, with two parameters corresponding to a pair of initial conditions for the differential equation.  For any 
+
+
+
+t
+∈
+
+R
+
+
+
+{\displaystyle t\in \mathbb {R} }
+
+, let 
+
+
+
+
+e
+
+t
+
+
+:
+V
+→
+
+R
+
+
+
+{\displaystyle e_{t}:V\to \mathbb {R} }
+
+ be the evaluation functional, which associates to each 
+
+
+
+f
+∈
+V
+
+
+{\displaystyle f\in V}
+
+ the value 
+
+
+
+
+e
+
+t
+
+
+(
+f
+)
+=
+f
+(
+t
+)
+
+
+{\displaystyle e_{t}(f)=f(t)}
+
+ of the function f at the real point t.  Then, for each t, the kernel of 
+
+
+
+
+e
+
+t
+
+
+
+
+{\displaystyle e_{t}}
+
+ is a one-dimensional linear subspace of V.  Hence 
+
+
+
+t
+↦
+ker
+⁡
+
+e
+
+t
+
+
+
+
+{\displaystyle t\mapsto \ker e_{t}}
+
+ defines a function from 
+
+
+
+
+R
+
+→
+
+P
+
+(
+V
+)
+
+
+{\displaystyle \mathbb {R} \to \mathbb {P} (V)}
+
+ from the real line to the real projective line.   This function is periodic, and the quantity π can be characterized as the period of this map.[166]
+
+The constant π appears in the Gauss–Bonnet formula which relates the differential geometry of surfaces to their topology.  Specifically, if a compact surface Σ has Gauss curvature K, then
+
+where χ(Σ) is the Euler characteristic, which is an integer.[167]  An example is the surface area of a sphere S of curvature 1 (so that its radius of curvature, which coincides with its radius, is also 1.)  The Euler characteristic of a sphere can be computed from its homology groups and is found to be equal to two.  Thus we have
+
+reproducing the formula for the surface area of a sphere of radius 1.
+
+The constant appears in many other integral formulae in topology, in particular, those involving characteristic classes via the Chern–Weil homomorphism.[168]
+
+Vector calculus is a branch of calculus that is concerned with the properties of vector fields, and has many physical applications such as to electricity and magnetism.  The Newtonian potential for a point source Q situated at the origin of a three-dimensional Cartesian coordinate system is[169]
+
+which represents the potential energy of a unit mass (or charge) placed a distance |x| from the source, and k is a dimensional constant.  The field, denoted here by E, which may be the (Newtonian) gravitational field or the (Coulomb) electric field, is the negative gradient of the potential:
+
+Special cases include Coulomb's law and Newton's law of universal gravitation. Gauss' law states that the outward flux of the field through any smooth, simple, closed, orientable surface S containing the origin is equal to 4πkQ:
+
+It is standard to absorb this factor of 4π into the constant k, but this argument shows why it must appear somewhere.  Furthermore, 4π is the surface area of the unit sphere, but we have not assumed that S is the sphere.  However, as a consequence of the divergence theorem, because the region away from the origin is vacuum (source-free) it is only the homology class of the surface S in R3\{0}  that matters in computing the integral, so it can be replaced by any convenient surface in the same homology class, in particular, a sphere, where spherical coordinates can be used to calculate the integral.
+
+A consequence of the Gauss law is that the negative Laplacian of the potential V is equal to 4πkQ times the Dirac delta function:
+
+More general distributions of matter (or charge) are obtained from this by convolution, giving the Poisson equation
+
+where ρ is the distribution function.
+
+The constant π also plays an analogous role in four-dimensional potentials associated with Einstein's equations, a fundamental formula which forms the basis of the general theory of relativity and describes the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy:[170]
+
+where Rμν is the Ricci curvature tensor, R is the scalar curvature, gμν is the metric tensor, Λ is the cosmological constant, G is Newton's gravitational constant, c is the speed of light in vacuum, and Tμν is the stress–energy tensor.  The left-hand side of Einstein's equation is a non-linear analogue of the Laplacian of the metric tensor, and reduces to that in the weak field limit, with the 
+
+
+
+Λ
+g
+
+
+{\displaystyle \Lambda g}
+
+ term playing the role of a Lagrange multiplier, and the right-hand side is the analogue of the distribution function, times 8π.
+
+One of the key tools in complex analysis is contour integration of a function over a positively oriented (rectifiable) Jordan curve γ.  A form of Cauchy's integral formula states that if a point z0 is interior to γ, then[171]
+
+Although the curve γ is not a circle, and hence does not have any obvious connection to the constant π, a standard proof of this result uses Morera's theorem, which implies that the integral is invariant under homotopy of the curve, so that it can be deformed to a circle and then integrated explicitly in polar coordinates.  More generally, it is true that if a rectifiable closed curve γ does not contain z0, then the above integral is 2πi times the winding number of the curve.
+
+The general form of Cauchy's integral formula establishes the relationship between the values of a complex analytic function f(z) on the Jordan curve γ and the value of f(z) at any interior point z0 of γ:[172][173]
+
+provided f(z) is analytic in the region enclosed by γ and extends continuously to γ.  Cauchy's integral formula is a special case of the residue theorem, that if g(z) is a meromorphic function the region enclosed by γ and is continuous in a neighbourhood of γ, then
+
+where the sum is of the residues at the poles of g(z).
+
+The factorial function n! is the product of all of the positive integers through n.  The gamma function extends the concept of factorial (normally defined only for non-negative integers) to all complex numbers, except the negative real integers. When the gamma function is evaluated at half-integers, the result contains π; for example 
+
+
+
+Γ
+(
+1
+
+/
+
+2
+)
+=
+
+
+π
+
+
+
+
+{\displaystyle \Gamma (1/2)={\sqrt {\pi }}}
+
+ and 
+
+
+
+Γ
+(
+5
+
+/
+
+2
+)
+=
+
+
+
+3
+
+
+π
+
+
+
+4
+
+
+
+
+{\textstyle \Gamma (5/2)={\frac {3{\sqrt {\pi }}}{4}}}
+
+.[174]
+
+The gamma function is defined by its Weierstrass product development:[175]
+
+where γ is the Euler–Mascheroni constant.  Evaluated at z = 1/2 and squared, the equation Γ(1/2)2 = π reduces to the Wallis product formula.  The gamma function is also connected to the Riemann zeta function and identities for the functional determinant, in which the constant π plays an important role.
+
+The gamma function is used to calculate the volume Vn(r) of the n-dimensional ball of radius r in Euclidean n-dimensional space, and the surface area Sn−1(r) of its boundary, the (n−1)-dimensional sphere:[176]
+
+Further, it follows from the functional equation that
+
+The gamma function can be used to create a simple approximation to the factorial function n! for large n: 
+
+
+
+n
+!
+∼
+
+
+2
+π
+n
+
+
+
+
+(
+
+
+n
+e
+
+
+)
+
+
+n
+
+
+
+
+{\textstyle n!\sim {\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}}
+
+ which is known as Stirling's approximation.[177]  Equivalently,
+
+As a geometrical application of Stirling's approximation, let Δn denote the standard simplex in n-dimensional Euclidean space, and (n + 1)Δn denote the simplex having all of its sides scaled up by a factor of n + 1.  Then
+
+Ehrhart's volume conjecture is that this is the (optimal) upper bound on the volume of a convex body containing only one lattice point.[178]
+
+The Riemann zeta function ζ(s) is used in many areas of mathematics. When evaluated at s = 2 it can be written as
+
+Finding a simple solution for this infinite series was a famous problem in mathematics called the Basel problem. Leonhard Euler solved it in 1735 when he showed it was equal to π2/6.[88] Euler's result leads to the number theory result that the probability of two random numbers being relatively prime (that is, having no shared factors) is equal to 6/π2.[179][180] This probability is based on the observation that the probability that any number is divisible by a prime p is 1/p (for example, every 7th integer is divisible by 7.) Hence the probability that two numbers are both divisible by this prime is 1/p2, and the probability that at least one of them is not is 1 − 1/p2. For distinct primes, these divisibility events are mutually independent; so the probability that two numbers are relatively prime is given by a product over all primes:[181]
+
+This probability can be used in conjunction with a random number generator to approximate π using a Monte Carlo approach.[182]
+
+The solution to the Basel problem implies that the geometrically derived quantity π is connected in a deep way to the distribution of prime numbers.  This is a special case of Weil's conjecture on Tamagawa numbers, which asserts the equality of similar such infinite products of arithmetic quantities, localized at each prime p, and a geometrical quantity: the reciprocal of the volume of a certain locally symmetric space.  In the case of the Basel problem, it is the hyperbolic 3-manifold SL2(R)/SL2(Z).[183]
+
+The zeta function also satisfies Riemann's functional equation, which involves π as well as the gamma function:
+
+Furthermore, the derivative of the zeta function satisfies
+
+A consequence is that π can be obtained from the functional determinant of the harmonic oscillator.  This functional determinant can be computed via a product expansion, and is equivalent to the Wallis product formula.[184]  The calculation can be recast in quantum mechanics, specifically the variational approach to the spectrum of the hydrogen atom.[185]
+
+The constant π also appears naturally in Fourier series of periodic functions.  Periodic functions are functions on the group T =R/Z of fractional parts of real numbers.  The Fourier decomposition shows that a complex-valued function f on T can be written as an infinite linear superposition of unitary characters of T.   That is, continuous group homomorphisms from T to the circle group U(1) of unit modulus complex numbers.  It is a theorem that every character of T is one of the complex exponentials 
+
+
+
+
+e
+
+n
+
+
+(
+x
+)
+=
+
+e
+
+2
+π
+i
+n
+x
+
+
+
+
+{\displaystyle e_{n}(x)=e^{2\pi inx}}
+
+.
+
+There is a unique character on T, up to complex conjugation, that is a group isomorphism.  Using the Haar measure on the circle group, the constant π is half the magnitude of the Radon–Nikodym derivative of this character.  The other characters have derivatives whose magnitudes are positive integral multiples of 2π.[18]  As a result, the constant π is the unique number such that the group T, equipped with its Haar measure, is Pontrjagin dual to the lattice of integral multiples of 2π.[187]   This is a version of the one-dimensional Poisson summation formula.
+
+The constant π is connected in a deep way with the theory of modular forms and theta functions.  For example, the Chudnovsky algorithm involves in an essential way the j-invariant of an elliptic curve.
+
+Modular forms are holomorphic functions in the upper half plane characterized by their transformation properties under the modular group 
+
+
+
+
+
+S
+L
+
+
+2
+
+
+(
+
+Z
+
+)
+
+
+{\displaystyle \mathrm {SL} _{2}(\mathbb {Z} )}
+
+ (or its various subgroups), a lattice in the group 
+
+
+
+
+
+S
+L
+
+
+2
+
+
+(
+
+R
+
+)
+
+
+{\displaystyle \mathrm {SL} _{2}(\mathbb {R} )}
+
+.  An example is the Jacobi theta function
+
+which is a kind of modular form called a Jacobi form.[188]  This is sometimes written in terms of the nome 
+
+
+
+q
+=
+
+e
+
+π
+i
+τ
+
+
+
+
+{\displaystyle q=e^{\pi i\tau }}
+
+.
+
+The constant π is the unique constant making the Jacobi theta function an automorphic form, which means that it transforms in a specific way.  Certain identities hold for all automorphic forms.  An example is
+
+which implies that θ transforms as a representation under the discrete Heisenberg group.  General modular forms and other theta functions also involve π, once again because of the Stone–von Neumann theorem.[188]
+
+The Cauchy distribution
+
+is a probability density function.  The total probability is equal to one, owing to the integral:
+
+The Shannon entropy of the Cauchy distribution is equal to ln(4π), which also involves π.
+
+The Cauchy distribution plays an important role in potential theory because it is the simplest Furstenberg measure, the classical Poisson kernel associated with a Brownian motion in a half-plane.[189] Conjugate harmonic functions and so also the Hilbert transform are associated with the asymptotics of the Poisson kernel. The Hilbert transform H is the integral transform given by the Cauchy principal value of the singular integral
+
+The constant π is the unique (positive) normalizing factor such that H defines a linear complex structure on the Hilbert space of square-integrable real-valued functions on the real line.[190]  The Hilbert transform, like the Fourier transform, can be characterized purely in terms of its transformation properties on the Hilbert space L2(R): up to a normalization factor, it is the unique bounded linear operator that commutes with positive dilations and anti-commutes with all reflections of the real line.[191]  The constant π is the unique normalizing factor that makes this transformation unitary.
+
+An occurrence of π in the Mandelbrot set fractal was discovered by David Boll in 1991.[192] He examined the behaviour of the Mandelbrot set near the "neck" at (−0.75, 0). If points with coordinates (−0.75, ε) are considered, as ε tends to zero, the number of iterations until divergence for the point multiplied by ε converges to π. The point (0.25 + ε, 0) at the cusp of the large "valley" on the right side of the Mandelbrot set behaves similarly: the number of iterations until divergence multiplied by the square root of ε tends to π.[192][193]
+
+Although not a physical constant, π appears routinely in equations describing fundamental principles of the universe, often because of π's relationship to the circle and to spherical coordinate systems. A simple formula from the field of classical mechanics gives the approximate period T of a simple pendulum of length L, swinging with a small amplitude (g is the earth's gravitational acceleration):[194]
+
+One of the key formulae of quantum mechanics is Heisenberg's uncertainty principle, which shows that the uncertainty in the measurement of a particle's position (Δx) and momentum (Δp) cannot both be arbitrarily small at the same time (where h is Planck's constant):[195]
+
+The fact that π is approximately equal to 3 plays a role in the relatively long lifetime of orthopositronium. The inverse lifetime to lowest order in the fine-structure constant α is[196]
+
+where m is the mass of the electron.
+
+π is present in some structural engineering formulae, such as the buckling formula derived by Euler, which gives the maximum axial load F that a long, slender column of length L, modulus of elasticity E, and area moment of inertia I can carry without buckling:[197]
+
+The field of fluid dynamics contains π in Stokes' law, which approximates the frictional force F exerted on small, spherical objects of radius R, moving with velocity v in a fluid with dynamic viscosity η:[198]
+
+In electromagnetics, the vacuum permeability constant μ0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation. Before 20 May 2019, it was defined as exactly
+
+A relation for the speed of light in vacuum, c can be derived from Maxwell's equations in the medium of classical vacuum using a relationship between μ0 and the electric constant (vacuum permittivity), ε0 in SI units:
+
+Under ideal conditions (uniform gentle slope on a homogeneously erodible substrate), the sinuosity of a meandering river approaches π. The sinuosity is the ratio between the actual length and the straight-line distance from source to mouth. Faster currents along the outside edges of a river's bends cause more erosion than along the inside edges, thus pushing the bends even farther out, and increasing the overall loopiness of the river. However, that loopiness eventually causes the river to double back on itself in places and "short-circuit", creating an ox-bow lake in the process. The balance between these two opposing factors leads to an average ratio of π between the actual length and the direct distance between source and mouth.[199][200]
+
+Piphilology is the practice of memorizing large numbers of digits of π,[201] and world-records are kept by the Guinness World Records.  The record for memorizing digits of π, certified by Guinness World Records, is 70,000 digits, recited in India by Rajveer Meena in 9 hours and 27 minutes on 21 March 2015.[202]  In 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places, but the claim was not verified by Guinness World Records.[203]
+
+One common technique is to memorize a story or poem in which the word lengths represent the digits of π: The first word has three letters, the second word has one, the third has four, the fourth has one, the fifth has five, and so on. Such memorization aids are called mnemonics. An early example of a mnemonic for pi, originally devised by English scientist James Jeans, is "How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics."[201] When a poem is used, it is sometimes referred to as a piem. Poems for memorizing π have been composed in several languages in addition to English.[201]  Record-setting π memorizers typically do not rely on poems, but instead use methods such as remembering number patterns and the method of loci.[204]
+
+A few authors have used the digits of π to establish a new form of constrained writing, where the word lengths are required to represent the digits of π. The Cadaeic Cadenza contains the first 3835 digits of π in this manner,[205] and the full-length book Not a Wake contains 10,000 words, each representing one digit of π.[206]
+
+Perhaps because of the simplicity of its definition and its ubiquitous presence in formulae, π has been represented in popular culture more than other mathematical constructs.[207]
+
+In the 2008 Open University and BBC documentary co-production, The Story of Maths, aired in October 2008 on BBC Four, British mathematician Marcus du Sautoy shows a visualization of the – historically first exact – formula for calculating π when visiting India and exploring its contributions to trigonometry.[208]
+
+In the Palais de la Découverte (a science museum in Paris) there is a circular room known as the pi room. On its wall are inscribed 707 digits of π. The digits are large wooden characters attached to the dome-like ceiling. The digits were based on an 1853 calculation by English mathematician William Shanks, which included an error beginning at the 528th digit. The error was detected in 1946 and corrected in 1949.[209]
+
+In Carl Sagan's novel Contact it is suggested that the creator of the universe buried a message deep within the digits of π.[210] The digits of π have also been incorporated into the lyrics of the song "Pi" from the album Aerial by Kate Bush.[211]
+
+In the United States, Pi Day falls on 14 March (written 3/14 in the US style), and is popular among students.[212] π and its digital representation are often used by self-described "math geeks" for inside jokes among mathematically and technologically minded groups. Several college cheers at the Massachusetts Institute of Technology include "3.14159".[213] Pi Day in 2015 was particularly significant because the date and time 3/14/15 9:26:53 reflected many more digits of pi.[214] In parts of the world where dates are commonly noted in day/month/year format, 22 July represents "Pi Approximation Day," as 22/7 = 3.142857.[215]
+
+During the 2011 auction for Nortel's portfolio of valuable technology patents, Google made a series of unusually specific bids based on mathematical and scientific constants, including π.[216]
+
+In 1958 Albert Eagle proposed replacing π by τ (tau), where τ = π/2, to simplify formulas.[217] However, no other authors are known to use τ in this way. Some people use a different value, τ = 2π = 6.28318...,[218] arguing that τ, as the number of radians in one turn, or as the ratio of a circle's circumference to its radius rather than its diameter, is more natural than π and simplifies many formulas.[219][220] Celebrations of this number, because it approximately equals 6.28, by making 28 June "Tau Day" and eating "twice the pie",[221] have been reported in the media. However, this use of τ has not made its way into mainstream mathematics.[222]
+
+In 1897, an amateur mathematician attempted to persuade the Indiana legislature to pass the Indiana Pi Bill, which described a method to square the circle and contained text that implied various incorrect values for π, including 3.2. The bill is notorious as an attempt to establish a value of scientific constant by legislative fiat. The bill was passed by the Indiana House of Representatives, but rejected by the Senate, meaning it did not become a law.[223]
+
+In contemporary internet culture, individuals and organizations frequently pay homage to the number π. For instance, the computer scientist Donald Knuth let the version numbers of his program TeX approach π. The versions are 3, 3.1, 3.14, and so forth.[224]
+

en/4159.html.txt

@@ -0,0 +1,2916 @@
+
+
+
+
+A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
+However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
+
+The property of being prime is called primality. A simple but slow method of checking the primality of a given number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+, called trial division, tests whether 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is a multiple of any integer between 2 and 
+
+
+
+
+
+n
+
+
+
+
+{\displaystyle {\sqrt {n}}}
+
+. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018[update] the largest known prime number has 24,862,048 decimal digits.
+
+There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm.
+
+Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.
+
+A natural number (1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it is greater than 1 and cannot be written as the product of two smaller natural numbers. The numbers greater than 1 that are not prime are called composite numbers.[1] In other words, 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime if 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ items cannot be divided up into smaller equal-size groups of more than one item,[2] or if it is not possible to arrange 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ dots into a rectangular grid that is more than one dot wide and more than one dot high.[3]
+For example, among the numbers 1 through 6, the numbers 2, 3, and 5 are the prime numbers,[4] as there are no other numbers that divide them evenly (without a remainder).
+1 is not prime, as it is specifically excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite.
+
+The divisors of a natural number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ are the natural numbers that divide 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ evenly.
+Every natural number has both 1 and itself as a divisor. If it has any other divisor, it cannot be prime. This idea leads to a different but equivalent definition of the primes: they are the numbers with exactly two positive divisors, 1 and the number itself.[5]
+Yet another way to express the same thing is that a number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime if it is greater than one and if none of the numbers 
+
+
+
+2
+,
+3
+,
+…
+,
+n
+−
+1
+
+
+{\displaystyle 2,3,\dots ,n-1}
+
+ divides 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ evenly.[6]
+
+The first 25 prime numbers (all the prime numbers less than 100) are:[7]
+
+No even number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ greater than 2 is prime because any such number can be expressed as the product 
+
+
+
+2
+×
+n
+
+/
+
+2
+
+
+{\displaystyle 2\times n/2}
+
+. Therefore, every prime number other than 2 is an odd number, and is called an odd prime.[8] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite:
+decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in 0 or 5 are divisible by 5.[9]
+
+The set of all primes is sometimes denoted by 
+
+
+
+
+P
+
+
+
+{\displaystyle \mathbf {P} }
+
+ (a boldface capital P)[10] or by 
+
+
+
+
+P
+
+
+
+{\displaystyle \mathbb {P} }
+
+ (a blackboard bold capital P).[11]
+
+The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptian fraction expansions of different forms for prime and composite numbers.[12] However, the earliest surviving records of the explicit study of prime numbers come from ancient Greek mathematics. Euclid's Elements (c. 300 BC) proves the infinitude of primes and the fundamental theorem of arithmetic, and shows how to construct a perfect number from a Mersenne prime.[13] Another Greek invention, the Sieve of Eratosthenes, is still used to construct lists of primes.[14][15]
+
+Around 1000 AD, the Islamic mathematician Ibn al-Haytham (Alhazen) found Wilson's theorem, characterizing the prime numbers as the numbers 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ that evenly divide 
+
+
+
+(
+n
+−
+1
+)
+!
++
+1
+
+
+{\displaystyle (n-1)!+1}
+
+. He also conjectured that all even perfect numbers come from Euclid's construction using Mersenne primes, but was unable to prove it.[16] Another Islamic mathematician, Ibn al-Banna' al-Marrakushi, observed that the sieve of Eratosthenes can be sped up by testing only the divisors up to the square root of the largest number to be tested. Fibonacci brought the innovations from Islamic mathematics back to Europe. His book Liber Abaci (1202) was the first to describe trial division for testing primality, again using divisors only up to the square root.[15]
+
+In 1640 Pierre de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler).[17] Fermat also investigated the primality of the Fermat numbers
+
+
+
+
+
+2
+
+
+2
+
+n
+
+
+
+
++
+1
+
+
+{\displaystyle 2^{2^{n}}+1}
+
+,[18] and Marin Mersenne studied the Mersenne primes, prime numbers of the form 
+
+
+
+
+2
+
+p
+
+
+−
+1
+
+
+{\displaystyle 2^{p}-1}
+
+ with 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ itself a prime.[19] Christian Goldbach formulated Goldbach's conjecture, that every even number is the sum of two primes, in a 1742 letter to Euler.[20] Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be constructed from Mersenne primes.[13] He introduced methods from mathematical analysis to this area in his proofs of the infinitude of the primes and the divergence of the sum of the reciprocals of the primes 
+
+
+
+
+
+
+1
+2
+
+
+
++
+
+
+
+1
+3
+
+
+
++
+
+
+
+1
+5
+
+
+
++
+
+
+
+1
+7
+
+
+
++
+
+
+
+1
+11
+
+
+
++
+⋯
+
+
+{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+\cdots }
+
+.[21]
+At the start of the 19th century, Legendre and Gauss conjectured that as 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ tends to infinity, the number of primes up to 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ is asymptotic to 
+
+
+
+x
+
+/
+
+log
+⁡
+x
+
+
+{\displaystyle x/\log x}
+
+, where 
+
+
+
+log
+⁡
+x
+
+
+{\displaystyle \log x}
+
+ is the natural logarithm of 
+
+
+
+x
+
+
+{\displaystyle x}
+
+.   Ideas of Bernhard Riemann in his 1859 paper on the zeta-function sketched an outline for proving this. Although the closely related Riemann hypothesis remains unproven, Riemann's outline was completed in 1896 by Hadamard and de la Vallée Poussin, and the result is now known as the prime number theorem.[22] Another important 19th century result was Dirichlet's theorem on arithmetic progressions, that certain arithmetic progressions contain infinitely many primes.[23]
+
+Many mathematicians have worked on primality tests for numbers larger than those where trial division is practicably applicable. Methods that are restricted to specific number forms include Pépin's test for Fermat numbers (1877),[24] Proth's theorem (c. 1878),[25] the Lucas–Lehmer primality test (originated 1856), and the generalized Lucas primality test.[15]
+
+Since 1951 all the largest known primes have been found using these tests on computers.[a] The search for ever larger primes has generated interest outside mathematical circles, through the Great Internet Mersenne Prime Search and other distributed computing projects.[7][27] The idea that prime numbers had few applications outside of pure mathematics[b] was shattered in the 1970s when public-key cryptography and the RSA cryptosystem were invented, using prime numbers as their basis.[30]
+
+The increased practical importance of computerized primality testing and factorization led to the development of improved methods capable of handling large numbers of unrestricted form.[14][31][32] The mathematical theory of prime numbers also moved forward with the Green–Tao theorem (2004) that there are arbitrarily long arithmetic progressions of prime numbers, and Yitang Zhang's 2013 proof that there exist infinitely many prime gaps of bounded size.[33]
+
+Most early Greeks did not even consider 1 to be a number,[34][35] so they could not consider its primality. A few mathematicians from this time also considered the prime numbers to be a subdivision of the odd numbers, so they also did not consider 2 to be prime. However, Euclid and a majority of the other Greek mathematicians considered 2 as prime. The medieval Islamic mathematicians largely followed the Greeks in viewing 1 as not being a number.[34]
+By the Middle Ages and Renaissance mathematicians began treating 1 as a number, and some of them included it as the first prime number.[36] In the mid-18th century Christian Goldbach listed 1 as prime in his correspondence with Leonhard Euler; however, Euler himself did not consider 1 to be prime.[37] In the 19th century many mathematicians still considered 1 to be prime,[38] and lists of primes that included 1 continued to be published as recently as 1956.[39][40]
+
+If the definition of a prime number were changed to call 1 a prime, many statements involving prime numbers would need to be reworded in a more awkward way. For example, the fundamental theorem of arithmetic would need to be rephrased in terms of factorizations into primes greater than 1, because every number would have multiple factorizations with different numbers of copies of 1.[38] Similarly, the sieve of Eratosthenes would not work correctly if it handled 1 as a prime, because it would eliminate all multiples of 1 (that is, all other numbers) and output only the single number 1.[40] Some other more technical properties of prime numbers also do not hold for the number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1.[41] By the early 20th century, mathematicians began to agree that 1 should not be listed as prime, but rather in its own special category as a "unit".[38]
+
+Writing a number as a product of prime numbers is called a prime factorization of the number. For example:
+
+The terms in the product are called prime factors. The same prime factor may occur more than once; this example has two copies of the prime factor 
+
+
+
+3.
+
+
+{\displaystyle 3.}
+
+  When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 
+
+
+
+
+3
+
+2
+
+
+
+
+{\displaystyle 3^{2}}
+
+ denotes the square or second power of 
+
+
+
+3.
+
+
+{\displaystyle 3.}
+
+The central importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic.[42] This theorem states that every integer larger than 1 can be written as a product of one or more primes. More strongly,
+this product is unique in the sense that any two prime factorizations of the same number will have the same numbers of copies of the same primes,
+although their ordering may differ.[43]  So, although there are many different ways of finding a factorization using an integer factorization algorithm, they all must produce the same result. Primes can thus be considered the "basic building blocks" of the natural numbers.[44]
+
+Some proofs of the uniqueness of prime factorizations are based on Euclid's lemma: If 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is a prime number and 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides a product 
+
+
+
+a
+b
+
+
+{\displaystyle ab}
+
+ of integers 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+,
+
+
+{\displaystyle b,}
+
+ then 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ or 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ (or both).[45] Conversely, if a number 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ has the property that when it divides a product it always divides at least one factor of the product, then 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ must be prime.[46]
+
+There are infinitely many prime numbers. Another way of saying this is that the sequence
+
+of prime numbers never ends. This statement is referred to as Euclid's theorem in honor of the ancient Greek mathematician Euclid, since the first known proof for this statement is attributed to him. Many more proofs of the infinitude of primes are known, including an analytical proof by Euler, Goldbach's proof based on  Fermat numbers,[47] Furstenberg's proof using general topology,[48] and Kummer's elegant proof.[49]
+
+Euclid's proof[50] shows that every finite list of primes is incomplete. The key idea is to multiply together the primes in any given list and add 
+
+
+
+1.
+
+
+{\displaystyle 1.}
+
+ If the list consists of the primes 
+
+
+
+
+p
+
+1
+
+
+,
+
+p
+
+2
+
+
+,
+…
+,
+
+p
+
+n
+
+
+,
+
+
+{\displaystyle p_{1},p_{2},\ldots ,p_{n},}
+
+ this gives the number
+
+By the fundamental theorem, 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ has a prime factorization
+
+with one or more prime factors. 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ is evenly divisible by each of these factors, but 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ has a remainder of one when divided by any of the prime numbers in the given list, so none of the prime factors of 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ can be in the given list. Because there is no finite list of all the primes, there must be infinitely many primes.
+
+The numbers formed by adding one to the products of the smallest primes are called Euclid numbers.[51] The first five of them are prime, but the sixth,
+
+is a composite number.
+
+There is no known efficient formula for primes.  For example, there is no non-constant polynomial, even in several variables, that takes only prime values.[52]  However, there are numerous expressions that do encode all primes, or only primes. One possible formula is based on Wilson's theorem and generates the number 2 many times and all other primes exactly once.[53]  There is also a set of Diophantine equations in nine variables and one parameter with the following property: the parameter is prime if and only if the resulting system of equations has a solution over the natural numbers. This can be used to obtain a single formula with the property that all its positive values are prime.[52]
+
+Other examples of prime-generating formulas come from Mills' theorem and a theorem of Wright.  These assert that there are real constants 
+
+
+
+A
+>
+1
+
+
+{\displaystyle A>1}
+
+ and 
+
+
+
+μ
+
+
+{\displaystyle \mu }
+
+ such that
+
+are prime for any natural number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ in the first formula, and any number of exponents in the second formula.[54] Here 
+
+
+
+⌊
+
+
+⋅
+
+
+⌋
+
+
+{\displaystyle \lfloor {}\cdot {}\rfloor }
+
+ represents the floor function, the largest integer less than or equal to the number in question. However, these are not useful for generating primes, as the primes must be generated first in order to compute the values of 
+
+
+
+A
+
+
+{\displaystyle A}
+
+ or 
+
+
+
+μ
+.
+
+
+{\displaystyle \mu .}
+
+[52]
+
+Many  conjectures revolving about primes have been posed. Often having an elementary formulation, many of these conjectures have withstood proof for decades: all four of Landau's problems from 1912 are still unsolved.[55] One of them is Goldbach's conjecture, which asserts that every even integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ greater than 2 can be written as a sum of two primes.[56] As of 2014[update], this conjecture has been verified for all numbers up to 
+
+
+
+n
+=
+4
+⋅
+
+10
+
+18
+
+
+.
+
+
+{\displaystyle n=4\cdot 10^{18}.}
+
+[57] Weaker statements than this have been proven, for example, Vinogradov's theorem says that every sufficiently large odd integer can be written as a sum of three primes.[58] Chen's theorem says that every sufficiently large even number can be expressed as the sum of a prime and a semiprime (the product of two primes).[59] Also, any even integer greater than 10 can be written as the sum of six primes.[60] The branch of number theory studying such questions is called additive number theory.[61]
+
+Another type of problem concerns prime gaps, the differences between consecutive primes.
+The existence of arbitrarily large prime gaps can be seen by noting that the sequence 
+
+
+
+n
+!
++
+2
+,
+n
+!
++
+3
+,
+…
+,
+n
+!
++
+n
+
+
+{\displaystyle n!+2,n!+3,\dots ,n!+n}
+
+ consists of 
+
+
+
+n
+−
+1
+
+
+{\displaystyle n-1}
+
+ composite numbers, for any natural number 
+
+
+
+n
+.
+
+
+{\displaystyle n.}
+
+[62] However, large prime gaps occur much earlier than this argument shows.[63] For example, the first prime gap of length 8 is between the primes 89 and 97,[64] much smaller than 
+
+
+
+8
+!
+=
+40320.
+
+
+{\displaystyle 8!=40320.}
+
+ It is conjectured that there are infinitely many twin primes, pairs of primes with difference 2; this is the twin prime conjecture. Polignac's conjecture states more generally that for every positive integer 
+
+
+
+k
+,
+
+
+{\displaystyle k,}
+
+ there are infinitely many pairs of consecutive primes that differ by 
+
+
+
+2
+k
+.
+
+
+{\displaystyle 2k.}
+
+[65]
+Andrica's conjecture,[65] Brocard's conjecture,[66] Legendre's conjecture,[67] and Oppermann's conjecture[66] all suggest that the largest gaps between primes from 
+
+
+
+1
+
+
+{\displaystyle 1}
+
+ to 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ should be at most approximately 
+
+
+
+
+
+n
+
+
+,
+
+
+{\displaystyle {\sqrt {n}},}
+
+ a result that is known to follow from the Riemann hypothesis, while the much stronger Cramér conjecture sets the largest gap size at 
+
+
+
+O
+(
+(
+log
+⁡
+n
+
+)
+
+2
+
+
+)
+.
+
+
+{\displaystyle O((\log n)^{2}).}
+
+[65]  Prime gaps can be generalized to prime 
+
+
+
+k
+
+
+{\displaystyle k}
+
+-tuples, patterns in the differences between more than two prime numbers. Their infinitude and density are the subject of the first Hardy–Littlewood conjecture, which can be motivated by the heuristic that the prime numbers behave similarly to a random sequence of numbers with density given by the prime number theorem.[68]
+
+Analytic number theory studies number theory through the lens of continuous functions, limits, infinite series, and the related mathematics of the infinite and infinitesimal.
+
+This area of study began with Leonhard Euler and his first major result, the solution to the Basel problem.
+The problem asked for the value of the infinite sum 
+
+
+
+1
++
+
+
+
+1
+4
+
+
+
++
+
+
+
+1
+9
+
+
+
++
+
+
+
+1
+16
+
+
+
++
+…
+,
+
+
+{\displaystyle 1+{\tfrac {1}{4}}+{\tfrac {1}{9}}+{\tfrac {1}{16}}+\dots ,}
+
+
+which today can be recognized as the value 
+
+
+
+ζ
+(
+2
+)
+
+
+{\displaystyle \zeta (2)}
+
+ of the Riemann zeta function. This function is closely connected to the prime numbers and to one of the most significant unsolved problems in mathematics, the Riemann hypothesis. Euler showed that 
+
+
+
+ζ
+(
+2
+)
+=
+
+π
+
+2
+
+
+
+/
+
+6
+
+
+{\displaystyle \zeta (2)=\pi ^{2}/6}
+
+.[69]
+The reciprocal of this number, 
+
+
+
+6
+
+/
+
+
+π
+
+2
+
+
+
+
+{\displaystyle 6/\pi ^{2}}
+
+, is the limiting probability that two random numbers selected uniformly from a large range are relatively prime (have no factors in common).[70]
+
+The distribution of primes in the large, such as the question how many primes are smaller than a given, large threshold, is described by the prime number theorem, but no efficient formula for the 
+
+
+
+n
+
+
+{\displaystyle n}
+
+-th prime is known.
+Dirichlet's theorem on arithmetic progressions, in its basic form, asserts that linear polynomials
+
+with relatively prime integers 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ take infinitely many prime values. Stronger forms of the theorem state that the sum of the reciprocals of these prime values diverges, and that different linear polynomials with the same 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ have approximately the same proportions of primes.
+Although conjectures have been formulated about the proportions of primes in higher-degree polynomials, they remain unproven, and it is unknown whether there exists a quadratic polynomial that (for integer arguments) is prime infinitely often.
+
+Euler's proof that there are infinitely many primes considers the sums of reciprocals of primes,
+
+Euler showed that, for any arbitrary real number 
+
+
+
+x
+
+
+{\displaystyle x}
+
+, there exists a prime 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ for which this sum is bigger than 
+
+
+
+x
+
+
+{\displaystyle x}
+
+.[71] This shows that there are infinitely many primes, because if there were finitely many primes the sum would reach its maximum value at the biggest prime rather than growing past every 
+
+
+
+x
+
+
+{\displaystyle x}
+
+.
+The growth rate of this sum is described more precisely by Mertens' second theorem.[72] For comparison, the sum
+
+does not grow to infinity as 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ goes to infinity (see the Basel problem). In this sense, prime numbers occur more often than squares of natural numbers,
+although both sets are infinite.[73] Brun's theorem states that the sum of the reciprocals of twin primes,
+
+is finite. Because of Brun's theorem, it is not possible to use Euler's method to solve the twin prime conjecture, that there exist infinitely many twin primes.[73]
+
+The prime counting function 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ is defined as the number of primes not greater than 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[74] For example, 
+
+
+
+π
+(
+11
+)
+=
+5
+
+
+{\displaystyle \pi (11)=5}
+
+, since there are five primes less than or equal to 11. Methods such as the Meissel–Lehmer algorithm can compute exact values of 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ faster than it would be possible to list each prime up to 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[75] The prime number theorem states that 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ is asymptotic to 
+
+
+
+n
+
+/
+
+log
+⁡
+n
+
+
+{\displaystyle n/\log n}
+
+, which is denoted as
+
+and means that the ratio of 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ to the right-hand fraction approaches 1 as 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ grows to infinity.[76] This implies that the likelihood that a randomly chosen number less than 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime is (approximately) inversely proportional to the number of digits in 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[77]
+It also implies that the 
+
+
+
+n
+
+
+{\displaystyle n}
+
+th prime number is proportional to 
+
+
+
+n
+log
+⁡
+n
+
+
+{\displaystyle n\log n}
+
+[78]
+and therefore that the average size of a prime gap is proportional to 
+
+
+
+log
+⁡
+n
+
+
+{\displaystyle \log n}
+
+.[63]
+A more accurate estimate for 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ is given by the offset logarithmic integral[76]
+
+An arithmetic progression is a finite or infinite sequence of numbers such that consecutive numbers in the sequence all have the same difference.[79] This difference is called the modulus of the progression.[80] For example,
+
+is an infinite arithmetic progression with modulus 9. In an arithmetic progression, all the numbers have the same remainder when divided by the modulus; in this example, the remainder is 3. Because both the modulus 9 and the remainder 3 are multiples of 3, so is every element in the sequence. Therefore, this progression contains only one prime number, 3 itself. In general, the infinite progression
+
+can have more than one prime only when its remainder 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and modulus 
+
+
+
+q
+
+
+{\displaystyle q}
+
+ are relatively prime. If they are relatively prime, Dirichlet's theorem on arithmetic progressions asserts that the progression contains infinitely many primes.[81]
+
+The Green–Tao theorem shows that there are arbitrarily long finite arithmetic progressions consisting only of primes.[33][82]
+
+Euler noted that the function
+
+yields prime numbers for 
+
+
+
+1
+≤
+n
+≤
+40
+
+
+{\displaystyle 1\leq n\leq 40}
+
+, although composite numbers appear among its later values.[83][84] The search for an explanation for this phenomenon led to the deep algebraic number theory of Heegner numbers and the class number problem.[85] The Hardy-Littlewood conjecture F predicts the density of primes among the values of quadratic polynomials with integer coefficients
+in terms of the logarithmic integral and the polynomial coefficients. No quadratic polynomial has been proven to take infinitely many prime values.[86]
+
+The Ulam spiral arranges the natural numbers in a two-dimensional grid, spiraling in concentric squares surrounding the origin with the prime numbers highlighted. Visually, the primes appear to cluster on certain diagonals and not others, suggesting that some quadratic polynomials take prime values more often than others.[86]
+
+One of the most famous unsolved questions in mathematics, dating from 1859, and one of the Millennium Prize Problems, is the Riemann hypothesis, which asks where the zeros of the Riemann zeta function 
+
+
+
+ζ
+(
+s
+)
+
+
+{\displaystyle \zeta (s)}
+
+ are located.
+This function is an analytic function on the complex numbers. For complex numbers 
+
+
+
+s
+
+
+{\displaystyle s}
+
+ with real part greater than one it equals both an infinite sum over all integers, and an infinite product over the prime numbers,
+
+This equality between a sum and a product, discovered by Euler, is called an Euler product.[87] The Euler product can be derived from the fundamental theorem of arithmetic, and shows the close connection between the zeta function and the prime numbers.[88]
+It leads to another proof that there are infinitely many primes: if there were only finitely many,
+then the sum-product equality would also be valid at 
+
+
+
+s
+=
+1
+
+
+{\displaystyle s=1}
+
+, but the sum would diverge (it is the harmonic series 
+
+
+
+1
++
+
+
+
+1
+2
+
+
+
++
+
+
+
+1
+3
+
+
+
++
+…
+
+
+{\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{3}}+\dots }
+
+) while the product would be finite, a contradiction.[89]
+
+The Riemann hypothesis states that the zeros of the zeta-function are all either negative even numbers, or complex numbers with real part equal to 1/2.[90]  The original proof of the prime number theorem was based on a weak form of this hypothesis, that there are no zeros with real part equal to 1,[91][92] although other more elementary proofs have been found.[93]
+The prime-counting function can be expressed by Riemann's explicit formula as a sum in which each term comes from one of the zeros of the zeta function; the main term of this sum is the logarithmic integral, and the remaining terms cause the sum to fluctuate above and below the main term.[94]
+In this sense, the zeros control how regularly the prime numbers are distributed. If the Riemann hypothesis is true, these fluctuations will be small, and the
+asymptotic distribution of primes given by the prime number theorem will also hold over much shorter intervals (of length about the square root of 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ for intervals near a number 
+
+
+
+x
+
+
+{\displaystyle x}
+
+).[92]
+
+Modular arithmetic modifies usual arithmetic by only using the numbers 
+
+
+
+{
+0
+,
+1
+,
+2
+,
+…
+,
+n
+−
+1
+}
+
+
+{\displaystyle \{0,1,2,\dots ,n-1\}}
+
+, for a natural number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ called the modulus.
+Any other natural number can be mapped into this system by replacing it by its remainder after division by 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[95]
+Modular sums, differences and products are calculated by performing the same replacement by the remainder
+on the result of the usual sum, difference, or product of integers.[96] Equality of integers corresponds to congruence in modular arithmetic:
+
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+ are congruent (written 
+
+
+
+x
+≡
+y
+
+
+{\displaystyle x\equiv y}
+
+ mod 
+
+
+
+n
+
+
+{\displaystyle n}
+
+) when they have the same remainder after division by 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[97] However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number 
+
+
+
+7
+
+
+{\displaystyle 7}
+
+ as modulus, division by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ is possible: 
+
+
+
+2
+
+/
+
+3
+≡
+3
+
+mod
+
+7
+
+
+
+
+{\displaystyle 2/3\equiv 3{\bmod {7}}}
+
+, because clearing denominators by multiplying both sides by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ gives the  valid formula 
+
+
+
+2
+≡
+9
+
+mod
+
+7
+
+
+
+
+{\displaystyle 2\equiv 9{\bmod {7}}}
+
+. However, with the composite modulus 
+
+
+
+6
+
+
+{\displaystyle 6}
+
+, division by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ is impossible. There is no valid solution to 
+
+
+
+2
+
+/
+
+3
+≡
+x
+
+mod
+
+6
+
+
+
+
+{\displaystyle 2/3\equiv x{\bmod {6}}}
+
+: clearing denominators by multiplying by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ causes the left-hand side to become 
+
+
+
+2
+
+
+{\displaystyle 2}
+
+ while the right-hand side becomes either 
+
+
+
+0
+
+
+{\displaystyle 0}
+
+ or 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+.
+In the terminology of abstract algebra, the ability to perform division means that modular arithmetic modulo a prime number forms a field or, more specifically, a finite field, while other moduli only give a ring but not a field.[98]
+
+Several theorems about primes can be formulated using modular arithmetic. For instance, Fermat's little theorem states that if
+
+
+
+
+a
+≢
+0
+
+
+{\displaystyle a\not \equiv 0}
+
+ (mod 
+
+
+
+p
+
+
+{\displaystyle p}
+
+), then 
+
+
+
+
+a
+
+p
+−
+1
+
+
+≡
+1
+
+
+{\displaystyle a^{p-1}\equiv 1}
+
+ (mod 
+
+
+
+p
+
+
+{\displaystyle p}
+
+).[99]
+Summing this over all choices of 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ gives the equation
+
+valid whenever 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is prime.
+Giuga's conjecture says that this equation is also a sufficient condition for 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ to be prime.[100]
+Wilson's theorem says that an integer 
+
+
+
+p
+>
+1
+
+
+{\displaystyle p>1}
+
+ is prime if and only if the factorial 
+
+
+
+(
+p
+−
+1
+)
+!
+
+
+{\displaystyle (p-1)!}
+
+ is congruent to 
+
+
+
+−
+1
+
+
+{\displaystyle -1}
+
+ mod 
+
+
+
+p
+
+
+{\displaystyle p}
+
+. For a composite number 
+
+
+
+
+n
+=
+r
+⋅
+s
+
+
+
+{\displaystyle \;n=r\cdot s\;}
+
+ this cannot hold, since one of its factors divides both n and 
+
+
+
+(
+n
+−
+1
+)
+!
+
+
+{\displaystyle (n-1)!}
+
+, and so 
+
+
+
+(
+n
+−
+1
+)
+!
+≡
+−
+1
+
+
+(
+mod
+
+n
+)
+
+
+
+{\displaystyle (n-1)!\equiv -1{\pmod {n}}}
+
+ is impossible.[101]
+
+The 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic order 
+
+
+
+
+ν
+
+p
+
+
+(
+n
+)
+
+
+{\displaystyle \nu _{p}(n)}
+
+ of an integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is the number of copies of 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ in the prime factorization of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. The same concept can be extended from integers to rational numbers by defining the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic order of a fraction 
+
+
+
+m
+
+/
+
+n
+
+
+{\displaystyle m/n}
+
+ to be 
+
+
+
+
+ν
+
+p
+
+
+(
+m
+)
+−
+
+ν
+
+p
+
+
+(
+n
+)
+
+
+{\displaystyle \nu _{p}(m)-\nu _{p}(n)}
+
+. The 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic absolute value 
+
+
+
+
+|
+
+q
+
+
+|
+
+
+p
+
+
+
+
+{\displaystyle |q|_{p}}
+
+ of any rational number 
+
+
+
+q
+
+
+{\displaystyle q}
+
+ is then defined as
+
+
+
+
+
+|
+
+q
+
+
+|
+
+
+p
+
+
+=
+
+p
+
+−
+
+ν
+
+p
+
+
+(
+q
+)
+
+
+
+
+{\displaystyle |q|_{p}=p^{-\nu _{p}(q)}}
+
+. Multiplying an integer by its 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic absolute value cancels out the factors of 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ in its factorization, leaving only the other primes. Just as the distance between two real numbers can be measured by the absolute value of their distance, the distance between two rational numbers can be measured by their 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic distance, the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic absolute value of their difference. For this definition of distance, two numbers are close together (they have a small distance) when their difference is divisible by a high power of 
+
+
+
+p
+
+
+{\displaystyle p}
+
+. In the same way that the real numbers can be formed from the rational numbers and their distances, by adding extra limiting values to form a complete field, the rational numbers with the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic distance can be extended to a different complete field, the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic numbers.[102][103]
+
+This picture of an order, absolute value, and complete field derived from them can be generalized to algebraic number fields and their valuations (certain mappings from the multiplicative group of the field to a totally ordered additive group, also called orders), absolute values (certain multiplicative mappings from the field to the real numbers, also called norms),[102] and places (extensions to complete fields in which the given field is a dense set, also called completions).[104] The extension from the rational numbers to the real numbers, for instance, is a place in which the distance between numbers is the usual absolute value of their difference. The corresponding mapping to an additive group would be the logarithm of the absolute value, although this does not meet all the requirements of a valuation. According to Ostrowski's theorem, up to a natural notion of equivalence, the real numbers and 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic numbers, with their orders and absolute values, are the only valuations, absolute values, and places on the rational numbers.[102] The local-global principle allows certain problems over the rational numbers to be solved by piecing together solutions from each of their places, again underlining the importance of primes to number theory.[105]
+
+A commutative ring is an algebraic structure where addition, subtraction and multiplication are defined. The integers are a ring, and the prime numbers in the integers have been generalized to rings in two different ways, prime elements and irreducible elements. An element 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ of a ring 
+
+
+
+R
+
+
+{\displaystyle R}
+
+ is called prime if it is nonzero, has no multiplicative inverse (that is, it is not a unit), and satisfies the following requirement: whenever 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides the product 
+
+
+
+x
+y
+
+
+{\displaystyle xy}
+
+ of two elements of 
+
+
+
+R
+
+
+{\displaystyle R}
+
+, it also divides at least one of 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ or 
+
+
+
+y
+
+
+{\displaystyle y}
+
+. An element is irreducible if it is neither a unit nor the product of two other non-unit elements. In the ring of integers, the prime and irreducible elements form the same set,
+
+In an arbitrary ring, all prime elements are irreducible. The converse does not hold in general, but does hold for unique factorization domains.[106]
+
+The fundamental theorem of arithmetic continues to hold (by definition) in unique factorization domains. An example of such a domain is the Gaussian integers 
+
+
+
+
+Z
+
+[
+i
+]
+
+
+{\displaystyle \mathbb {Z} [i]}
+
+, the ring of complex numbers of the form 
+
+
+
+a
++
+b
+i
+
+
+{\displaystyle a+bi}
+
+ where 
+
+
+
+i
+
+
+{\displaystyle i}
+
+ denotes the imaginary unit and 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ are arbitrary integers. Its prime elements are known as Gaussian primes. Not every number that is prime among the integers remains prime in the Gaussian integers; for instance, the number 2 can be written as a product of the two Gaussian primes 
+
+
+
+1
++
+i
+
+
+{\displaystyle 1+i}
+
+ and 
+
+
+
+1
+−
+i
+
+
+{\displaystyle 1-i}
+
+. Rational primes (the prime elements in the integers) congruent to 3 mod 4 are Gaussian primes, but rational primes congruent to 1 mod 4 are not.[107] This is a consequence of Fermat's theorem on sums of two squares,
+which states that an odd prime 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is expressible as the sum of two squares, 
+
+
+
+p
+=
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+{\displaystyle p=x^{2}+y^{2}}
+
+, and therefore factorizable as 
+
+
+
+p
+=
+(
+x
++
+i
+y
+)
+(
+x
+−
+i
+y
+)
+
+
+{\displaystyle p=(x+iy)(x-iy)}
+
+, exactly when 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is 1 mod 4.[108]
+
+Not every ring is a unique factorization domain. For instance, in the ring of numbers 
+
+
+
+a
++
+b
+
+
+−
+5
+
+
+
+
+{\displaystyle a+b{\sqrt {-5}}}
+
+ (for integers 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+) the number 
+
+
+
+21
+
+
+{\displaystyle 21}
+
+ has two factorizations 
+
+
+
+21
+=
+3
+⋅
+7
+=
+(
+1
++
+2
+
+
+−
+5
+
+
+)
+(
+1
+−
+2
+
+
+−
+5
+
+
+)
+
+
+{\displaystyle 21=3\cdot 7=(1+2{\sqrt {-5}})(1-2{\sqrt {-5}})}
+
+, where neither of the four factors can be reduced any further, so it does not have a unique factorization. In order to extend unique factorization to a larger class of rings, the notion of a number can be replaced with that of an ideal, a subset of the elements of a ring that contains all sums of pairs of its elements, and all products of its elements with ring elements.
+Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), ... The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.[109]
+
+The spectrum of a ring is a geometric space whose points are the prime ideals of the ring.[110] Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. These concepts can even assist with in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the existence of square roots modulo integer prime numbers.[111]
+Early attempts to prove Fermat's Last Theorem led to Kummer's introduction of regular primes, integer prime numbers connected with the failure of unique factorization in the cyclotomic integers.[112]
+The question of how many integer prime numbers factor into a product of multiple prime ideals in an algebraic number field is addressed by Chebotarev's density theorem, which (when applied to the cyclotomic integers) has Dirichlet's theorem on primes in arithmetic progressions as a special case.[113]
+
+In the theory of finite groups the Sylow theorems imply that, if a power of a prime number 
+
+
+
+
+p
+
+n
+
+
+
+
+{\displaystyle p^{n}}
+
+ divides the order of a group, then it has a subgroup of order 
+
+
+
+
+p
+
+n
+
+
+
+
+{\displaystyle p^{n}}
+
+. By Lagrange's theorem, any group of prime order is a cyclic group,
+and by Burnside's theorem any group whose order is divisible by only two primes is solvable.[114]
+
+For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of mathematics[b] other than the use of prime numbered gear teeth to distribute wear evenly.[115] In particular, number theorists such as British mathematician G. H. Hardy prided themselves on doing work that had absolutely no military significance.[116]
+
+This vision of the purity of number theory was shattered in the 1970s, when it was publicly announced that prime numbers could be used as the basis for the creation of public key cryptography algorithms.[30]
+These applications have led to significant study of algorithms for computing with prime numbers, and in particular of primality testing, methods for determining whether a given number is prime.
+The most basic primality testing routine, trial division, is too slow to be useful for large numbers. One group of modern primality tests is applicable to arbitrary numbers, while more efficient tests are available for numbers of special types. Most primality tests only tell whether their argument is prime or not. Routines that also provide a prime factor of composite arguments (or all of its prime factors) are called factorization algorithms.
+Prime numbers are also used in computing for checksums, hash tables, and pseudorandom number generators.
+
+The most basic method of checking the primality of a given integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is called trial division. This method divides 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ by each integer from 2 up to the square root of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. Any such integer dividing 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ evenly establishes 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ as composite; otherwise it is prime.
+Integers larger than the square root do not need to be checked because, whenever 
+
+
+
+n
+=
+a
+⋅
+b
+
+
+{\displaystyle n=a\cdot b}
+
+, one of the two factors 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ is less than or equal to the square root of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. Another optimization is to check only primes as factors in this range.[117]
+For instance, to check whether 37 is prime, this method divides it by the primes in the range from 2 to √37, which are 2, 3, and 5. Each division produces a nonzero remainder, so 37 is indeed prime.
+
+Although this method is simple to describe, it is impractical for testing the primality of large integers, because the number of tests that it performs grows exponentially as a function of the number of digits of these integers.[118] However, trial division is still used, with a smaller limit than the square root on the divisor size, to quickly discover composite numbers with small factors, before using more complicated methods on the numbers that pass this filter.[119]
+
+Before computers, mathematical tables listing all of the primes or prime factorizations up to a given limit were commonly printed.[120] The oldest method for generating a list of primes is called the sieve of Eratosthenes.[121] The animation shows an optimized variant of this method.[122]
+Another more asymptotically efficient sieving method for the same problem is the sieve of Atkin.[123] In advanced mathematics, sieve theory applies similar methods to other problems.[124]
+
+Some of the fastest modern tests for whether an arbitrary given number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime are probabilistic (or Monte Carlo) algorithms, meaning that they have a small random chance of producing an incorrect answer.[125]
+For instance the Solovay–Strassen primality test on a given number 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ chooses a number 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ randomly from 
+
+
+
+2
+
+
+{\displaystyle 2}
+
+ through 
+
+
+
+p
+−
+2
+
+
+{\displaystyle p-2}
+
+ and uses modular exponentiation to check
+whether 
+
+
+
+
+a
+
+(
+p
+−
+1
+)
+
+/
+
+2
+
+
+±
+1
+
+
+{\displaystyle a^{(p-1)/2}\pm 1}
+
+ is divisible by 
+
+
+
+p
+
+
+{\displaystyle p}
+
+.[c] If so, it answers yes and otherwise it answers no. If 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ really is prime, it will always answer yes, but if 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is composite then it answers yes with probability at most 1/2 and no with probability at least 1/2.[126]
+If this test is repeated 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ times on the same number,
+the probability that a composite number could pass the test every time is at most 
+
+
+
+1
+
+/
+
+
+2
+
+n
+
+
+
+
+{\displaystyle 1/2^{n}}
+
+. Because this decreases exponentially with the number of tests, it provides high confidence (although not certainty) that a number that passes the repeated test is prime. On the other hand, if the test ever fails, then the number is certainly composite.[127]
+A composite number that passes such a test is called a pseudoprime.[126]
+
+In contrast, some other algorithms guarantee that their answer will always be correct: primes will always be determined to be prime and composites will always be determined to be composite.
+For instance, this is true of trial division.
+The algorithms with guaranteed-correct output include both deterministic (non-random) algorithms, such as the AKS primality test,[128]
+and randomized Las Vegas algorithms where the random choices made by the algorithm do not affect its final answer, such as some variations of elliptic curve primality proving.[125]
+When the elliptic curve method concludes that a number is prime, it provides primality certificate that can be verified quickly.[129]
+The elliptic curve primality test is the fastest in practice of the guaranteed-correct primality tests, but its runtime analysis is based on heuristic arguments rather than rigorous proofs. The AKS primality test has mathematically proven time complexity, but is slower than elliptic curve primality proving in practice.[130] These methods can be used to generate large random prime numbers, by generating and testing random numbers until finding one that is prime;
+when doing this, a faster probabilistic test can quickly eliminate most composite numbers before a guaranteed-correct algorithm is used to verify that the remaining numbers are prime.[d]
+
+The following table lists some of these tests. Their running time is given in terms of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+, the number to be tested and, for probabilistic algorithms, the number 
+
+
+
+k
+
+
+{\displaystyle k}
+
+ of tests performed. Moreover, 
+
+
+
+ε
+
+
+{\displaystyle \varepsilon }
+
+ is an arbitrarily small positive number, and log is the logarithm to an unspecified base. The big O notation means that each time bound should be multiplied by a constant factor to convert it from dimensionless units to units of time; this factor depends on implementation details such as the type of computer used to run the algorithm, but not on the input parameters 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ and 
+
+
+
+k
+
+
+{\displaystyle k}
+
+.
+
+In addition to the aforementioned tests that apply to any natural number, some numbers of a special form can be tested for primality more quickly.
+For example, the Lucas–Lehmer primality test can determine whether a Mersenne number (one less than a power of two) is prime, deterministically,
+in the same time as a single iteration of the Miller–Rabin test.[135] This is why since 1992 (as of December 2018[update]) the largest known prime has always been a Mersenne prime.[136]
+It is conjectured that there are infinitely many Mersenne primes.[137]
+
+The following table gives the largest known primes of various types. Some of these primes have been found using distributed computing. In 2009, the Great Internet Mersenne Prime Search project was awarded a US$100,000 prize for first discovering a prime with at least 10 million digits.[138] The Electronic Frontier Foundation also offers $150,000 and $250,000 for primes with at least 100 million digits and 1 billion digits, respectively.[139]
+
+Given a composite integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+, the task of providing one (or all) prime factors is referred to as factorization of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. It is significantly more difficult than primality testing,[147] and although many factorization algorithms are known, they are slower than the fastest primality testing methods. Trial division and Pollard's rho algorithm can be used to find very small factors of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+,[119] and elliptic curve factorization can be effective when 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ has factors of moderate size.[148] Methods suitable for arbitrary large numbers that do not depend on the size of its factors include the quadratic sieve and general number field sieve. As with primality testing, there are also factorization algorithms that require their input to have a special form, including the special number field sieve.[149] As of December 2019[update] the largest number known to have been factored by a general-purpose algorithm is RSA-240, which has 240 decimal digits (795 bits) and is the product of two large primes.[150]
+
+Shor's algorithm can factor any integer in a polynomial number of steps on a quantum computer.[151] However, current technology can only run this algorithm for very small numbers. As of October 2012[update] the largest number that has been factored by a quantum computer running Shor's algorithm is 21.[152]
+
+Several public-key cryptography algorithms, such as RSA and the Diffie–Hellman key exchange, are based on large prime numbers (2048-bit primes are common).[153] RSA relies on the assumption that it is much easier (that is, more efficient) to perform the multiplication of two (large) numbers 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+ than to calculate 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+ (assumed coprime) if only the product 
+
+
+
+x
+y
+
+
+{\displaystyle xy}
+
+ is known.[30] The Diffie–Hellman key exchange relies on the fact that there are efficient algorithms for modular exponentiation (computing 
+
+
+
+
+a
+
+b
+
+
+
+mod
+
+c
+
+
+
+
+{\displaystyle a^{b}{\bmod {c}}}
+
+), while the reverse operation (the discrete logarithm) is thought to be a hard problem.[154]
+
+Prime numbers are frequently used for hash tables. For instance the original method of Carter and Wegman for universal hashing was based on computing hash functions by choosing random linear functions modulo large prime numbers. Carter and Wegman generalized this method to 
+
+
+
+k
+
+
+{\displaystyle k}
+
+-independent hashing by using higher-degree polynomials, again modulo large primes.[155] As well as in the hash function, prime numbers are used for the hash table size in quadratic probing based hash tables to ensure that the probe sequence covers the whole table.[156]
+
+Some checksum methods are based on the mathematics of prime numbers. For instance the checksums used in International Standard Book Numbers are defined by taking the rest of the number modulo 11, a prime number. Because 11 is prime this method can detect both single-digit errors and transpositions of adjacent digits.[157] Another checksum method, Adler-32, uses arithmetic modulo 65521, the largest prime number less than 
+
+
+
+
+2
+
+16
+
+
+
+
+{\displaystyle 2^{16}}
+
+.[158]
+Prime numbers are also used in pseudorandom number generators including linear congruential generators[159] and the Mersenne Twister.[160]
+
+Prime numbers are of central importance to number theory but also have many applications to other areas within mathematics, including abstract algebra and elementary geometry. For example, it is possible to place prime numbers of points in a two-dimensional grid so that no three are in a line, or so that every triangle formed by three of the points has large area.[161] Another example is Eisenstein's criterion, a test for whether a polynomial is irreducible based on divisibility of its coefficients by a prime number and its square.[162]
+
+The concept of prime number is so important that it has been generalized in different ways in various branches of mathematics. Generally, "prime" indicates minimality or indecomposability, in an appropriate sense. For example, the prime field of a given field is its smallest subfield that contains both 0 and 1. It is either the field of rational numbers or a finite field with a prime number of elements, whence the name.[163] Often a second, additional meaning is intended by using the word prime, namely that any object can be, essentially uniquely, decomposed into its prime components. For example, in knot theory, a prime knot is a knot that is indecomposable in the sense that it cannot be written as the connected sum of two nontrivial knots. Any knot can be uniquely expressed as a connected sum of prime knots.[164] The prime decomposition of 3-manifolds is another example of this type.[165]
+
+Beyond mathematics and computing, prime numbers have potential connections to quantum mechanics, and have been used metaphorically in the arts and literature.  They have also been used in evolutionary biology to explain the life cycles of cicadas.
+
+Fermat primes are primes of the form
+
+with 
+
+
+
+k
+
+
+{\displaystyle k}
+
+ a nonnegative integer.[166] They are named after Pierre de Fermat, who conjectured that all such numbers are prime. The first five of these numbers – 3, 5, 17, 257, and 65,537 – are prime,[167] but 
+
+
+
+
+F
+
+5
+
+
+
+
+{\displaystyle F_{5}}
+
+ is composite and so are all other Fermat numbers that have been verified as of 2017.[168] A regular 
+
+
+
+n
+
+
+{\displaystyle n}
+
+-gon is constructible using straightedge and compass if and only if the odd prime factors of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ (if any) are distinct Fermat primes.[167] Likewise, a regular 
+
+
+
+n
+
+
+{\displaystyle n}
+
+-gon may be constructed using straightedge, compass, and an angle trisector if and only if the prime factors of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ are any number of copies of 2 or 3 together with a (possibly empty) set of distinct Pierpont primes, primes of the form 
+
+
+
+
+2
+
+a
+
+
+
+3
+
+b
+
+
++
+1
+
+
+{\displaystyle 2^{a}3^{b}+1}
+
+.[169]
+
+It is possible to partition any convex polygon into 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ smaller convex polygons of equal area and equal perimeter, when 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is a power of a prime number, but this is not known for other values of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[170]
+
+Beginning with the work of Hugh Montgomery and Freeman Dyson in the 1970s, mathematicians and physicists have speculated that the zeros of the Riemann zeta function are connected to the energy levels of quantum systems.[171][172] Prime numbers are also significant in quantum information science, thanks to mathematical structures such as mutually unbiased bases and symmetric informationally complete positive-operator-valued measures.[173][174]
+
+The evolutionary strategy used by cicadas of the genus Magicicada makes use of prime numbers.[175] These insects spend most of their lives as grubs underground. They only pupate and then emerge from their burrows after 7, 13 or 17 years, at which point they fly about, breed, and then die after a few weeks at most. Biologists theorize that these prime-numbered breeding cycle lengths have evolved in order to prevent predators from synchronizing with these cycles.[176][177]
+In contrast, the multi-year periods between flowering in bamboo plants are hypothesized to be smooth numbers, having only small prime numbers in their factorizations.[178]
+
+Prime numbers have influenced many artists and writers.
+The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47  and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".[179]
+
+In his science fiction novel Contact, scientist Carl Sagan suggested that prime factorization could be used as a means of establishing two-dimensional image planes in communications with aliens, an idea that he had first developed informally with American astronomer Frank Drake in 1975.[180] In the novel The Curious Incident of the Dog in the Night-Time by Mark Haddon, the narrator arranges the sections of the story by consecutive prime numbers as a way to convey the mental state of its main character, a mathematically gifted teen with Asperger syndrome.[181] Prime numbers are used as a metaphor for loneliness and isolation in the Paolo Giordano novel The Solitude of Prime Numbers, in which they are portrayed as "outsiders" among integers.[182]

en/416.html.txt

@@ -0,0 +1,194 @@
+
+
+Asteroids are minor planets, especially of the inner Solar System. Larger asteroids have also been called planetoids. These terms have historically been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered that were found to have volatile-rich surfaces similar to comets, these came to be distinguished from the objects found in the main asteroid belt.[1]
+
+In this article, the term "asteroid" refers to the minor planets of the inner Solar System, including those co-orbital with Jupiter.
+
+Millions of asteroids exist, many the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets.[2] The vast majority of known asteroids orbit within the main asteroid belt located between the orbits of Mars and Jupiter, or are co-orbital with Jupiter (the Jupiter trojans). However, other orbital families exist with significant populations, including the near-Earth objects. Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, and S-type. These were named after and are generally identified with carbon-rich, metallic, and silicate (stony) compositions, respectively. The sizes of asteroids varies greatly; the largest, Ceres, is almost 1,000 km (600 mi) across and massive enough to qualify as a dwarf planet.
+
+Asteroids are somewhat arbitrarily differentiated from comets and meteoroids. In the case of comets, the difference is one of composition: while asteroids are mainly composed of mineral and rock, comets are primarily composed of dust and ice. Furthermore, asteroids formed closer to the sun, preventing the development of cometary ice.[3] The difference between asteroids and meteoroids is mainly one of size: meteoroids have a diameter of one meter or less, whereas asteroids have a diameter of greater than one meter.[4] Finally, meteoroids can be composed of either cometary or asteroidal materials.[5]
+
+Only one asteroid, 4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the naked eye for a short time.[6] As of March 2020[update], the Minor Planet Center had data on 930,000 minor planets in the inner and outer Solar System, of which about 545,000 had enough information to be given numbered designations.[7]
+
+The United Nations declared 30 June as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908.[8][9]
+
+In April 2018, the B612 Foundation reported "It is 100 percent certain we'll be hit [by a devastating asteroid], but we're not 100 percent sure when."[10] Also in 2018, physicist Stephen Hawking,
+in his final book Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet.[11][12][13] In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, and has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.[14][15][16][17][18] According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched.[19]
+
+The first asteroid to be discovered, Ceres, was originally considered to be a new planet.[a] This was followed by the discovery of other similar bodies, which, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though readily distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid",[b] coined in Greek as ἀστεροειδής, or asteroeidēs, meaning 'star-like, star-shaped', and derived from the Ancient Greek ἀστήρ astēr 'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" (not always qualified as "minor") were still used interchangeably.[c]
+
+Discovery timeline:[23]
+
+Asteroid discovery methods have dramatically improved over the past two centuries.
+
+In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law, partly because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law.[26] This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, be spotted. The expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers.
+
+The first object, Ceres, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily. He discovered a new star-like object in Taurus and followed the displacement of this object during several nights. Later that year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, which was found to be between the planets Mars and Jupiter. Piazzi named it after Ceres, the Roman goddess of agriculture.[26]
+
+Three other asteroids (2 Pallas, 3 Juno, and 4 Vesta) were discovered over the next few years, with Vesta found in 1807. After eight more years of fruitless searches, most astronomers assumed that there were no more and abandoned any further searches.[citation needed]
+
+However, Karl Ludwig Hencke persisted, and began searching for more asteroids in 1830. Fifteen years later, he found 5 Astraea, the first new asteroid in 38 years. He also found 6 Hebe less than two years later. After this, other astronomers joined in the search and at least one new asteroid was discovered every year after that (except the wartime year 1945). Notable asteroid hunters of this early era were J.R. Hind, A. de Gasparis, R. Luther, H.M.S. Goldschmidt, J. Chacornac, J. Ferguson, N.R. Pogson, E.W. Tempel, J.C. Watson, C.H.F. Peters, A. Borrelly, J. Palisa, the Henry brothers and A. Charlois.
+
+In 1891, Max Wolf pioneered the use of astrophotography to detect asteroids, which appeared as short streaks on long-exposure photographic plates. This dramatically increased the rate of detection compared with earlier visual methods: Wolf alone discovered 248 asteroids, beginning with 323 Brucia, whereas only slightly more than 300 had been discovered up to that point. It was known that there were many more, but most astronomers did not bother with them, some calling them "vermin of the skies",[27] a phrase variously attributed to E. Suess[28] and E. Weiss.[29] Even a century later, only a few thousand asteroids were identified, numbered and named.
+
+Until 1998, asteroids were discovered by a four-step process. First, a region of the sky was photographed by a wide-field telescope, or astrograph. Pairs of photographs were taken, typically one hour apart. Multiple pairs could be taken over a series of days. Second, the two films or plates of the same region were viewed under a stereoscope. Any body in orbit around the Sun would move slightly between the pair of films. Under the stereoscope, the image of the body would seem to float slightly above the background of stars. Third, once a moving body was identified, its location would be measured precisely using a digitizing microscope. The location would be measured relative to known star locations.[30]
+
+These first three steps do not constitute asteroid discovery: the observer has only found an apparition, which gets a provisional designation, made up of the year of discovery, a letter representing the half-month of discovery, and finally a letter and a number indicating the discovery's sequential number (example: 1998 FJ74).
+
+The last step of discovery is to send the locations and time of observations to the Minor Planet Center, where computer programs determine whether an apparition ties together earlier apparitions into a single orbit. If so, the object receives a catalogue number and the observer of the first apparition with a calculated orbit is declared the discoverer, and granted the honor of naming the object subject to the approval of the International Astronomical Union.
+
+There is increasing interest in identifying asteroids whose orbits cross Earth's, and that could, given enough time, collide with Earth (see Earth-crosser asteroids). The three most important groups of near-Earth asteroids are the Apollos, Amors, and Atens. Various asteroid deflection strategies have been proposed, as early as the 1960s.
+
+The near-Earth asteroid 433 Eros had been discovered as long ago as 1898, and the 1930s brought a flurry of similar objects. In order of discovery, these were: 1221 Amor, 1862 Apollo, 2101 Adonis, and finally 69230 Hermes, which approached within 0.005 AU of Earth in 1937. Astronomers began to realize the possibilities of Earth impact.
+
+Two events in later decades increased the alarm: the increasing acceptance of the Alvarez hypothesis that an impact event resulted in the Cretaceous–Paleogene extinction, and the 1994 observation of Comet Shoemaker-Levy 9 crashing into Jupiter. The U.S. military also declassified the information that its military satellites, built to detect nuclear explosions, had detected hundreds of upper-atmosphere impacts by objects ranging from one to ten meters across.
+
+All these considerations helped spur the launch of highly efficient surveys that consist of charge-coupled device (CCD) cameras and computers directly connected to telescopes. As of 2011[update], it was estimated that 89% to 96% of near-Earth asteroids one kilometer or larger in diameter had been discovered.[31] A list of teams using such systems includes:[32]
+[33]
+
+As of 29 October 2018[update], the LINEAR system alone has discovered 147,132 asteroids.[34] Among all the surveys, 19,266 near-Earth asteroids have been discovered[35] including almost 900 more than 1 km (0.6 mi) in diameter.[36]
+
+Traditionally, small bodies orbiting the Sun were classified as comets, asteroids, or meteoroids, with anything smaller than one meter across being called a meteoroid. Beech and Steel's 1995 paper proposed a meteoroid definition including size limits.[37][38] The term "asteroid", from the Greek word for "star-like", never had a formal definition, with the broader term minor planet being preferred by the International Astronomical Union.
+
+However, following the discovery of asteroids below ten meters in size, Rubin and Grossman's 2010 paper revised the previous definition of meteoroid to objects between 10 µm and 1 meter in size in order to maintain the distinction between asteroids and meteoroids.[4] The smallest asteroids discovered (based on absolute magnitude H) are 2008 TS26 with {{{1}}} and 2011 CQ1 with {{{1}}} both with an estimated size of about 1 meter.[39]
+
+In 2006, the term "small Solar System body" was also introduced to cover both most minor planets and comets.[40][d] Other languages prefer "planetoid" (Greek for "planet-like"), and this term is occasionally used in English especially for larger minor planets such as the dwarf planets as well as an alternative for asteroids since they are not star-like.[41] The word "planetesimal" has a similar meaning, but refers specifically to the small building blocks of the planets that existed when the Solar System was forming. The term "planetule" was coined by the geologist William Daniel Conybeare to describe minor planets,[42] but is not in common use. The three largest objects in the asteroid belt, Ceres, Pallas, and Vesta, grew to the stage of protoplanets. Ceres is a dwarf planet, the only one in the inner Solar System.
+
+When found, asteroids were seen as a class of objects distinct from comets, and there was no unified term for the two until "small Solar System body" was coined in 2006. The main difference between an asteroid and a comet is that a comet shows a coma due to sublimation of near surface ices by solar radiation. A few objects have ended up being dual-listed because they were first classified as minor planets but later showed evidence of cometary activity. Conversely, some (perhaps all) comets are eventually depleted of their surface volatile ices and become asteroid-like. A further distinction is that comets typically have more eccentric orbits than most asteroids; most "asteroids" with notably eccentric orbits are probably dormant or extinct comets.[43]
+
+For almost two centuries, from the discovery of Ceres in 1801 until the discovery of the first centaur, Chiron in 1977, all known asteroids spent most of their time at or within the orbit of Jupiter, though a few such as Hidalgo ventured far beyond Jupiter for part of their orbit. Those located between the orbits of Mars and Jupiter were known for many years simply as The Asteroids.[44] When astronomers started finding more small bodies that permanently resided further out than Jupiter, now called centaurs, they numbered them among the traditional asteroids, though there was debate over whether they should be considered asteroids or as a new type of object. Then, when the first trans-Neptunian object (other than Pluto), Albion, was discovered in 1992, and especially when large numbers of similar objects started turning up, new terms were invented to sidestep the issue: Kuiper-belt object, trans-Neptunian object, scattered-disc object, and so on. These inhabit the cold outer reaches of the Solar System where ices remain solid and comet-like bodies are not expected to exhibit much cometary activity; if centaurs or trans-Neptunian objects were to venture close to the Sun, their volatile ices would sublimate, and traditional approaches would classify them as comets and not asteroids.
+
+The innermost of these are the Kuiper-belt objects, called "objects" partly to avoid the need to classify them as asteroids or comets.[45] They are thought to be predominantly comet-like in composition, though some may be more akin to asteroids.[46] Furthermore, most do not have the highly eccentric orbits associated with comets, and the ones so far discovered are larger than traditional comet nuclei. (The much more distant Oort cloud is hypothesized to be the main reservoir of dormant comets.) Other recent observations, such as the analysis of the cometary dust collected by the Stardust probe, are increasingly blurring the distinction between comets and asteroids,[47] suggesting "a continuum between asteroids and comets" rather than a sharp dividing line.[48]
+
+The minor planets beyond Jupiter's orbit are sometimes also called "asteroids", especially in popular presentations.[e] However, it is becoming increasingly common for the term "asteroid" to be restricted to minor planets of the inner Solar System.[45] Therefore, this article will restrict itself for the most part to the classical asteroids: objects of the asteroid belt, Jupiter trojans, and near-Earth objects.
+
+When the IAU introduced the class small Solar System bodies in 2006 to include most objects previously classified as minor planets and comets, they created the class of dwarf planets for the largest minor planets – those that have enough mass to have become ellipsoidal under their own gravity. According to the IAU, "the term 'minor planet' may still be used, but generally the term 'Small Solar System Body' will be preferred."[49] Currently only the largest object in the asteroid belt, Ceres, at about 975 km (606 mi) across, has been placed in the dwarf planet category.
+
+It is thought that planetesimals in the asteroid belt evolved much like the rest of the solar nebula until Jupiter neared its current mass, at which point excitation from orbital resonances with Jupiter ejected over 99% of planetesimals in the belt. Simulations and a discontinuity in spin rate and spectral properties suggest that asteroids larger than approximately 120 km (75 mi) in diameter accreted during that early era, whereas smaller bodies are fragments from collisions between asteroids during or after the Jovian disruption.[51] Ceres and Vesta grew large enough to melt and differentiate, with heavy metallic elements sinking to the core, leaving rocky minerals in the crust.[52]
+
+In the Nice model, many Kuiper-belt objects are captured in the outer asteroid belt, at distances greater than 2.6 AU. Most were later ejected by Jupiter, but those that remained may be the D-type asteroids, and possibly include Ceres.[53]
+
+Various dynamical groups of asteroids have been discovered orbiting in the inner Solar System. Their orbits are perturbed by the gravity of other bodies in the Solar System and by the Yarkovsky effect. Significant populations include:
+
+The majority of known asteroids orbit within the asteroid belt between the orbits of Mars and Jupiter, generally in relatively low-eccentricity (i.e. not very elongated) orbits. This belt is now estimated to contain between 1.1 and 1.9 million asteroids larger than 1 km (0.6 mi) in diameter,[54] and millions of smaller ones. These asteroids may be remnants of the protoplanetary disk, and in this region the accretion of planetesimals into planets during the formative period of the Solar System was prevented by large gravitational perturbations by Jupiter.
+
+Trojans are populations that share an orbit with a larger planet or moon, but do not collide with it because they orbit in one of the two Lagrangian points of stability, L4 and L5, which lie 60° ahead of and behind the larger body.
+The most significant population of trojans are the Jupiter trojans. Although fewer Jupiter trojans have been discovered (As of 2010[update]), it is thought that they are as numerous as the asteroids in the asteroid belt. Trojans have been found in the orbits of other planets, including Venus, Earth, Mars, Uranus, and Neptune.
+
+Near-Earth asteroids, or NEAs, are asteroids that have orbits that pass close to that of Earth. Asteroids that actually cross Earth's orbital path are known as Earth-crossers. As of June 2016[update], 14,464 near-Earth asteroids are known[31] and the number over one kilometer in diameter is estimated to be 900–1,000.
+
+Asteroids vary greatly in size, from almost 1000 km for the largest down to rocks just 1 meter across.[f] The three largest are very much like miniature planets: they are roughly spherical, have at least partly differentiated interiors,[55] and are thought to be surviving protoplanets. The vast majority, however, are much smaller and are irregularly shaped; they are thought to be either battered planetesimals or fragments of larger bodies.
+
+The dwarf planet Ceres is by far the largest asteroid, with a diameter of 940 km (580 mi). The next largest are 4 Vesta and 2 Pallas, both with diameters of just over 500 km (300 mi). Vesta is the only main-belt asteroid that can, on occasion, be visible to the naked eye. On some rare occasions, a near-Earth asteroid may briefly become visible without technical aid; see 99942 Apophis.
+
+The mass of all the objects of the asteroid belt, lying between the orbits of Mars and Jupiter, is estimated to be in the range of (2.8–3.2)×1021 kg, about 4% of the mass of the Moon. Of this, Ceres comprises 0.938×1021 kg, about a third of the total. Adding in the next three most massive objects, Vesta (9%), Pallas (7%), and Hygiea (3%), brings this figure up to half, whereas the three most-massive asteroids after that, 511 Davida (1.2%), 704 Interamnia (1.0%), and 52 Europa (0.9%), constitute only another 3%. The number of asteroids increases rapidly as their individual masses decrease.
+
+The number of asteroids decreases markedly with size. Although this generally follows a power law, there are 'bumps' at 5 km and 100 km, where more asteroids than expected from a logarithmic distribution are found.[56]
+
+Although their location in the asteroid belt excludes them from planet status, the three largest objects, Ceres, Vesta, and Pallas, are intact protoplanets that share many characteristics common to planets, and are atypical compared to the majority of irregularly shaped asteroids. The fourth largest asteroid, Hygiea, appears nearly spherical although it may have an undifferentiated interior[citation needed], like the majority of asteroids. Between them, the four largest asteroids constitute half the mass of the asteroid belt.
+
+Ceres is the only asteroid with a fully ellipsoidal shape and hence the only one that is a dwarf planet.[40] It has a much higher absolute magnitude than the other asteroids, of around 3.32,[57] and may possess a surface layer of ice.[58] Like the planets, Ceres is differentiated: it has a crust, a mantle and a core.[58] No meteorites from Ceres have been found on Earth.
+
+Vesta, too, has a differentiated interior, though it formed inside the Solar System's frost line, and so is devoid of water;[59][60] its composition is mainly of basaltic rock with minerals such as olivine.[61] Aside from the large crater at its southern pole, Rheasilvia, Vesta also has an ellipsoidal shape. Vesta is the parent body of the Vestian family and other V-type asteroids, and is the source of the HED meteorites, which constitute 5% of all meteorites on Earth.
+
+Pallas is unusual in that, like Uranus, it rotates on its side, with its axis of rotation tilted at high angles to its orbital plane.[62] Its composition is similar to that of Ceres: high in carbon and silicon, and perhaps partially differentiated.[63] Pallas is the parent body of the Palladian family of asteroids.
+
+Hygiea is the largest carbonaceous asteroid[64] and, unlike the other largest asteroids, lies relatively close to the plane of the ecliptic.[65] It is the largest member and presumed parent body of the Hygiean family of asteroids. Because there is no sufficiently large crater on the surface to be the source of that family, as there is on Vesta, it is thought that Hygiea may have been completely disrupted in the collision that formed the Hygiean family, and recoalesced after losing a bit less than 2% of its mass. Observations taken with the Very Large Telescope's SPHERE imager in 2017 and 2018, and announced in late 2019, revealed that Hygiea has a nearly spherical shape, which is at consistent both with it being in hydrostatic equilibrium (and thus a dwarf planet), or formerly being in hydrostatic equilibrium, or with being disrupted and recoalescing.[66][67]
+
+Measurements of the rotation rates of large asteroids in the asteroid belt show that there is an upper limit. Very few asteroids with a diameter larger than 100 meters have a rotation period smaller than 2.2 hours.[70] For asteroids rotating faster than approximately this rate, the inertial force at the surface is greater than the gravitational force, so any loose surface material would be flung out. However, a solid object should be able to rotate much more rapidly. This suggests that most asteroids with a diameter over 100 meters are rubble piles formed through accumulation of debris after collisions between asteroids.[71]
+
+The physical composition of asteroids is varied and in most cases poorly understood. Ceres appears to be composed of a rocky core covered by an icy mantle, where Vesta is thought to have a nickel-iron core, olivine mantle, and basaltic crust.[72] 10 Hygiea, however, which appears to have a uniformly primitive composition of carbonaceous chondrite, is thought to be the largest undifferentiated asteroid. Most of the smaller asteroids are thought to be piles of rubble held together loosely by gravity, though the largest are probably solid. Some asteroids have moons or are co-orbiting binaries: Rubble piles, moons, binaries, and scattered asteroid families are thought to be the results of collisions that disrupted a parent asteroid, or, possibly, a planet.[73]
+
+Asteroids contain traces of amino acids and other organic compounds, and some speculate that asteroid impacts may have seeded the early Earth with the chemicals necessary to initiate life, or may have even brought life itself to Earth (also see panspermia).[74][75] In August 2011, a report, based on NASA studies with meteorites found on Earth, was published suggesting DNA and RNA components (adenine, guanine and related organic molecules) may have been formed on asteroids and comets in outer space.[76][77][78]
+
+Composition is calculated from three primary sources: albedo, surface spectrum, and density. The last can only be determined accurately by observing the orbits of moons the asteroid might have. So far, every asteroid with moons has turned out to be a rubble pile, a loose conglomeration of rock and metal that may be half empty space by volume. The investigated asteroids are as large as 280 km in diameter, and include 121 Hermione (268×186×183 km), and 87 Sylvia (384×262×232 km). Only half a dozen asteroids are larger than 87 Sylvia, though none of them have moons; however, some smaller asteroids are thought to be more massive, suggesting they may not have been disrupted, and indeed 511 Davida, the same size as Sylvia to within measurement error, is estimated to be two and a half times as massive, though this is highly uncertain. The fact that such large asteroids as Sylvia can be rubble piles, presumably due to disruptive impacts, has important consequences for the formation of the Solar System: Computer simulations of collisions involving solid bodies show them destroying each other as often as merging, but colliding rubble piles are more likely to merge. This means that the cores of the planets could have formed relatively quickly.[79]
+
+On 7 October 2009, the presence of water ice was confirmed on the surface of 24 Themis using NASA's Infrared Telescope Facility. The surface of the asteroid appears completely covered in ice. As this ice layer is sublimating, it may be getting replenished by a reservoir of ice under the surface. Organic compounds were also detected on the surface.[80][81][82][83] Scientists hypothesize that some of the first water brought to Earth was delivered by asteroid impacts after the collision that produced the Moon. The presence of ice on 24 Themis supports this theory.[82]
+
+In October 2013, water was detected on an extrasolar body for the first time, on an asteroid orbiting the white dwarf GD 61.[84] On 22 January 2014, European Space Agency (ESA) scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt.[85] The detection was made by using the far-infrared abilities of the Herschel Space Observatory.[86] The finding is unexpected because comets, not asteroids, are typically considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids."[86]
+
+In May 2016, significant asteroid data arising from the Wide-field Infrared Survey Explorer and NEOWISE missions have been questioned.[87][88][89] Although the early original criticism had not undergone peer review,[90] a more recent peer-reviewed study was subsequently published.[91][18]
+
+In November 2019, scientists reported detecting, for the first time, sugar molecules, including ribose, in meteorites, suggesting that chemical processes on asteroids can produce some fundamentally essential bio-ingredients important to life, and supporting the notion of an RNA world prior to a DNA-based origin of life on Earth, and possibly, as well, the notion of panspermia.[92][93]
+
+Most asteroids outside the "big four" (Ceres, Pallas, Vesta, and Hygiea) are likely to be broadly similar in appearance, if irregular in shape. 50 km (31 mi) 253 Mathilde is a rubble pile saturated with craters with diameters the size of the asteroid's radius, and Earth-based observations of 300 km (186 mi) 511 Davida, one of the largest asteroids after the big four, reveal a similarly angular profile, suggesting it is also saturated with radius-size craters.[94] Medium-sized asteroids such as Mathilde and 243 Ida that have been observed up close also reveal a deep regolith covering the surface. Of the big four, Pallas and Hygiea are practically unknown. Vesta has compression fractures encircling a radius-size crater at its south pole but is otherwise a spheroid. Ceres seems quite different in the glimpses Hubble has provided, with surface features that are unlikely to be due to simple craters and impact basins, but details will be expanded with the Dawn spacecraft, which entered Ceres orbit on 6 March 2015.[95]
+
+Asteroids become darker and redder with age due to space weathering.[96] However evidence suggests most of the color change occurs rapidly, in the first hundred thousands years, limiting the usefulness of spectral measurement for determining the age of asteroids.[97]
+
+Asteroids are commonly categorized according to two criteria: the characteristics of their orbits, and features of their reflectance spectrum.
+
+Many asteroids have been placed in groups and families based on their orbital characteristics. Apart from the broadest divisions, it is customary to name a group of asteroids after the first member of that group to be discovered. Groups are relatively loose dynamical associations, whereas families are tighter and result from the catastrophic break-up of a large parent asteroid sometime in the past.[98] Families are more common and easier to identify within the main asteroid belt, but several small families have been reported among the Jupiter trojans.[99] Main belt families were first recognized by Kiyotsugu Hirayama in 1918 and are often called Hirayama families in his honor.
+
+About 30–35% of the bodies in the asteroid belt belong to dynamical families each thought to have a common origin in a past collision between asteroids. A family has also been associated with the plutoid dwarf planet Haumea.
+
+Some asteroids have unusual horseshoe orbits that are co-orbital with Earth or some other planet. Examples are 3753 Cruithne and 2002 AA29. The first instance of this type of orbital arrangement was discovered between Saturn's moons Epimetheus and Janus.
+
+Sometimes these horseshoe objects temporarily become quasi-satellites for a few decades or a few hundred years, before returning to their earlier status. Both Earth and Venus are known to have quasi-satellites.
+
+Such objects, if associated with Earth or Venus or even hypothetically Mercury, are a special class of Aten asteroids. However, such objects could be associated with outer planets as well.
+
+In 1975, an asteroid taxonomic system based on color, albedo, and spectral shape was developed by Chapman, Morrison, and Zellner.[100] These properties are thought to correspond to the composition of the asteroid's surface material. The original classification system had three categories: C-types for dark carbonaceous objects (75% of known asteroids), S-types for stony (silicaceous) objects (17% of known asteroids) and U for those that did not fit into either C or S. This classification has since been expanded to include many other asteroid types. The number of types continues to grow as more asteroids are studied.
+
+The two most widely used taxonomies now used are the Tholen classification and SMASS classification. The former was proposed in 1984 by David J. Tholen, and was based on data collected from an eight-color asteroid survey performed in the 1980s. This resulted in 14 asteroid categories.[101] In 2002, the Small Main-Belt Asteroid Spectroscopic Survey resulted in a modified version of the Tholen taxonomy with 24 different types. Both systems have three broad categories of C, S, and X asteroids, where X consists of mostly metallic asteroids, such as the M-type. There are also several smaller classes.[102]
+
+The proportion of known asteroids falling into the various spectral types does not necessarily reflect the proportion of all asteroids that are of that type; some types are easier to detect than others, biasing the totals.
+
+Originally, spectral designations were based on inferences of an asteroid's composition.[103] However, the correspondence between spectral class and composition is not always very good, and a variety of classifications are in use. This has led to significant confusion. Although asteroids of different spectral classifications are likely to be composed of different materials, there are no assurances that asteroids within the same taxonomic class are composed of the same (or similar) materials.
+
+A newly discovered asteroid is given a provisional designation (such as 2002 AT4) consisting of the year of discovery and an alphanumeric code indicating the half-month of discovery and the sequence within that half-month. Once an asteroid's orbit has been confirmed, it is given a number, and later may also be given a name (e.g. 433 Eros). The formal naming convention uses parentheses around the number – e.g. (433) Eros – but dropping the parentheses is quite common. Informally, it is common to drop the number altogether, or to drop it after the first mention when a name is repeated in running text.[104] In addition, names can be proposed by the asteroid's discoverer, within guidelines established by the International Astronomical Union.[105]
+
+The first asteroids to be discovered were assigned iconic symbols like the ones traditionally used to designate the planets. By 1855 there were two dozen asteroid symbols, which often occurred in multiple variants.[106]
+
+In 1851,[111] after the fifteenth asteroid (Eunomia) had been discovered, Johann Franz Encke made a major change in the upcoming 1854 edition of the Berliner Astronomisches Jahrbuch (BAJ, Berlin Astronomical Yearbook). He introduced a disk (circle), a traditional symbol for a star, as the generic symbol for an asteroid. The circle was then numbered in order of discovery to indicate a specific asteroid (although he assigned ① to the fifth, Astraea, while continuing to designate the first four only with their existing iconic symbols). The numbered-circle convention was quickly adopted by astronomers, and the next asteroid to be discovered (16 Psyche, in 1852) was the first to be designated in that way at the time of its discovery. However, Psyche was given an iconic symbol as well, as were a few other asteroids discovered over the next few years (see chart above). 20 Massalia was the first asteroid that was not assigned an iconic symbol, and no iconic symbols were created after the 1855 discovery of 37 Fides.[h] That year Astraea's number was increased to ⑤, but the first four asteroids, Ceres to Vesta, were not listed by their numbers until the 1867 edition. The circle was soon abbreviated to a pair of parentheses, which were easier to typeset and sometimes omitted altogether over the next few decades, leading to the modern convention.[107]
+
+Until the age of space travel, objects in the asteroid belt were merely pinpricks of light in even the largest telescopes and their shapes and terrain remained a mystery. The best modern ground-based telescopes and the Earth-orbiting Hubble Space Telescope can resolve a small amount of detail on the surfaces of the largest asteroids, but even these mostly remain little more than fuzzy blobs. Limited information about the shapes and compositions of asteroids can be inferred from their light curves (their variation in brightness as they rotate) and their spectral properties, and asteroid sizes can be estimated by timing the lengths of star occulations (when an asteroid passes directly in front of a star). Radar imaging can yield good information about asteroid shapes and orbital and rotational parameters, especially for near-Earth asteroids. In terms of delta-v and propellant requirements, NEOs are more easily accessible than the Moon.[112]
+
+The first close-up photographs of asteroid-like objects were taken in 1971, when the Mariner 9 probe imaged Phobos and Deimos, the two small moons of Mars, which are probably captured asteroids. These images revealed the irregular, potato-like shapes of most asteroids, as did later images from the Voyager probes of the small moons of the gas giants.
+
+The first true asteroid to be photographed in close-up was 951 Gaspra in 1991, followed in 1993 by 243 Ida and its moon Dactyl, all of which were imaged by the Galileo probe en route to Jupiter.
+
+The first dedicated asteroid probe was NEAR Shoemaker, which photographed 253 Mathilde in 1997, before entering into orbit around 433 Eros, finally landing on its surface in 2001.
+
+Other asteroids briefly visited by spacecraft en route to other destinations include 9969 Braille (by Deep Space 1 in 1999), and 5535 Annefrank (by Stardust in 2002).
+
+From September to November 2005, the Japanese Hayabusa probe studied 25143 Itokawa in detail and was plagued with difficulties, but returned samples of its surface to Earth on 13 June 2010.
+
+The European Rosetta probe (launched in 2004) flew by 2867 Šteins in 2008 and 21 Lutetia, the third-largest asteroid visited to date, in 2010.
+
+In September 2007, NASA launched the Dawn spacecraft, which orbited 4 Vesta from July 2011 to September 2012, and has been orbiting the dwarf planet 1 Ceres since 2015. 4 Vesta is the second-largest asteroid visited to date.
+
+On 13 December 2012, China's lunar orbiter Chang'e 2 flew within 3.2 km (2 mi) of the asteroid 4179 Toutatis on an extended mission.
+
+The Japan Aerospace Exploration Agency (JAXA) launched the Hayabusa2 probe in December 2014, and plans to return samples from 162173 Ryugu in December 2020.
+
+In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, and has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.[14][15][16][18]
+
+In September 2016, NASA launched the OSIRIS-REx sample return mission to asteroid 101955 Bennu, which it reached in December 2018. As of June 2019[update], the probe is in orbit around the asteroid.[113]
+
+In early 2013, NASA announced the planning stages of a mission to capture a near-Earth asteroid and move it into lunar orbit where it could possibly be visited by astronauts and later impacted into the Moon.[114] On 19 June 2014, NASA reported that asteroid 2011 MD was a prime candidate for capture by a robotic mission, perhaps in the early 2020s.[115]
+
+It has been suggested that asteroids might be used as a source of materials that may be rare or exhausted on Earth (asteroid mining), or materials for constructing space habitats (see Colonization of the asteroids). Materials that are heavy and expensive to launch from Earth may someday be mined from asteroids and used for space manufacturing and construction.
+
+In the U.S. Discovery program the Psyche spacecraft proposal to 16 Psyche and Lucy spacecraft to Jupiter trojans made it to the semi-finalist stage of mission selection.
+
+In January 2017, Lucy and Psyche mission were both selected as NASA's Discovery Program missions 13 and 14 respectively.[116]
+
+Location of Ceres (within asteroid belt) compared to other bodies of the Solar System
+
+Distances of selected bodies of the Solar System from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively, hence long bars denote high orbital eccentricity. The radius of the Sun is 0.7 million km, and the radius of Jupiter (the largest planet) is 0.07 million km, both too small to resolve on this image.
+
+Asteroids and the asteroid belt are a staple of science fiction stories. Asteroids play several potential roles in science fiction: as places human beings might colonize, resources for extracting minerals, hazards encountered by spacecraft traveling between two other points, and as a threat to life on Earth or other inhabited planets, dwarf planets, and natural satellites by potential impact.
+
+951 Gaspra is the first asteroid to be imaged in close-up, imaged by Galileo on 29 October 1991 (enhanced color)
+
+Several views of 433 Eros in natural color, imaged by NEAR on 12 February 2000
+
+Vesta imaged by Dawn on 9 July 2011
+
+Ceres imaged by Dawn on 4 February 2015
+
+"We include Trojans (bodies captured in Jupiter's 4th and 5th Lagrange points), Centaurs (bodies in orbit between Jupiter and Neptune), and trans-Neptunian objects (orbiting beyond Neptune) in our definition of "asteroid" as used on this site, even though they may more correctly be called "minor planets" instead of asteroids."[citation needed]
+
+Further information about asteroids
+
+Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Observable universe → UniverseEach arrow (→) may be read as "within" or "part of".

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@@ -0,0 +1,162 @@
+
+
+An integer (from the Latin integer meaning "whole")[a] is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
+
+The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers,[2][3] and their additive inverses (the negative integers, i.e., −1, −2, −3, ...). The set of integers is often denoted by a boldface letter ‘Z’ ("Z") or blackboard bold 
+
+
+
+
+Z
+
+
+
+{\displaystyle \mathbb {Z} }
+
+ (Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").[4][5]
+
+ℤ is a subset of the set of all rational numbers ℚ, in turn a subset of the real numbers ℝ.  Like the natural numbers, ℤ is countably infinite.
+
+The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, the (rational) integers are the algebraic integers that are also rational numbers.
+
+The symbol ℤ can be annotated to denote various sets, with varying usage amongst different authors: ℤ+, ℤ+ or ℤ> for the positive integers, ℤ0+ or ℤ≥ for non-negative integers, ℤ≠ for non-zero integers. Some authors use ℤ* for non-zero integers, others use it for non-negative integers, or for {–1, 1}. Additionally, ℤp is used to denote either the set of integers modulo p, i.e., a set of congruence classes of integers, or the set of p-adic integers.[6][7][8]
+
+Ring homomorphisms
+
+Algebraic structures
+
+Related structures
+
+Algebraic number theory
+
+p-adic number theory and decimals
+
+Algebraic geometry
+
+Noncommutative algebraic geometry
+
+Free algebra
+
+Clifford algebra
+
+Like the natural numbers, ℤ is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly, 0, ℤ (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring ℤ.
+
+ℤ is not closed under division, since the quotient of two integers (e.g., 1 divided by 2), need not be an integer. Although the natural numbers are closed under exponentiation, the integers are not (since the result can be a fraction when the exponent is negative).
+
+The following table lists some of the basic properties of addition and multiplication for any integers a, b and c.
+
+In the language of abstract algebra, the first five properties listed above for addition say that ℤ under addition is an abelian group. It is also a cyclic group, since every non-zero integer can be written as a finite sum 1 + 1 + … + 1 or (−1) + (−1) + … + (−1). In fact, ℤ under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to ℤ.
+
+The first four properties listed above for multiplication say that ℤ under multiplication is a commutative monoid. However, not every integer has a multiplicative inverse; e.g., there is no integer x such that 2x = 1. This means that ℤ under multiplication is not a group.
+
+All the rules from the above property table, except for the last, taken together say that ℤ together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of such algebraic structure. Only those equalities of expressions are true in ℤ for all values of variables, which are true in any unital commutative ring. Certain non-zero integers map to zero in certain rings.
+
+The lack of zero divisors in the integers (last property in the table) means that the commutative ring ℤ is an integral domain.
+
+The lack of multiplicative inverses, which is equivalent to the fact that ℤ is not closed under division, means that ℤ is not a field. The smallest field containing the integers as a subring is the field of rational numbers. The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain. And back, starting from an algebraic number field (an extension of rational numbers), its ring of integers can be extracted, which includes ℤ as its subring.
+
+Although ordinary division is not defined on ℤ, the division "with remainder" is defined on them. It is called Euclidean division and possesses the following important property: that is, given two integers a and b with b ≠ 0, there exist unique integers q and r such that a = q × b + r and 0 ≤ r <  | b |, where | b | denotes the absolute value of b. The integer q is called the quotient and r is called the remainder of the division of a by b. The Euclidean algorithm for computing greatest common divisors works by a sequence of Euclidean divisions.
+
+Again, in the language of abstract algebra, the above says that ℤ is a Euclidean domain. This implies that ℤ is a principal ideal domain and any positive integer can be written as the products of primes in an essentially unique way.[9] This is the fundamental theorem of arithmetic.
+
+ℤ is a totally ordered set without upper or lower bound. The ordering of ℤ is given by:
+:... −3 < −2 < −1 < 0 < 1 < 2 < 3 < ...
+An integer is positive if it is greater than zero and negative if it is less than zero. Zero is defined as neither negative nor positive.
+
+The ordering of integers is compatible with the algebraic operations in the following way:
+
+It follows that ℤ together with the above ordering is an ordered ring.
+
+The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.[10] This is equivalent to the statement that any Noetherian valuation ring is either a field or a discrete valuation ring.
+
+In elementary school teaching, integers are often intuitively defined as the (positive) natural numbers, zero, and the negations of the natural numbers. However, this style of definition leads to many different cases (each arithmetic operation needs to be defined on each combination of types of integer) and makes it tedious to prove that these operations obey the laws of arithmetic.[11] Therefore, in modern set-theoretic mathematics a more abstract construction,[12] which allows one to define the arithmetical operations without any case distinction, is often used instead.[13] The integers can thus be formally constructed as the equivalence classes of ordered pairs of natural numbers (a,b).[14]
+
+The intuition is that (a,b) stands for the result of subtracting b from a.[14] To confirm our expectation that 1 − 2 and 4 − 5 denote the same number, we define an equivalence relation ~ on these pairs with the following rule:
+
+precisely when
+
+Addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers;[14] denoting by [(a,b)] the equivalence class having (a,b) as a member, one has:
+
+The negation (or additive inverse) of an integer is obtained by reversing the order of the pair:
+
+Hence subtraction can be defined as the addition of the additive inverse:
+
+The standard ordering on the integers is given by:
+
+It is easily verified that these definitions are independent of the choice of representatives of the equivalence classes.
+
+Every equivalence class has a unique member that is of the form (n,0) or (0,n) (or both at once). The natural number n is identified with the class [(n,0)] (in other words the natural numbers are embedded into the integers by map sending n to [(n,0)]), and the class [(0,n)] is denoted −n (this covers all remaining classes, and gives the class [(0,0)] a second time since −0 = 0.
+
+Thus, [(a,b)] is denoted by
+
+If the natural numbers are identified with the corresponding integers (using the embedding mentioned above), this convention creates no ambiguity.
+
+This notation recovers the familiar representation of the integers as  {…, −2, −1, 0, 1, 2, …}.
+
+Some examples are:
+
+In theoretical computer science, other approaches for the construction of integers are used by automated theorem provers and term rewrite engines.
+Integers are represented as algebraic terms built using a few basic operations  (such as zero, succ, pred, etc.) and, possibly, using natural numbers, which are assumed to be already constructed (e.g., using the Peano approach).
+
+There exist at least ten such constructions of signed integers.[15] These constructions differ in several ways: the number of basic operations used for the construction, the number (usually, between 0 and 2) and the types of arguments accepted by these operations; the presence or absence of natural numbers as arguments of some of these operations, and the fact that these operations are free constructors or not, i.e., that the same integer can be represented using only one or many algebraic terms.
+
+The technique for the construction of integers presented above in this section corresponds to the particular case where there is a single basic operation pair
+
+
+
+(
+x
+,
+y
+)
+
+
+{\displaystyle (x,y)}
+
+ that takes as arguments two natural numbers 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+, and returns an integer (equal to 
+
+
+
+x
+−
+y
+
+
+{\displaystyle x-y}
+
+). This operation is not free since the integer 0 can be written pair(0,0), or pair(1,1), or pair(2,2), etc. This technique of construction is used by the proof assistant Isabelle; however, many other tools use alternative construction techniques, notable those based upon free constructors, which are simpler and can be implemented more efficiently in computers.
+
+An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in the common two's complement representation, the inherent definition of sign distinguishes between "negative" and "non-negative" rather than "negative, positive, and 0". (It is, however, certainly possible for a computer to determine whether an integer value is truly positive.) Fixed length integer approximation data types (or subsets) are denoted int or Integer in several programming languages (such as Algol68, C, Java, Delphi, etc.).
+
+Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10).
+
+The cardinality of the set of integers is equal to ℵ0 (aleph-null). This is readily demonstrated by the construction of a bijection, that is, a function that is injective and surjective from ℤ to ℕ.
+If ℕ₀ ≡ {0, 1, 2, ...} then consider the function:
+
+{… (−4,8) (−3,6) (−2,4) (−1,2) (0,0) (1,1) (2,3) (3,5) ...}
+
+If ℕ ≡ {1, 2, 3, ...} then consider the function:
+
+{... (−4,8) (−3,6) (−2,4) (−1,2) (0,1) (1,3) (2,5) (3,7) ...}
+
+If the domain is restricted to ℤ then each and every member of ℤ has one and only one corresponding member of ℕ and by the definition of cardinal equality the two sets have equal cardinality.
+
+This article incorporates material from Integer on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

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+A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.[1] For being manipulated, individual numbers need to be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows representing any number by a combination of ten basic numerals called digits.[2][3] In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
+
+In mathematics, the notion of number has been extended over the centuries to include 0,[4] negative numbers,[5] rational numbers such as 1/2 and −2/3, real numbers[6] such as √2 and π, and complex numbers,[7] which extend the real numbers with a square root of −1 (and its combinations with real numbers by addition and multiplication).[5] Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers.
+
+Besides their practical uses, numbers have cultural significance throughout the world.[8][9] For example, in Western society, the number 13 is regarded as unlucky, and "a million" may signify "a lot."[8] Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought.[10] Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.[10]
+
+During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Today, number systems are considered important special examples of much more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.[11]
+
+Numbers should be distinguished from numerals, the symbols used to represent numbers. The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets.[12] Roman numerals, a system that used combinations of letters from the Roman alphabet, remained dominant in Europe until the spread of the superior Hindu–Arabic numeral system around the late 14th century, and the Hindu–Arabic numeral system remains the most common system for representing numbers in the world today.[13] The key to the effectiveness of the system was the symbol for zero, which was developed by ancient Indian mathematicians around 500 AD.[13]
+
+Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks.[14] These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals.
+
+A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless tallying systems are considered the first kind of abstract numeral system.
+
+The first known system with place value was the Mesopotamian base 60 system (ca. 3400 BC) and the earliest known base 10 system dates to 3100 BC in Egypt.[15]
+
+The first known documented use of zero dates to AD 628, and appeared in the Brāhmasphuṭasiddhānta, the main work of the Indian mathematician Brahmagupta.  He treated 0 as a number and discussed operations involving it, including division. By this time (the 7th century) the concept had clearly reached Cambodia as Khmer numerals, and documentation shows the idea later spreading to China and the Islamic world.
+
+Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, hence Brahmagupta is usually considered the first to formulate the concept of zero. He gave rules of using zero with negative and positive numbers, such as "zero plus a positive number is a positive number, and a negative number plus zero is the negative number." The Brāhmasphuṭasiddhānta is the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit in representing another number as was done by the Babylonians or as a symbol for a lack of quantity as was done by Ptolemy and the Romans.
+
+The use of 0 as a number should be distinguished from its use as a placeholder numeral in place-value systems. Many ancient texts used 0. Babylonian and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting. Indian texts used a Sanskrit word Shunye or shunya to refer to the concept of void. In mathematics texts this word often refers to the number zero.[16] In a similar vein, Pāṇini (5th century BC) used the null (zero) operator in the Ashtadhyayi, an early example of an algebraic grammar for the Sanskrit language (also see Pingala).
+
+There are other uses of zero before Brahmagupta, though the documentation is not as complete as it is in the Brāhmasphuṭasiddhānta.
+
+Records show that the Ancient Greeks seemed unsure about the status of 0 as a number: they asked themselves "how can 'nothing' be something?" leading to interesting philosophical and, by the Medieval period, religious arguments about the nature and existence of 0 and the vacuum. The paradoxes of Zeno of Elea depend in part on the uncertain interpretation of 0. (The ancient Greeks even questioned whether 1 was a number.)
+
+The late Olmec people of south-central Mexico began to use a symbol for zero, a shell glyph, in the New World, possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar. Mayan arithmetic used base 4 and base 5 written as base 20. Sanchez in 1961 reported a base 4, base 5 "finger" abacus.
+
+By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for 0 (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not as just a placeholder, this Hellenistic zero was the first documented use of a true zero in the Old World. In later Byzantine manuscripts of his Syntaxis Mathematica (Almagest), the Hellenistic zero had morphed into the Greek letter Omicron (otherwise meaning 70).
+
+Another true zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning nothing, not as a symbol. When division produced 0 as a remainder, nihil, also meaning nothing, was used. These medieval zeros were used by all future medieval computists (calculators of Easter). An isolated use of their initial, N, was used in a table of Roman numerals by Bede or a colleague about 725, a true zero symbol.
+
+The abstract concept of negative numbers was recognized as early as 100–50 BC in China.  The Nine Chapters on the Mathematical Art contains methods for finding the areas of figures; red rods were used to denote positive coefficients, black for negative.[17] The first reference in a Western work was in the 3rd century AD in Greece. Diophantus referred to the equation equivalent to 4x + 20 = 0 (the solution is negative) in Arithmetica, saying that the equation gave an absurd result.
+
+During the 600s, negative numbers were in use in India to represent debts. Diophantus' previous reference was discussed more explicitly by Indian mathematician Brahmagupta, in Brāhmasphuṭasiddhānta in 628, who used negative numbers to produce the general form quadratic formula that remains in use today. However, in the 12th century in India, Bhaskara gives negative roots for quadratic equations but says the negative value "is in this case not to be taken, for it is inadequate; people do not approve of negative roots."
+
+European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debts (chapter 13 of Liber Abaci, 1202) and later as losses (in Flos). At the same time, the Chinese were indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit of the corresponding positive number's numeral.[18] The first use of negative numbers in a European work was by Nicolas Chuquet during the 15th century. He used them as exponents, but referred to them as "absurd numbers".
+
+As recently as the 18th century, it was common practice to ignore any negative results returned by equations on the assumption that they were meaningless, just as René Descartes did with negative solutions in a Cartesian coordinate system.
+
+It is likely that the concept of fractional numbers dates to prehistoric times. The Ancient Egyptians used their Egyptian fraction notation for rational numbers in mathematical texts such as the Rhind Mathematical Papyrus and the Kahun Papyrus. Classical Greek and Indian mathematicians made studies of the theory of rational numbers, as part of the general study of number theory. The best known of these is Euclid's Elements, dating to roughly 300 BC. Of the Indian texts, the most relevant is the Sthananga Sutra, which also covers number theory as part of a general study of mathematics.
+
+The concept of decimal fractions is closely linked with decimal place-value notation; the two seem to have developed in tandem. For example, it is common for the Jain math sutra to include calculations of decimal-fraction approximations to pi or the square root of 2. Similarly, Babylonian math texts used sexagesimal (base 60) fractions with great frequency.
+
+The earliest known use of irrational numbers was in the Indian Sulba Sutras composed between 800 and 500 BC.[19] The first existence proofs of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2. The story goes that Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. However, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. He could not disprove their existence through logic, but he could not accept irrational numbers, and so, allegedly and frequently reported, he sentenced Hippasus to death by drowning, to impede spreading of this disconcerting news.[20]
+
+The 16th century brought final European acceptance of negative integral and fractional numbers. By the 17th  century, mathematicians generally used decimal fractions with modern notation. It was not, however, until the 19th century that mathematicians separated irrationals into algebraic and transcendental parts, and once more undertook the scientific study of irrationals. It had remained almost dormant since Euclid. In 1872, the publication of the theories of Karl Weierstrass (by his pupil E. Kossak), Eduard Heine (Crelle, 74), Georg Cantor (Annalen, 5), and Richard Dedekind was brought about. In 1869, Charles Méray had taken the same point of departure as Heine, but the theory is generally referred to the year 1872. Weierstrass's method was completely set forth by Salvatore Pincherle (1880), and Dedekind's has received additional prominence through the author's later work (1888) and endorsement by Paul Tannery (1894). Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on the idea of a cut (Schnitt) in the system of real numbers, separating all rational numbers into two groups having certain characteristic properties. The subject has received later contributions at the hands of Weierstrass, Kronecker (Crelle, 101), and Méray.
+
+The search for roots of quintic and higher degree equations was an important development, the Abel–Ruffini theorem (Ruffini 1799, Abel 1824) showed that they could not be solved by radicals (formulas involving only arithmetical operations and roots). Hence it was necessary to consider the wider set of algebraic numbers (all solutions to polynomial equations). Galois (1832) linked polynomial equations to group theory giving rise to the field of Galois theory.
+
+Continued fractions, closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler, and at the opening of the 19th century were brought into prominence through the writings of Joseph Louis Lagrange. Other noteworthy contributions have been made by Druckenmüller (1837), Kunze (1857), Lemke (1870), and Günther (1872). Ramus (1855) first connected the subject with determinants, resulting, with the subsequent contributions of Heine, Möbius, and Günther, in the theory of Kettenbruchdeterminantencode: deu promoted to code: de .
+
+The existence of transcendental numbers[21] was first established by Liouville (1844, 1851). Hermite proved in 1873 that e is transcendental and Lindemann proved in 1882 that π is transcendental. Finally, Cantor showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite, so there is an uncountably infinite number of transcendental numbers.
+
+The earliest known conception of mathematical infinity appears in the Yajur Veda, an ancient Indian script, which at one point states, "If you remove a part from infinity or add a part to infinity, still what remains is infinity." Infinity was a popular topic of philosophical study among the Jain mathematicians c. 400 BC. They distinguished between five types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
+
+Aristotle defined the traditional Western notion of mathematical infinity. He distinguished between actual infinity and potential infinity—the general consensus being that only the latter had true value. Galileo Galilei's Two New Sciences discussed the idea of one-to-one correspondences between infinite sets. But the next major advance in the theory was made by Georg Cantor; in 1895 he published a book about his new set theory, introducing, among other things, transfinite numbers and formulating the continuum hypothesis.
+
+In the 1960s, Abraham Robinson showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis. The system of hyperreal numbers represents a rigorous method of treating the ideas about infinite and infinitesimal numbers that had been used casually by mathematicians, scientists, and engineers ever since the invention of infinitesimal calculus by Newton and Leibniz.
+
+A modern geometrical version of infinity is given by projective geometry, which introduces "ideal points at infinity", one for each spatial direction. Each family of parallel lines in a given direction is postulated to converge to the corresponding ideal point. This is closely related to the idea of vanishing points in perspective drawing.
+
+The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid. They became more prominent when in the 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians such as Niccolò Fontana Tartaglia and Gerolamo Cardano. It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers.
+
+This was doubly unsettling since they did not even consider negative numbers to be on firm ground at the time. When René Descartes coined the term "imaginary" for these quantities in 1637, he intended it as derogatory. (See imaginary number for a discussion of the "reality" of complex numbers.) A further source of confusion was that the equation
+
+seemed capriciously inconsistent with the algebraic identity
+
+which is valid for positive real numbers a and b, and was also used in complex number calculations with one of a, b positive and the other negative. The incorrect use of this identity, and the related identity
+
+in the case when both a and b are negative even bedeviled Euler. This difficulty eventually led him to the convention of using the special symbol i in place of 
+
+
+
+
+
+−
+1
+
+
+
+
+{\displaystyle {\sqrt {-1}}}
+
+ to guard against this mistake.
+
+The 18th century saw the work of Abraham de Moivre and Leonhard Euler. De Moivre's formula (1730) states:
+
+while Euler's formula of complex analysis (1748) gave us:
+
+The existence of complex numbers was not completely accepted until Caspar Wessel described the geometrical interpretation in 1799. Carl Friedrich Gauss rediscovered and popularized it several years later, and as a result the theory of complex numbers received a notable expansion. The idea of the graphic representation of complex numbers had appeared, however, as early as 1685, in Wallis's De Algebra tractatus.
+
+Also in 1799, Gauss provided the first generally accepted proof of the fundamental theorem of algebra, showing that every polynomial over the complex numbers has a full set of solutions in that realm. The general acceptance of the theory of complex numbers is due to the labors of Augustin Louis Cauchy and Niels Henrik Abel, and especially the latter, who was the first to boldly use complex numbers with a success that is well known.
+
+Gauss studied complex numbers of the form a + bi, where a and b are integral, or rational (and i is one of the two roots of x2 + 1 = 0). His student, Gotthold Eisenstein, studied the type a + bω, where ω is a complex root of x3 − 1 = 0. Other such classes (called cyclotomic fields) of complex numbers derive from the roots of unity xk − 1 = 0 for higher values of k. This generalization is largely due to Ernst Kummer, who also invented ideal numbers, which were expressed as geometrical entities by Felix Klein in 1893.
+
+In 1850 Victor Alexandre Puiseux took the key step of distinguishing between poles and branch points, and introduced the concept of essential singular points. This eventually led to the concept of the extended complex plane.
+
+Prime numbers have been studied throughout recorded history. Euclid devoted one book of the Elements to the theory of primes; in it he proved the infinitude of the primes and the fundamental theorem of arithmetic, and presented the Euclidean algorithm for finding the greatest common divisor of two numbers.
+
+In 240 BC, Eratosthenes used the Sieve of Eratosthenes to quickly isolate prime numbers. But most further development of the theory of primes in Europe dates to the Renaissance and later eras.
+
+In 1796, Adrien-Marie Legendre conjectured the prime number theorem, describing the asymptotic distribution of primes. Other results concerning the distribution of the primes include Euler's proof that the sum of the reciprocals of the primes diverges, and the Goldbach conjecture, which claims that any sufficiently large even number is the sum of two primes. Yet another conjecture related to the distribution of prime numbers is the Riemann hypothesis, formulated by Bernhard Riemann in 1859. The prime number theorem was finally proved by Jacques Hadamard and Charles de la Vallée-Poussin in 1896. Goldbach and Riemann's conjectures remain unproven and unrefuted.
+
+Numbers can be classified into sets, called number systems, such as the natural numbers and the real numbers.[22] The major categories of numbers are as follows:
+
+N
+
+
+0
+
+
+
+
+{\displaystyle \mathbb {N} _{0}}
+
+ or 
+
+
+
+
+
+N
+
+
+1
+
+
+
+
+{\displaystyle \mathbb {N} _{1}}
+
+ are sometimes used.
+
+There is generally no problem in identifying each number system with a proper subset of the next one (by abuse of notation), because each of these number systems is canonically isomorphic to a proper subset of the next one.[citation needed] The resulting hierarchy allows, for example, to talk, formally correctly, about real numbers that are rational numbers, and is expressed symbolically by writing
+
+The most familiar numbers are the natural numbers (sometimes called whole numbers or counting numbers): 1, 2, 3, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.) However, in the 19th century, set theorists and other mathematicians started including 0 (cardinality of the empty set, i.e. 0 elements, where 0 is thus the smallest cardinal number) in the set of natural numbers.[23][24]  Today, different mathematicians use the term to describe both sets, including 0 or not. The mathematical symbol for the set of all natural numbers is N, also written 
+
+
+
+
+N
+
+
+
+{\displaystyle \mathbb {N} }
+
+, and sometimes 
+
+
+
+
+
+N
+
+
+0
+
+
+
+
+{\displaystyle \mathbb {N} _{0}}
+
+ or 
+
+
+
+
+
+N
+
+
+1
+
+
+
+
+{\displaystyle \mathbb {N} _{1}}
+
+ when it is necessary to indicate whether the set should start with 0 or 1, respectively.
+
+In the base 10 numeral system, in almost universal use today for mathematical operations, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The radix or base is the number of unique numerical digits, including zero, that a numeral system uses to represent numbers (for the decimal system, the radix is 10). In this base 10 system, the rightmost digit of a natural number has a place value of 1, and every other digit has a place value ten times that of the place value of the digit to its right.
+
+In set theory, which is capable of acting as an axiomatic foundation for modern mathematics,[25] natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three elements. Alternatively, in Peano Arithmetic, the number 3 is represented as sss0, where s is the "successor" function (i.e., 3 is the third successor of 0). Many different representations are possible; all that is needed to formally represent 3 is to inscribe a certain symbol or pattern of symbols three times.
+
+The negative of a positive integer is defined as a number that produces 0 when it is added to the corresponding positive integer. Negative numbers are usually written with a negative sign (a minus sign). As an example, the negative of 7 is written −7, and 7 + (−7) = 0. When the set of negative numbers is combined with the set of natural numbers (including 0), the result is defined as the set of integers, Z also written 
+
+
+
+
+Z
+
+
+
+{\displaystyle \mathbb {Z} }
+
+. Here the letter Z comes from German  Zahl, meaning 'number'. The set of integers forms a ring with the operations addition and multiplication.[26]
+
+The natural numbers form a subset of the integers. As there is no common standard for the inclusion or not of zero in the natural numbers, the natural numbers without zero are commonly referred to as positive integers, and the natural numbers with zero are referred to as non-negative integers.
+
+A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator. Fractions are written as two integers, the numerator and the denominator, with a dividing bar between them. The fraction m/n represents m parts of a whole divided into n equal parts. Two different fractions may correspond to the same rational number; for example 1/2 and 2/4 are equal, that is:
+
+In general,
+
+If the absolute value of m is greater than n (supposed to be positive), then the absolute value of the fraction is greater than 1. Fractions can be greater than, less than, or equal to 1 and can also be positive, negative, or 0. The set of all rational numbers includes the integers since every integer can be written as a fraction with denominator 1. For example −7 can be written −7/1. The symbol for the rational numbers is Q (for quotient), also written 
+
+
+
+
+Q
+
+
+
+{\displaystyle \mathbb {Q} }
+
+.
+
+The symbol for the real numbers is R, also written as 
+
+
+
+
+R
+
+.
+
+
+{\displaystyle \mathbb {R} .}
+
+ They include all the measuring numbers. Every real number corresponds to a point on the number line. The following paragraph will focus primarily on positive real numbers. The treatment of negative real numbers is according to the general rules of arithmetic and their denotation is simply prefixing the corresponding positive numeral by a minus sign, e.g. −123.456.
+
+Most real numbers can only be approximated by decimal numerals, in which a decimal point is placed to the right of the digit with place value 1. Each digit to the right of the decimal point has a place value one-tenth of the place value of the digit to its left. For example, 123.456 represents 123456/1000, or, in words, one hundred, two tens, three ones, four tenths, five hundredths, and six thousandths. A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.  Representing other real numbers as decimals would require an infinite sequence of digits to the right of the decimal point. If this infinite sequence of digits follows a pattern, it can be written with an ellipsis or another notation that indicates the repeating pattern.  Such a decimal is called a repeating decimal. Thus 1/3 can be written as 0.333..., with an ellipsis to indicate that the pattern continues. Forever repeating 3s are also written as 0.3.[27]
+
+It turns out that these repeating decimals (including the repetition of zeroes) denote exactly the rational numbers, i.e., all rational numbers are also real numbers, but it is not the case that every real number is rational. A real number that is not rational is called irrational. A famous irrational real number is the number π, the ratio of the circumference of any circle to its diameter. When pi is written as
+
+as it sometimes is, the ellipsis does not mean that the decimals repeat (they do not), but rather that there is no end to them. It has been proved that π is irrational. Another well-known number, proven to be an irrational real number, is
+
+the square root of 2, that is, the unique positive real number whose square is 2. Both these numbers have been approximated (by computer) to trillions ( 1 trillion =  1012 = 1,000,000,000,000 ) of digits.
+
+Not only these prominent examples but almost all real numbers are irrational and therefore have no repeating patterns and hence no corresponding decimal numeral. They can only be approximated by decimal numerals, denoting rounded or truncated real numbers. Any rounded or truncated number is necessarily a rational number, of which there are only countably many. All measurements are, by their nature, approximations, and always have a margin of error. Thus 123.456 is considered an approximation of any real number greater or equal to 1234555/10000 and strictly less than 1234565/10000 (rounding to 3 decimals), or of any real number  greater or equal to 123456/1000 and strictly less than 123457/1000 (truncation after the 3. decimal). Digits that suggest a greater accuracy than the measurement itself does, should be removed. The remaining digits are then called significant digits. For example, measurements with a ruler can seldom be made without a margin of error of at least 0.001  meters. If the sides of a rectangle are measured as 1.23 meters and 4.56 meters, then multiplication gives an area for the rectangle between 5.614591 square meters and 5.603011 square meters. Since not even the second digit after the decimal place is preserved, the following digits are not significant. Therefore, the result is usually rounded to 5.61.
+
+Just as the same fraction can be written in more than one way, the same real number may have more than one decimal representation. For example, 0.999..., 1.0, 1.00, 1.000, ..., all represent the natural number 1. A given real number has only the following decimal representations: an approximation to some finite number of decimal places, an approximation in which a pattern is established that continues for an unlimited number of decimal places or an exact value with only finitely many decimal places.  In this last case, the last non-zero digit may be replaced by the digit one smaller followed by an unlimited number of 9's, or the last non-zero digit may be followed by an unlimited number of zeros.  Thus the exact real number 3.74 can also be written 3.7399999999... and 3.74000000000.... Similarly, a decimal numeral with an unlimited number of 0's can be rewritten by dropping the 0's to the right of the decimal place, and a decimal numeral with an unlimited number of 9's can be rewritten by increasing the rightmost -9 digit by one, changing all the 9's to the right of that digit to 0's. Finally, an unlimited sequence of 0's to the right of the decimal place can be dropped. For example, 6.849999999999... = 6.85 and 6.850000000000... = 6.85.  Finally, if all of the digits in a numeral are 0, the number is 0, and if all of the digits in a numeral are an unending string of 9's, you can drop the nines to the right of the decimal place, and add one to the string of 9s to the left of the decimal place.  For example, 99.999... = 100.
+
+The real numbers also have an important but highly technical property called the least upper bound property.
+
+It can be shown that any ordered field, which is also complete, is isomorphic to the real numbers. The real numbers are not, however, an algebraically closed field, because they do not include a solution (often called a square root of minus one) to the algebraic equation 
+
+
+
+
+x
+
+2
+
+
++
+1
+=
+0
+
+
+{\displaystyle x^{2}+1=0}
+
+.
+
+Moving to a greater level of abstraction, the real numbers can be extended to the complex numbers. This set of numbers arose historically from trying to find closed formulas for the roots of cubic and quadratic polynomials. This led to expressions involving the square roots of negative numbers, and eventually to the definition of a new number: a square root of −1, denoted by i, a symbol assigned by Leonhard Euler, and called the imaginary unit. The complex numbers consist of all numbers of the form
+
+where a and b are real numbers. Because of this, complex numbers correspond to points on the complex plane, a vector space of two real dimensions. In the expression a + bi, the real number a is called the real part and b is called the imaginary part. If the real part of a complex number is 0, then the number is called an imaginary number or is referred to as purely imaginary; if the imaginary part is 0, then the number is a real number. Thus the real numbers are a subset of the complex numbers. If the real and imaginary parts of a complex number are both integers, then the number is called a Gaussian integer. The symbol for the complex numbers is C or 
+
+
+
+
+C
+
+
+
+{\displaystyle \mathbb {C} }
+
+.
+
+The fundamental theorem of algebra asserts that the complex numbers form an algebraically closed field, meaning that every polynomial with complex coefficients has a root in the complex numbers. Like the reals, the complex numbers form a field, which is complete, but unlike the real numbers, it is not ordered. That is, there is no consistent meaning assignable to saying that  I is greater than 1, nor is there any meaning in saying that  I is less than 1. In technical terms, the complex numbers lack a total order that is compatible with field operations.
+
+An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula n = 2k + 1, for a suitable integer k. Starting with k = 0, the first non-negative odd numbers are {1, 3, 5, 7, ...}. Any even number m has the form m = 2k where k is again an integer. Similarly, the first non-negative even numbers are {0, 2, 4, 6, ...}.
+
+A prime number is an integer greater than 1 that is not the product of two smaller positive integers. The first few prime numbers are 2, 3, 5, 7, and 11. There is no such simple formula as for odd and even numbers to generate the prime numbers. The primes have been widely studied for more than 2000 years and have led to many questions, only some of which have been answered.  The study of these questions belongs to number theory.  An example of a still unanswered question is, whether every even number is the sum of two primes.  This is called Goldbach's conjecture.
+
+The question, whether every integer greater than one is a product of primes in only one way, except for a rearrangement of the primes, has been answered to the positive: this proven claim is called fundamental theorem of arithmetic. A proof appears in Euclid's Elements.
+
+Many subsets of the natural numbers have been the subject of specific studies and have been named, often after the first mathematician that has studied them. Example of such sets of integers are Fibonacci numbers and perfect numbers. For more examples, see Integer sequence.
+
+Algebraic numbers are those that are a solution to a polynomial equation with integer coefficients. Real numbers that are not rational numbers are called irrational numbers. Complex numbers which are not algebraic are called transcendental numbers. The algebraic numbers that are solutions of a monic polynomial equation with integer coefficients are called algebraic integers.
+
+Motivated by the classical problems of constructions with straightedge and compass, the constructible numbers are those complex numbers whose real and imaginary parts can be constructed using straightedge and compass, starting from a given segment of unit length, in a finite number of steps.
+
+A computable number, also known as recursive number, is a real number such that there exists an algorithm which, given a positive number n as input, produces the first n digits of the computable number's decimal representation. Equivalent definitions can be given using μ-recursive functions, Turing machines or λ-calculus. The computable numbers are stable for all usual arithmetic operations, including the computation of the roots of a polynomial, and thus form a real closed field that contains the real algebraic numbers.
+
+The computable numbers may be viewed as the real numbers that may be exactly represented in a computer: a computable number is exactly represented by its first digits and a program for computing further digits. However, the computable numbers are rarely used in practice. One reason is that there is no algorithm for testing the equality of two computable numbers. More precisely, there cannot exist any algorithm which takes any computable number as an input, and decides in every case if this number is equal to zero or not.
+
+The set of computable numbers has the same cardinality as the natural numbers. Therefore, almost all real numbers are non-computable. However, it is very difficult to produce explicitly a real number that is not computable.
+
+The p-adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right. The number system that results depends on what base is used for the digits: any base is possible, but a prime number base provides the best mathematical properties. The set of the p-adic numbers contains the rational numbers, but is not contained in the complex numbers.
+
+The elements of an algebraic function field over a finite field and algebraic numbers have many similar properties (see Function field analogy). Therefore, they are often regarded as numbers by number theorists. The p-adic numbers play an important role in this analogy.
+
+Some number systems that are not included in the complex numbers may be constructed from the real numbers in a way that generalize the construction of the complex numbers. They are sometimes called hypercomplex numbers. They include the quaternions H, introduced by Sir William Rowan Hamilton, in which multiplication is not commutative, the octonions, in which multiplication is not associative in addition to not being commutative, and the sedenions, in which multiplication is not alternative, neither associative nor commutative.
+
+For dealing with infinite sets, the natural numbers have been generalized to the ordinal numbers and to the cardinal numbers. The former gives the ordering of the set, while the latter gives its size. For finite sets, both ordinal and cardinal numbers are identified with the natural numbers. In the infinite case, many ordinal numbers correspond to the same cardinal number.
+
+Hyperreal numbers are used in non-standard analysis. The hyperreals, or nonstandard reals (usually denoted as *R), denote an ordered field that is a proper extension of the ordered field of real numbers R and satisfies the transfer principle. This principle allows true first-order statements about R to be reinterpreted as true first-order statements about *R.
+
+Superreal and surreal numbers extend the real numbers by adding infinitesimally small numbers and infinitely large numbers, but still form fields.

en/4162.html.txt

@@ -0,0 +1,2916 @@
+
+
+
+
+A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
+However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
+
+The property of being prime is called primality. A simple but slow method of checking the primality of a given number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+, called trial division, tests whether 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is a multiple of any integer between 2 and 
+
+
+
+
+
+n
+
+
+
+
+{\displaystyle {\sqrt {n}}}
+
+. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018[update] the largest known prime number has 24,862,048 decimal digits.
+
+There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm.
+
+Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.
+
+A natural number (1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it is greater than 1 and cannot be written as the product of two smaller natural numbers. The numbers greater than 1 that are not prime are called composite numbers.[1] In other words, 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime if 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ items cannot be divided up into smaller equal-size groups of more than one item,[2] or if it is not possible to arrange 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ dots into a rectangular grid that is more than one dot wide and more than one dot high.[3]
+For example, among the numbers 1 through 6, the numbers 2, 3, and 5 are the prime numbers,[4] as there are no other numbers that divide them evenly (without a remainder).
+1 is not prime, as it is specifically excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite.
+
+The divisors of a natural number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ are the natural numbers that divide 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ evenly.
+Every natural number has both 1 and itself as a divisor. If it has any other divisor, it cannot be prime. This idea leads to a different but equivalent definition of the primes: they are the numbers with exactly two positive divisors, 1 and the number itself.[5]
+Yet another way to express the same thing is that a number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime if it is greater than one and if none of the numbers 
+
+
+
+2
+,
+3
+,
+…
+,
+n
+−
+1
+
+
+{\displaystyle 2,3,\dots ,n-1}
+
+ divides 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ evenly.[6]
+
+The first 25 prime numbers (all the prime numbers less than 100) are:[7]
+
+No even number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ greater than 2 is prime because any such number can be expressed as the product 
+
+
+
+2
+×
+n
+
+/
+
+2
+
+
+{\displaystyle 2\times n/2}
+
+. Therefore, every prime number other than 2 is an odd number, and is called an odd prime.[8] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite:
+decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in 0 or 5 are divisible by 5.[9]
+
+The set of all primes is sometimes denoted by 
+
+
+
+
+P
+
+
+
+{\displaystyle \mathbf {P} }
+
+ (a boldface capital P)[10] or by 
+
+
+
+
+P
+
+
+
+{\displaystyle \mathbb {P} }
+
+ (a blackboard bold capital P).[11]
+
+The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptian fraction expansions of different forms for prime and composite numbers.[12] However, the earliest surviving records of the explicit study of prime numbers come from ancient Greek mathematics. Euclid's Elements (c. 300 BC) proves the infinitude of primes and the fundamental theorem of arithmetic, and shows how to construct a perfect number from a Mersenne prime.[13] Another Greek invention, the Sieve of Eratosthenes, is still used to construct lists of primes.[14][15]
+
+Around 1000 AD, the Islamic mathematician Ibn al-Haytham (Alhazen) found Wilson's theorem, characterizing the prime numbers as the numbers 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ that evenly divide 
+
+
+
+(
+n
+−
+1
+)
+!
++
+1
+
+
+{\displaystyle (n-1)!+1}
+
+. He also conjectured that all even perfect numbers come from Euclid's construction using Mersenne primes, but was unable to prove it.[16] Another Islamic mathematician, Ibn al-Banna' al-Marrakushi, observed that the sieve of Eratosthenes can be sped up by testing only the divisors up to the square root of the largest number to be tested. Fibonacci brought the innovations from Islamic mathematics back to Europe. His book Liber Abaci (1202) was the first to describe trial division for testing primality, again using divisors only up to the square root.[15]
+
+In 1640 Pierre de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler).[17] Fermat also investigated the primality of the Fermat numbers
+
+
+
+
+
+2
+
+
+2
+
+n
+
+
+
+
++
+1
+
+
+{\displaystyle 2^{2^{n}}+1}
+
+,[18] and Marin Mersenne studied the Mersenne primes, prime numbers of the form 
+
+
+
+
+2
+
+p
+
+
+−
+1
+
+
+{\displaystyle 2^{p}-1}
+
+ with 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ itself a prime.[19] Christian Goldbach formulated Goldbach's conjecture, that every even number is the sum of two primes, in a 1742 letter to Euler.[20] Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be constructed from Mersenne primes.[13] He introduced methods from mathematical analysis to this area in his proofs of the infinitude of the primes and the divergence of the sum of the reciprocals of the primes 
+
+
+
+
+
+
+1
+2
+
+
+
++
+
+
+
+1
+3
+
+
+
++
+
+
+
+1
+5
+
+
+
++
+
+
+
+1
+7
+
+
+
++
+
+
+
+1
+11
+
+
+
++
+⋯
+
+
+{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}+{\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+\cdots }
+
+.[21]
+At the start of the 19th century, Legendre and Gauss conjectured that as 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ tends to infinity, the number of primes up to 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ is asymptotic to 
+
+
+
+x
+
+/
+
+log
+⁡
+x
+
+
+{\displaystyle x/\log x}
+
+, where 
+
+
+
+log
+⁡
+x
+
+
+{\displaystyle \log x}
+
+ is the natural logarithm of 
+
+
+
+x
+
+
+{\displaystyle x}
+
+.   Ideas of Bernhard Riemann in his 1859 paper on the zeta-function sketched an outline for proving this. Although the closely related Riemann hypothesis remains unproven, Riemann's outline was completed in 1896 by Hadamard and de la Vallée Poussin, and the result is now known as the prime number theorem.[22] Another important 19th century result was Dirichlet's theorem on arithmetic progressions, that certain arithmetic progressions contain infinitely many primes.[23]
+
+Many mathematicians have worked on primality tests for numbers larger than those where trial division is practicably applicable. Methods that are restricted to specific number forms include Pépin's test for Fermat numbers (1877),[24] Proth's theorem (c. 1878),[25] the Lucas–Lehmer primality test (originated 1856), and the generalized Lucas primality test.[15]
+
+Since 1951 all the largest known primes have been found using these tests on computers.[a] The search for ever larger primes has generated interest outside mathematical circles, through the Great Internet Mersenne Prime Search and other distributed computing projects.[7][27] The idea that prime numbers had few applications outside of pure mathematics[b] was shattered in the 1970s when public-key cryptography and the RSA cryptosystem were invented, using prime numbers as their basis.[30]
+
+The increased practical importance of computerized primality testing and factorization led to the development of improved methods capable of handling large numbers of unrestricted form.[14][31][32] The mathematical theory of prime numbers also moved forward with the Green–Tao theorem (2004) that there are arbitrarily long arithmetic progressions of prime numbers, and Yitang Zhang's 2013 proof that there exist infinitely many prime gaps of bounded size.[33]
+
+Most early Greeks did not even consider 1 to be a number,[34][35] so they could not consider its primality. A few mathematicians from this time also considered the prime numbers to be a subdivision of the odd numbers, so they also did not consider 2 to be prime. However, Euclid and a majority of the other Greek mathematicians considered 2 as prime. The medieval Islamic mathematicians largely followed the Greeks in viewing 1 as not being a number.[34]
+By the Middle Ages and Renaissance mathematicians began treating 1 as a number, and some of them included it as the first prime number.[36] In the mid-18th century Christian Goldbach listed 1 as prime in his correspondence with Leonhard Euler; however, Euler himself did not consider 1 to be prime.[37] In the 19th century many mathematicians still considered 1 to be prime,[38] and lists of primes that included 1 continued to be published as recently as 1956.[39][40]
+
+If the definition of a prime number were changed to call 1 a prime, many statements involving prime numbers would need to be reworded in a more awkward way. For example, the fundamental theorem of arithmetic would need to be rephrased in terms of factorizations into primes greater than 1, because every number would have multiple factorizations with different numbers of copies of 1.[38] Similarly, the sieve of Eratosthenes would not work correctly if it handled 1 as a prime, because it would eliminate all multiples of 1 (that is, all other numbers) and output only the single number 1.[40] Some other more technical properties of prime numbers also do not hold for the number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1.[41] By the early 20th century, mathematicians began to agree that 1 should not be listed as prime, but rather in its own special category as a "unit".[38]
+
+Writing a number as a product of prime numbers is called a prime factorization of the number. For example:
+
+The terms in the product are called prime factors. The same prime factor may occur more than once; this example has two copies of the prime factor 
+
+
+
+3.
+
+
+{\displaystyle 3.}
+
+  When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 
+
+
+
+
+3
+
+2
+
+
+
+
+{\displaystyle 3^{2}}
+
+ denotes the square or second power of 
+
+
+
+3.
+
+
+{\displaystyle 3.}
+
+The central importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic.[42] This theorem states that every integer larger than 1 can be written as a product of one or more primes. More strongly,
+this product is unique in the sense that any two prime factorizations of the same number will have the same numbers of copies of the same primes,
+although their ordering may differ.[43]  So, although there are many different ways of finding a factorization using an integer factorization algorithm, they all must produce the same result. Primes can thus be considered the "basic building blocks" of the natural numbers.[44]
+
+Some proofs of the uniqueness of prime factorizations are based on Euclid's lemma: If 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is a prime number and 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides a product 
+
+
+
+a
+b
+
+
+{\displaystyle ab}
+
+ of integers 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+,
+
+
+{\displaystyle b,}
+
+ then 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ or 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ (or both).[45] Conversely, if a number 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ has the property that when it divides a product it always divides at least one factor of the product, then 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ must be prime.[46]
+
+There are infinitely many prime numbers. Another way of saying this is that the sequence
+
+of prime numbers never ends. This statement is referred to as Euclid's theorem in honor of the ancient Greek mathematician Euclid, since the first known proof for this statement is attributed to him. Many more proofs of the infinitude of primes are known, including an analytical proof by Euler, Goldbach's proof based on  Fermat numbers,[47] Furstenberg's proof using general topology,[48] and Kummer's elegant proof.[49]
+
+Euclid's proof[50] shows that every finite list of primes is incomplete. The key idea is to multiply together the primes in any given list and add 
+
+
+
+1.
+
+
+{\displaystyle 1.}
+
+ If the list consists of the primes 
+
+
+
+
+p
+
+1
+
+
+,
+
+p
+
+2
+
+
+,
+…
+,
+
+p
+
+n
+
+
+,
+
+
+{\displaystyle p_{1},p_{2},\ldots ,p_{n},}
+
+ this gives the number
+
+By the fundamental theorem, 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ has a prime factorization
+
+with one or more prime factors. 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ is evenly divisible by each of these factors, but 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ has a remainder of one when divided by any of the prime numbers in the given list, so none of the prime factors of 
+
+
+
+N
+
+
+{\displaystyle N}
+
+ can be in the given list. Because there is no finite list of all the primes, there must be infinitely many primes.
+
+The numbers formed by adding one to the products of the smallest primes are called Euclid numbers.[51] The first five of them are prime, but the sixth,
+
+is a composite number.
+
+There is no known efficient formula for primes.  For example, there is no non-constant polynomial, even in several variables, that takes only prime values.[52]  However, there are numerous expressions that do encode all primes, or only primes. One possible formula is based on Wilson's theorem and generates the number 2 many times and all other primes exactly once.[53]  There is also a set of Diophantine equations in nine variables and one parameter with the following property: the parameter is prime if and only if the resulting system of equations has a solution over the natural numbers. This can be used to obtain a single formula with the property that all its positive values are prime.[52]
+
+Other examples of prime-generating formulas come from Mills' theorem and a theorem of Wright.  These assert that there are real constants 
+
+
+
+A
+>
+1
+
+
+{\displaystyle A>1}
+
+ and 
+
+
+
+μ
+
+
+{\displaystyle \mu }
+
+ such that
+
+are prime for any natural number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ in the first formula, and any number of exponents in the second formula.[54] Here 
+
+
+
+⌊
+
+
+⋅
+
+
+⌋
+
+
+{\displaystyle \lfloor {}\cdot {}\rfloor }
+
+ represents the floor function, the largest integer less than or equal to the number in question. However, these are not useful for generating primes, as the primes must be generated first in order to compute the values of 
+
+
+
+A
+
+
+{\displaystyle A}
+
+ or 
+
+
+
+μ
+.
+
+
+{\displaystyle \mu .}
+
+[52]
+
+Many  conjectures revolving about primes have been posed. Often having an elementary formulation, many of these conjectures have withstood proof for decades: all four of Landau's problems from 1912 are still unsolved.[55] One of them is Goldbach's conjecture, which asserts that every even integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ greater than 2 can be written as a sum of two primes.[56] As of 2014[update], this conjecture has been verified for all numbers up to 
+
+
+
+n
+=
+4
+⋅
+
+10
+
+18
+
+
+.
+
+
+{\displaystyle n=4\cdot 10^{18}.}
+
+[57] Weaker statements than this have been proven, for example, Vinogradov's theorem says that every sufficiently large odd integer can be written as a sum of three primes.[58] Chen's theorem says that every sufficiently large even number can be expressed as the sum of a prime and a semiprime (the product of two primes).[59] Also, any even integer greater than 10 can be written as the sum of six primes.[60] The branch of number theory studying such questions is called additive number theory.[61]
+
+Another type of problem concerns prime gaps, the differences between consecutive primes.
+The existence of arbitrarily large prime gaps can be seen by noting that the sequence 
+
+
+
+n
+!
++
+2
+,
+n
+!
++
+3
+,
+…
+,
+n
+!
++
+n
+
+
+{\displaystyle n!+2,n!+3,\dots ,n!+n}
+
+ consists of 
+
+
+
+n
+−
+1
+
+
+{\displaystyle n-1}
+
+ composite numbers, for any natural number 
+
+
+
+n
+.
+
+
+{\displaystyle n.}
+
+[62] However, large prime gaps occur much earlier than this argument shows.[63] For example, the first prime gap of length 8 is between the primes 89 and 97,[64] much smaller than 
+
+
+
+8
+!
+=
+40320.
+
+
+{\displaystyle 8!=40320.}
+
+ It is conjectured that there are infinitely many twin primes, pairs of primes with difference 2; this is the twin prime conjecture. Polignac's conjecture states more generally that for every positive integer 
+
+
+
+k
+,
+
+
+{\displaystyle k,}
+
+ there are infinitely many pairs of consecutive primes that differ by 
+
+
+
+2
+k
+.
+
+
+{\displaystyle 2k.}
+
+[65]
+Andrica's conjecture,[65] Brocard's conjecture,[66] Legendre's conjecture,[67] and Oppermann's conjecture[66] all suggest that the largest gaps between primes from 
+
+
+
+1
+
+
+{\displaystyle 1}
+
+ to 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ should be at most approximately 
+
+
+
+
+
+n
+
+
+,
+
+
+{\displaystyle {\sqrt {n}},}
+
+ a result that is known to follow from the Riemann hypothesis, while the much stronger Cramér conjecture sets the largest gap size at 
+
+
+
+O
+(
+(
+log
+⁡
+n
+
+)
+
+2
+
+
+)
+.
+
+
+{\displaystyle O((\log n)^{2}).}
+
+[65]  Prime gaps can be generalized to prime 
+
+
+
+k
+
+
+{\displaystyle k}
+
+-tuples, patterns in the differences between more than two prime numbers. Their infinitude and density are the subject of the first Hardy–Littlewood conjecture, which can be motivated by the heuristic that the prime numbers behave similarly to a random sequence of numbers with density given by the prime number theorem.[68]
+
+Analytic number theory studies number theory through the lens of continuous functions, limits, infinite series, and the related mathematics of the infinite and infinitesimal.
+
+This area of study began with Leonhard Euler and his first major result, the solution to the Basel problem.
+The problem asked for the value of the infinite sum 
+
+
+
+1
++
+
+
+
+1
+4
+
+
+
++
+
+
+
+1
+9
+
+
+
++
+
+
+
+1
+16
+
+
+
++
+…
+,
+
+
+{\displaystyle 1+{\tfrac {1}{4}}+{\tfrac {1}{9}}+{\tfrac {1}{16}}+\dots ,}
+
+
+which today can be recognized as the value 
+
+
+
+ζ
+(
+2
+)
+
+
+{\displaystyle \zeta (2)}
+
+ of the Riemann zeta function. This function is closely connected to the prime numbers and to one of the most significant unsolved problems in mathematics, the Riemann hypothesis. Euler showed that 
+
+
+
+ζ
+(
+2
+)
+=
+
+π
+
+2
+
+
+
+/
+
+6
+
+
+{\displaystyle \zeta (2)=\pi ^{2}/6}
+
+.[69]
+The reciprocal of this number, 
+
+
+
+6
+
+/
+
+
+π
+
+2
+
+
+
+
+{\displaystyle 6/\pi ^{2}}
+
+, is the limiting probability that two random numbers selected uniformly from a large range are relatively prime (have no factors in common).[70]
+
+The distribution of primes in the large, such as the question how many primes are smaller than a given, large threshold, is described by the prime number theorem, but no efficient formula for the 
+
+
+
+n
+
+
+{\displaystyle n}
+
+-th prime is known.
+Dirichlet's theorem on arithmetic progressions, in its basic form, asserts that linear polynomials
+
+with relatively prime integers 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ take infinitely many prime values. Stronger forms of the theorem state that the sum of the reciprocals of these prime values diverges, and that different linear polynomials with the same 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ have approximately the same proportions of primes.
+Although conjectures have been formulated about the proportions of primes in higher-degree polynomials, they remain unproven, and it is unknown whether there exists a quadratic polynomial that (for integer arguments) is prime infinitely often.
+
+Euler's proof that there are infinitely many primes considers the sums of reciprocals of primes,
+
+Euler showed that, for any arbitrary real number 
+
+
+
+x
+
+
+{\displaystyle x}
+
+, there exists a prime 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ for which this sum is bigger than 
+
+
+
+x
+
+
+{\displaystyle x}
+
+.[71] This shows that there are infinitely many primes, because if there were finitely many primes the sum would reach its maximum value at the biggest prime rather than growing past every 
+
+
+
+x
+
+
+{\displaystyle x}
+
+.
+The growth rate of this sum is described more precisely by Mertens' second theorem.[72] For comparison, the sum
+
+does not grow to infinity as 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ goes to infinity (see the Basel problem). In this sense, prime numbers occur more often than squares of natural numbers,
+although both sets are infinite.[73] Brun's theorem states that the sum of the reciprocals of twin primes,
+
+is finite. Because of Brun's theorem, it is not possible to use Euler's method to solve the twin prime conjecture, that there exist infinitely many twin primes.[73]
+
+The prime counting function 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ is defined as the number of primes not greater than 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[74] For example, 
+
+
+
+π
+(
+11
+)
+=
+5
+
+
+{\displaystyle \pi (11)=5}
+
+, since there are five primes less than or equal to 11. Methods such as the Meissel–Lehmer algorithm can compute exact values of 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ faster than it would be possible to list each prime up to 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[75] The prime number theorem states that 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ is asymptotic to 
+
+
+
+n
+
+/
+
+log
+⁡
+n
+
+
+{\displaystyle n/\log n}
+
+, which is denoted as
+
+and means that the ratio of 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ to the right-hand fraction approaches 1 as 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ grows to infinity.[76] This implies that the likelihood that a randomly chosen number less than 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime is (approximately) inversely proportional to the number of digits in 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[77]
+It also implies that the 
+
+
+
+n
+
+
+{\displaystyle n}
+
+th prime number is proportional to 
+
+
+
+n
+log
+⁡
+n
+
+
+{\displaystyle n\log n}
+
+[78]
+and therefore that the average size of a prime gap is proportional to 
+
+
+
+log
+⁡
+n
+
+
+{\displaystyle \log n}
+
+.[63]
+A more accurate estimate for 
+
+
+
+π
+(
+n
+)
+
+
+{\displaystyle \pi (n)}
+
+ is given by the offset logarithmic integral[76]
+
+An arithmetic progression is a finite or infinite sequence of numbers such that consecutive numbers in the sequence all have the same difference.[79] This difference is called the modulus of the progression.[80] For example,
+
+is an infinite arithmetic progression with modulus 9. In an arithmetic progression, all the numbers have the same remainder when divided by the modulus; in this example, the remainder is 3. Because both the modulus 9 and the remainder 3 are multiples of 3, so is every element in the sequence. Therefore, this progression contains only one prime number, 3 itself. In general, the infinite progression
+
+can have more than one prime only when its remainder 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and modulus 
+
+
+
+q
+
+
+{\displaystyle q}
+
+ are relatively prime. If they are relatively prime, Dirichlet's theorem on arithmetic progressions asserts that the progression contains infinitely many primes.[81]
+
+The Green–Tao theorem shows that there are arbitrarily long finite arithmetic progressions consisting only of primes.[33][82]
+
+Euler noted that the function
+
+yields prime numbers for 
+
+
+
+1
+≤
+n
+≤
+40
+
+
+{\displaystyle 1\leq n\leq 40}
+
+, although composite numbers appear among its later values.[83][84] The search for an explanation for this phenomenon led to the deep algebraic number theory of Heegner numbers and the class number problem.[85] The Hardy-Littlewood conjecture F predicts the density of primes among the values of quadratic polynomials with integer coefficients
+in terms of the logarithmic integral and the polynomial coefficients. No quadratic polynomial has been proven to take infinitely many prime values.[86]
+
+The Ulam spiral arranges the natural numbers in a two-dimensional grid, spiraling in concentric squares surrounding the origin with the prime numbers highlighted. Visually, the primes appear to cluster on certain diagonals and not others, suggesting that some quadratic polynomials take prime values more often than others.[86]
+
+One of the most famous unsolved questions in mathematics, dating from 1859, and one of the Millennium Prize Problems, is the Riemann hypothesis, which asks where the zeros of the Riemann zeta function 
+
+
+
+ζ
+(
+s
+)
+
+
+{\displaystyle \zeta (s)}
+
+ are located.
+This function is an analytic function on the complex numbers. For complex numbers 
+
+
+
+s
+
+
+{\displaystyle s}
+
+ with real part greater than one it equals both an infinite sum over all integers, and an infinite product over the prime numbers,
+
+This equality between a sum and a product, discovered by Euler, is called an Euler product.[87] The Euler product can be derived from the fundamental theorem of arithmetic, and shows the close connection between the zeta function and the prime numbers.[88]
+It leads to another proof that there are infinitely many primes: if there were only finitely many,
+then the sum-product equality would also be valid at 
+
+
+
+s
+=
+1
+
+
+{\displaystyle s=1}
+
+, but the sum would diverge (it is the harmonic series 
+
+
+
+1
++
+
+
+
+1
+2
+
+
+
++
+
+
+
+1
+3
+
+
+
++
+…
+
+
+{\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{3}}+\dots }
+
+) while the product would be finite, a contradiction.[89]
+
+The Riemann hypothesis states that the zeros of the zeta-function are all either negative even numbers, or complex numbers with real part equal to 1/2.[90]  The original proof of the prime number theorem was based on a weak form of this hypothesis, that there are no zeros with real part equal to 1,[91][92] although other more elementary proofs have been found.[93]
+The prime-counting function can be expressed by Riemann's explicit formula as a sum in which each term comes from one of the zeros of the zeta function; the main term of this sum is the logarithmic integral, and the remaining terms cause the sum to fluctuate above and below the main term.[94]
+In this sense, the zeros control how regularly the prime numbers are distributed. If the Riemann hypothesis is true, these fluctuations will be small, and the
+asymptotic distribution of primes given by the prime number theorem will also hold over much shorter intervals (of length about the square root of 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ for intervals near a number 
+
+
+
+x
+
+
+{\displaystyle x}
+
+).[92]
+
+Modular arithmetic modifies usual arithmetic by only using the numbers 
+
+
+
+{
+0
+,
+1
+,
+2
+,
+…
+,
+n
+−
+1
+}
+
+
+{\displaystyle \{0,1,2,\dots ,n-1\}}
+
+, for a natural number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ called the modulus.
+Any other natural number can be mapped into this system by replacing it by its remainder after division by 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[95]
+Modular sums, differences and products are calculated by performing the same replacement by the remainder
+on the result of the usual sum, difference, or product of integers.[96] Equality of integers corresponds to congruence in modular arithmetic:
+
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+ are congruent (written 
+
+
+
+x
+≡
+y
+
+
+{\displaystyle x\equiv y}
+
+ mod 
+
+
+
+n
+
+
+{\displaystyle n}
+
+) when they have the same remainder after division by 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[97] However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number 
+
+
+
+7
+
+
+{\displaystyle 7}
+
+ as modulus, division by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ is possible: 
+
+
+
+2
+
+/
+
+3
+≡
+3
+
+mod
+
+7
+
+
+
+
+{\displaystyle 2/3\equiv 3{\bmod {7}}}
+
+, because clearing denominators by multiplying both sides by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ gives the  valid formula 
+
+
+
+2
+≡
+9
+
+mod
+
+7
+
+
+
+
+{\displaystyle 2\equiv 9{\bmod {7}}}
+
+. However, with the composite modulus 
+
+
+
+6
+
+
+{\displaystyle 6}
+
+, division by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ is impossible. There is no valid solution to 
+
+
+
+2
+
+/
+
+3
+≡
+x
+
+mod
+
+6
+
+
+
+
+{\displaystyle 2/3\equiv x{\bmod {6}}}
+
+: clearing denominators by multiplying by 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+ causes the left-hand side to become 
+
+
+
+2
+
+
+{\displaystyle 2}
+
+ while the right-hand side becomes either 
+
+
+
+0
+
+
+{\displaystyle 0}
+
+ or 
+
+
+
+3
+
+
+{\displaystyle 3}
+
+.
+In the terminology of abstract algebra, the ability to perform division means that modular arithmetic modulo a prime number forms a field or, more specifically, a finite field, while other moduli only give a ring but not a field.[98]
+
+Several theorems about primes can be formulated using modular arithmetic. For instance, Fermat's little theorem states that if
+
+
+
+
+a
+≢
+0
+
+
+{\displaystyle a\not \equiv 0}
+
+ (mod 
+
+
+
+p
+
+
+{\displaystyle p}
+
+), then 
+
+
+
+
+a
+
+p
+−
+1
+
+
+≡
+1
+
+
+{\displaystyle a^{p-1}\equiv 1}
+
+ (mod 
+
+
+
+p
+
+
+{\displaystyle p}
+
+).[99]
+Summing this over all choices of 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ gives the equation
+
+valid whenever 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is prime.
+Giuga's conjecture says that this equation is also a sufficient condition for 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ to be prime.[100]
+Wilson's theorem says that an integer 
+
+
+
+p
+>
+1
+
+
+{\displaystyle p>1}
+
+ is prime if and only if the factorial 
+
+
+
+(
+p
+−
+1
+)
+!
+
+
+{\displaystyle (p-1)!}
+
+ is congruent to 
+
+
+
+−
+1
+
+
+{\displaystyle -1}
+
+ mod 
+
+
+
+p
+
+
+{\displaystyle p}
+
+. For a composite number 
+
+
+
+
+n
+=
+r
+⋅
+s
+
+
+
+{\displaystyle \;n=r\cdot s\;}
+
+ this cannot hold, since one of its factors divides both n and 
+
+
+
+(
+n
+−
+1
+)
+!
+
+
+{\displaystyle (n-1)!}
+
+, and so 
+
+
+
+(
+n
+−
+1
+)
+!
+≡
+−
+1
+
+
+(
+mod
+
+n
+)
+
+
+
+{\displaystyle (n-1)!\equiv -1{\pmod {n}}}
+
+ is impossible.[101]
+
+The 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic order 
+
+
+
+
+ν
+
+p
+
+
+(
+n
+)
+
+
+{\displaystyle \nu _{p}(n)}
+
+ of an integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is the number of copies of 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ in the prime factorization of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. The same concept can be extended from integers to rational numbers by defining the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic order of a fraction 
+
+
+
+m
+
+/
+
+n
+
+
+{\displaystyle m/n}
+
+ to be 
+
+
+
+
+ν
+
+p
+
+
+(
+m
+)
+−
+
+ν
+
+p
+
+
+(
+n
+)
+
+
+{\displaystyle \nu _{p}(m)-\nu _{p}(n)}
+
+. The 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic absolute value 
+
+
+
+
+|
+
+q
+
+
+|
+
+
+p
+
+
+
+
+{\displaystyle |q|_{p}}
+
+ of any rational number 
+
+
+
+q
+
+
+{\displaystyle q}
+
+ is then defined as
+
+
+
+
+
+|
+
+q
+
+
+|
+
+
+p
+
+
+=
+
+p
+
+−
+
+ν
+
+p
+
+
+(
+q
+)
+
+
+
+
+{\displaystyle |q|_{p}=p^{-\nu _{p}(q)}}
+
+. Multiplying an integer by its 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic absolute value cancels out the factors of 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ in its factorization, leaving only the other primes. Just as the distance between two real numbers can be measured by the absolute value of their distance, the distance between two rational numbers can be measured by their 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic distance, the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic absolute value of their difference. For this definition of distance, two numbers are close together (they have a small distance) when their difference is divisible by a high power of 
+
+
+
+p
+
+
+{\displaystyle p}
+
+. In the same way that the real numbers can be formed from the rational numbers and their distances, by adding extra limiting values to form a complete field, the rational numbers with the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic distance can be extended to a different complete field, the 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic numbers.[102][103]
+
+This picture of an order, absolute value, and complete field derived from them can be generalized to algebraic number fields and their valuations (certain mappings from the multiplicative group of the field to a totally ordered additive group, also called orders), absolute values (certain multiplicative mappings from the field to the real numbers, also called norms),[102] and places (extensions to complete fields in which the given field is a dense set, also called completions).[104] The extension from the rational numbers to the real numbers, for instance, is a place in which the distance between numbers is the usual absolute value of their difference. The corresponding mapping to an additive group would be the logarithm of the absolute value, although this does not meet all the requirements of a valuation. According to Ostrowski's theorem, up to a natural notion of equivalence, the real numbers and 
+
+
+
+p
+
+
+{\displaystyle p}
+
+-adic numbers, with their orders and absolute values, are the only valuations, absolute values, and places on the rational numbers.[102] The local-global principle allows certain problems over the rational numbers to be solved by piecing together solutions from each of their places, again underlining the importance of primes to number theory.[105]
+
+A commutative ring is an algebraic structure where addition, subtraction and multiplication are defined. The integers are a ring, and the prime numbers in the integers have been generalized to rings in two different ways, prime elements and irreducible elements. An element 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ of a ring 
+
+
+
+R
+
+
+{\displaystyle R}
+
+ is called prime if it is nonzero, has no multiplicative inverse (that is, it is not a unit), and satisfies the following requirement: whenever 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ divides the product 
+
+
+
+x
+y
+
+
+{\displaystyle xy}
+
+ of two elements of 
+
+
+
+R
+
+
+{\displaystyle R}
+
+, it also divides at least one of 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ or 
+
+
+
+y
+
+
+{\displaystyle y}
+
+. An element is irreducible if it is neither a unit nor the product of two other non-unit elements. In the ring of integers, the prime and irreducible elements form the same set,
+
+In an arbitrary ring, all prime elements are irreducible. The converse does not hold in general, but does hold for unique factorization domains.[106]
+
+The fundamental theorem of arithmetic continues to hold (by definition) in unique factorization domains. An example of such a domain is the Gaussian integers 
+
+
+
+
+Z
+
+[
+i
+]
+
+
+{\displaystyle \mathbb {Z} [i]}
+
+, the ring of complex numbers of the form 
+
+
+
+a
++
+b
+i
+
+
+{\displaystyle a+bi}
+
+ where 
+
+
+
+i
+
+
+{\displaystyle i}
+
+ denotes the imaginary unit and 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ are arbitrary integers. Its prime elements are known as Gaussian primes. Not every number that is prime among the integers remains prime in the Gaussian integers; for instance, the number 2 can be written as a product of the two Gaussian primes 
+
+
+
+1
++
+i
+
+
+{\displaystyle 1+i}
+
+ and 
+
+
+
+1
+−
+i
+
+
+{\displaystyle 1-i}
+
+. Rational primes (the prime elements in the integers) congruent to 3 mod 4 are Gaussian primes, but rational primes congruent to 1 mod 4 are not.[107] This is a consequence of Fermat's theorem on sums of two squares,
+which states that an odd prime 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is expressible as the sum of two squares, 
+
+
+
+p
+=
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+{\displaystyle p=x^{2}+y^{2}}
+
+, and therefore factorizable as 
+
+
+
+p
+=
+(
+x
++
+i
+y
+)
+(
+x
+−
+i
+y
+)
+
+
+{\displaystyle p=(x+iy)(x-iy)}
+
+, exactly when 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is 1 mod 4.[108]
+
+Not every ring is a unique factorization domain. For instance, in the ring of numbers 
+
+
+
+a
++
+b
+
+
+−
+5
+
+
+
+
+{\displaystyle a+b{\sqrt {-5}}}
+
+ (for integers 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+) the number 
+
+
+
+21
+
+
+{\displaystyle 21}
+
+ has two factorizations 
+
+
+
+21
+=
+3
+⋅
+7
+=
+(
+1
++
+2
+
+
+−
+5
+
+
+)
+(
+1
+−
+2
+
+
+−
+5
+
+
+)
+
+
+{\displaystyle 21=3\cdot 7=(1+2{\sqrt {-5}})(1-2{\sqrt {-5}})}
+
+, where neither of the four factors can be reduced any further, so it does not have a unique factorization. In order to extend unique factorization to a larger class of rings, the notion of a number can be replaced with that of an ideal, a subset of the elements of a ring that contains all sums of pairs of its elements, and all products of its elements with ring elements.
+Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), ... The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.[109]
+
+The spectrum of a ring is a geometric space whose points are the prime ideals of the ring.[110] Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. These concepts can even assist with in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the existence of square roots modulo integer prime numbers.[111]
+Early attempts to prove Fermat's Last Theorem led to Kummer's introduction of regular primes, integer prime numbers connected with the failure of unique factorization in the cyclotomic integers.[112]
+The question of how many integer prime numbers factor into a product of multiple prime ideals in an algebraic number field is addressed by Chebotarev's density theorem, which (when applied to the cyclotomic integers) has Dirichlet's theorem on primes in arithmetic progressions as a special case.[113]
+
+In the theory of finite groups the Sylow theorems imply that, if a power of a prime number 
+
+
+
+
+p
+
+n
+
+
+
+
+{\displaystyle p^{n}}
+
+ divides the order of a group, then it has a subgroup of order 
+
+
+
+
+p
+
+n
+
+
+
+
+{\displaystyle p^{n}}
+
+. By Lagrange's theorem, any group of prime order is a cyclic group,
+and by Burnside's theorem any group whose order is divisible by only two primes is solvable.[114]
+
+For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of mathematics[b] other than the use of prime numbered gear teeth to distribute wear evenly.[115] In particular, number theorists such as British mathematician G. H. Hardy prided themselves on doing work that had absolutely no military significance.[116]
+
+This vision of the purity of number theory was shattered in the 1970s, when it was publicly announced that prime numbers could be used as the basis for the creation of public key cryptography algorithms.[30]
+These applications have led to significant study of algorithms for computing with prime numbers, and in particular of primality testing, methods for determining whether a given number is prime.
+The most basic primality testing routine, trial division, is too slow to be useful for large numbers. One group of modern primality tests is applicable to arbitrary numbers, while more efficient tests are available for numbers of special types. Most primality tests only tell whether their argument is prime or not. Routines that also provide a prime factor of composite arguments (or all of its prime factors) are called factorization algorithms.
+Prime numbers are also used in computing for checksums, hash tables, and pseudorandom number generators.
+
+The most basic method of checking the primality of a given integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is called trial division. This method divides 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ by each integer from 2 up to the square root of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. Any such integer dividing 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ evenly establishes 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ as composite; otherwise it is prime.
+Integers larger than the square root do not need to be checked because, whenever 
+
+
+
+n
+=
+a
+⋅
+b
+
+
+{\displaystyle n=a\cdot b}
+
+, one of the two factors 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ and 
+
+
+
+b
+
+
+{\displaystyle b}
+
+ is less than or equal to the square root of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. Another optimization is to check only primes as factors in this range.[117]
+For instance, to check whether 37 is prime, this method divides it by the primes in the range from 2 to √37, which are 2, 3, and 5. Each division produces a nonzero remainder, so 37 is indeed prime.
+
+Although this method is simple to describe, it is impractical for testing the primality of large integers, because the number of tests that it performs grows exponentially as a function of the number of digits of these integers.[118] However, trial division is still used, with a smaller limit than the square root on the divisor size, to quickly discover composite numbers with small factors, before using more complicated methods on the numbers that pass this filter.[119]
+
+Before computers, mathematical tables listing all of the primes or prime factorizations up to a given limit were commonly printed.[120] The oldest method for generating a list of primes is called the sieve of Eratosthenes.[121] The animation shows an optimized variant of this method.[122]
+Another more asymptotically efficient sieving method for the same problem is the sieve of Atkin.[123] In advanced mathematics, sieve theory applies similar methods to other problems.[124]
+
+Some of the fastest modern tests for whether an arbitrary given number 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is prime are probabilistic (or Monte Carlo) algorithms, meaning that they have a small random chance of producing an incorrect answer.[125]
+For instance the Solovay–Strassen primality test on a given number 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ chooses a number 
+
+
+
+a
+
+
+{\displaystyle a}
+
+ randomly from 
+
+
+
+2
+
+
+{\displaystyle 2}
+
+ through 
+
+
+
+p
+−
+2
+
+
+{\displaystyle p-2}
+
+ and uses modular exponentiation to check
+whether 
+
+
+
+
+a
+
+(
+p
+−
+1
+)
+
+/
+
+2
+
+
+±
+1
+
+
+{\displaystyle a^{(p-1)/2}\pm 1}
+
+ is divisible by 
+
+
+
+p
+
+
+{\displaystyle p}
+
+.[c] If so, it answers yes and otherwise it answers no. If 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ really is prime, it will always answer yes, but if 
+
+
+
+p
+
+
+{\displaystyle p}
+
+ is composite then it answers yes with probability at most 1/2 and no with probability at least 1/2.[126]
+If this test is repeated 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ times on the same number,
+the probability that a composite number could pass the test every time is at most 
+
+
+
+1
+
+/
+
+
+2
+
+n
+
+
+
+
+{\displaystyle 1/2^{n}}
+
+. Because this decreases exponentially with the number of tests, it provides high confidence (although not certainty) that a number that passes the repeated test is prime. On the other hand, if the test ever fails, then the number is certainly composite.[127]
+A composite number that passes such a test is called a pseudoprime.[126]
+
+In contrast, some other algorithms guarantee that their answer will always be correct: primes will always be determined to be prime and composites will always be determined to be composite.
+For instance, this is true of trial division.
+The algorithms with guaranteed-correct output include both deterministic (non-random) algorithms, such as the AKS primality test,[128]
+and randomized Las Vegas algorithms where the random choices made by the algorithm do not affect its final answer, such as some variations of elliptic curve primality proving.[125]
+When the elliptic curve method concludes that a number is prime, it provides primality certificate that can be verified quickly.[129]
+The elliptic curve primality test is the fastest in practice of the guaranteed-correct primality tests, but its runtime analysis is based on heuristic arguments rather than rigorous proofs. The AKS primality test has mathematically proven time complexity, but is slower than elliptic curve primality proving in practice.[130] These methods can be used to generate large random prime numbers, by generating and testing random numbers until finding one that is prime;
+when doing this, a faster probabilistic test can quickly eliminate most composite numbers before a guaranteed-correct algorithm is used to verify that the remaining numbers are prime.[d]
+
+The following table lists some of these tests. Their running time is given in terms of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+, the number to be tested and, for probabilistic algorithms, the number 
+
+
+
+k
+
+
+{\displaystyle k}
+
+ of tests performed. Moreover, 
+
+
+
+ε
+
+
+{\displaystyle \varepsilon }
+
+ is an arbitrarily small positive number, and log is the logarithm to an unspecified base. The big O notation means that each time bound should be multiplied by a constant factor to convert it from dimensionless units to units of time; this factor depends on implementation details such as the type of computer used to run the algorithm, but not on the input parameters 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ and 
+
+
+
+k
+
+
+{\displaystyle k}
+
+.
+
+In addition to the aforementioned tests that apply to any natural number, some numbers of a special form can be tested for primality more quickly.
+For example, the Lucas–Lehmer primality test can determine whether a Mersenne number (one less than a power of two) is prime, deterministically,
+in the same time as a single iteration of the Miller–Rabin test.[135] This is why since 1992 (as of December 2018[update]) the largest known prime has always been a Mersenne prime.[136]
+It is conjectured that there are infinitely many Mersenne primes.[137]
+
+The following table gives the largest known primes of various types. Some of these primes have been found using distributed computing. In 2009, the Great Internet Mersenne Prime Search project was awarded a US$100,000 prize for first discovering a prime with at least 10 million digits.[138] The Electronic Frontier Foundation also offers $150,000 and $250,000 for primes with at least 100 million digits and 1 billion digits, respectively.[139]
+
+Given a composite integer 
+
+
+
+n
+
+
+{\displaystyle n}
+
+, the task of providing one (or all) prime factors is referred to as factorization of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+. It is significantly more difficult than primality testing,[147] and although many factorization algorithms are known, they are slower than the fastest primality testing methods. Trial division and Pollard's rho algorithm can be used to find very small factors of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+,[119] and elliptic curve factorization can be effective when 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ has factors of moderate size.[148] Methods suitable for arbitrary large numbers that do not depend on the size of its factors include the quadratic sieve and general number field sieve. As with primality testing, there are also factorization algorithms that require their input to have a special form, including the special number field sieve.[149] As of December 2019[update] the largest number known to have been factored by a general-purpose algorithm is RSA-240, which has 240 decimal digits (795 bits) and is the product of two large primes.[150]
+
+Shor's algorithm can factor any integer in a polynomial number of steps on a quantum computer.[151] However, current technology can only run this algorithm for very small numbers. As of October 2012[update] the largest number that has been factored by a quantum computer running Shor's algorithm is 21.[152]
+
+Several public-key cryptography algorithms, such as RSA and the Diffie–Hellman key exchange, are based on large prime numbers (2048-bit primes are common).[153] RSA relies on the assumption that it is much easier (that is, more efficient) to perform the multiplication of two (large) numbers 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+ than to calculate 
+
+
+
+x
+
+
+{\displaystyle x}
+
+ and 
+
+
+
+y
+
+
+{\displaystyle y}
+
+ (assumed coprime) if only the product 
+
+
+
+x
+y
+
+
+{\displaystyle xy}
+
+ is known.[30] The Diffie–Hellman key exchange relies on the fact that there are efficient algorithms for modular exponentiation (computing 
+
+
+
+
+a
+
+b
+
+
+
+mod
+
+c
+
+
+
+
+{\displaystyle a^{b}{\bmod {c}}}
+
+), while the reverse operation (the discrete logarithm) is thought to be a hard problem.[154]
+
+Prime numbers are frequently used for hash tables. For instance the original method of Carter and Wegman for universal hashing was based on computing hash functions by choosing random linear functions modulo large prime numbers. Carter and Wegman generalized this method to 
+
+
+
+k
+
+
+{\displaystyle k}
+
+-independent hashing by using higher-degree polynomials, again modulo large primes.[155] As well as in the hash function, prime numbers are used for the hash table size in quadratic probing based hash tables to ensure that the probe sequence covers the whole table.[156]
+
+Some checksum methods are based on the mathematics of prime numbers. For instance the checksums used in International Standard Book Numbers are defined by taking the rest of the number modulo 11, a prime number. Because 11 is prime this method can detect both single-digit errors and transpositions of adjacent digits.[157] Another checksum method, Adler-32, uses arithmetic modulo 65521, the largest prime number less than 
+
+
+
+
+2
+
+16
+
+
+
+
+{\displaystyle 2^{16}}
+
+.[158]
+Prime numbers are also used in pseudorandom number generators including linear congruential generators[159] and the Mersenne Twister.[160]
+
+Prime numbers are of central importance to number theory but also have many applications to other areas within mathematics, including abstract algebra and elementary geometry. For example, it is possible to place prime numbers of points in a two-dimensional grid so that no three are in a line, or so that every triangle formed by three of the points has large area.[161] Another example is Eisenstein's criterion, a test for whether a polynomial is irreducible based on divisibility of its coefficients by a prime number and its square.[162]
+
+The concept of prime number is so important that it has been generalized in different ways in various branches of mathematics. Generally, "prime" indicates minimality or indecomposability, in an appropriate sense. For example, the prime field of a given field is its smallest subfield that contains both 0 and 1. It is either the field of rational numbers or a finite field with a prime number of elements, whence the name.[163] Often a second, additional meaning is intended by using the word prime, namely that any object can be, essentially uniquely, decomposed into its prime components. For example, in knot theory, a prime knot is a knot that is indecomposable in the sense that it cannot be written as the connected sum of two nontrivial knots. Any knot can be uniquely expressed as a connected sum of prime knots.[164] The prime decomposition of 3-manifolds is another example of this type.[165]
+
+Beyond mathematics and computing, prime numbers have potential connections to quantum mechanics, and have been used metaphorically in the arts and literature.  They have also been used in evolutionary biology to explain the life cycles of cicadas.
+
+Fermat primes are primes of the form
+
+with 
+
+
+
+k
+
+
+{\displaystyle k}
+
+ a nonnegative integer.[166] They are named after Pierre de Fermat, who conjectured that all such numbers are prime. The first five of these numbers – 3, 5, 17, 257, and 65,537 – are prime,[167] but 
+
+
+
+
+F
+
+5
+
+
+
+
+{\displaystyle F_{5}}
+
+ is composite and so are all other Fermat numbers that have been verified as of 2017.[168] A regular 
+
+
+
+n
+
+
+{\displaystyle n}
+
+-gon is constructible using straightedge and compass if and only if the odd prime factors of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ (if any) are distinct Fermat primes.[167] Likewise, a regular 
+
+
+
+n
+
+
+{\displaystyle n}
+
+-gon may be constructed using straightedge, compass, and an angle trisector if and only if the prime factors of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ are any number of copies of 2 or 3 together with a (possibly empty) set of distinct Pierpont primes, primes of the form 
+
+
+
+
+2
+
+a
+
+
+
+3
+
+b
+
+
++
+1
+
+
+{\displaystyle 2^{a}3^{b}+1}
+
+.[169]
+
+It is possible to partition any convex polygon into 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ smaller convex polygons of equal area and equal perimeter, when 
+
+
+
+n
+
+
+{\displaystyle n}
+
+ is a power of a prime number, but this is not known for other values of 
+
+
+
+n
+
+
+{\displaystyle n}
+
+.[170]
+
+Beginning with the work of Hugh Montgomery and Freeman Dyson in the 1970s, mathematicians and physicists have speculated that the zeros of the Riemann zeta function are connected to the energy levels of quantum systems.[171][172] Prime numbers are also significant in quantum information science, thanks to mathematical structures such as mutually unbiased bases and symmetric informationally complete positive-operator-valued measures.[173][174]
+
+The evolutionary strategy used by cicadas of the genus Magicicada makes use of prime numbers.[175] These insects spend most of their lives as grubs underground. They only pupate and then emerge from their burrows after 7, 13 or 17 years, at which point they fly about, breed, and then die after a few weeks at most. Biologists theorize that these prime-numbered breeding cycle lengths have evolved in order to prevent predators from synchronizing with these cycles.[176][177]
+In contrast, the multi-year periods between flowering in bamboo plants are hypothesized to be smooth numbers, having only small prime numbers in their factorizations.[178]
+
+Prime numbers have influenced many artists and writers.
+The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47  and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".[179]
+
+In his science fiction novel Contact, scientist Carl Sagan suggested that prime factorization could be used as a means of establishing two-dimensional image planes in communications with aliens, an idea that he had first developed informally with American astronomer Frank Drake in 1975.[180] In the novel The Curious Incident of the Dog in the Night-Time by Mark Haddon, the narrator arranges the sections of the story by consecutive prime numbers as a way to convey the mental state of its main character, a mathematically gifted teen with Asperger syndrome.[181] Prime numbers are used as a metaphor for loneliness and isolation in the Paolo Giordano novel The Solitude of Prime Numbers, in which they are portrayed as "outsiders" among integers.[182]

en/4163.html.txt

@@ -0,0 +1,106 @@
+A pseudonym (/ˈsjuːdənɪm/) or alias (/ˈeɪliəs/) is a name that a person or group assumes for a particular purpose, which can differ from their first or true name (orthonym).[1] The term is not used when a new name entirely replaces an individual's own.
+
+Pseudonyms include stage names and user names, ring names, pen names, nicknames, aliases, superhero or villain identities and code names, gamer identifications, and regnal names of emperors, popes, and other monarchs. Historically, they have sometimes taken the form of anagrams, Graecisms, and Latinisations, although there are many other methods of choosing a pseudonym.[2]
+
+Pseudonyms should not be confused with new names that replace old ones and become the individual's full-time name. Pseudonyms are "part-time" names, used only in certain contexts – to provide a more clear-cut separation between one's private and professional lives, to showcase or enhance a particular persona, or to hide an individual's real identity, as with writers' pen names, graffiti artists' tags, resistance fighters' or terrorists' noms de guerre, and computer hackers' handles. Actors, voice-over artists, musicians, and other performers sometimes use stage names, for example, to better channel a relevant energy, gain a greater sense of security and comfort via privacy, more easily avoid troublesome fans/"stalkers", or to mask their ethnic backgrounds.
+
+In some cases, pseudonyms are adopted because they are part of a cultural or organisational tradition: for example devotional names used by members of some religious institutes, and "cadre names" used by Communist party leaders such as Trotsky and Lenin.
+
+A pseudonym may also be used for personal reasons: for example, an individual may prefer to be called or known by a name that differs from their given or legal name, but is not ready to take the numerous steps to get their name legally changed; or an individual may simply feel that the context and content of an exchange offer no reason, legal or otherwise, to provide their given or legal name.
+
+A collective name or collective pseudonym is one shared by two or more persons, for example the co-authors of a work, such as Carolyn Keene, Ellery Queen, Nicolas Bourbaki, or James S. A. Corey.
+
+The term pseudonym is derived from the Greek ψευδώνυμον (pseudṓnymon), literally "false name", from ψεῦδος (pseûdos), "lie, falsehood"[3] and ὄνομα (ónoma), "name".[4] The term alias is a Latin adverb meaning "at another time, elsewhere".[5]
+
+A pseudonym is distinct from an allonym, which is the (real) name of another person, assumed by the author of a work of art.[6] This may occur when someone is ghostwriting a book or play, or in parody, or when using a "front" name, such as by screenwriters blacklisted in Hollywood in the 1950s and 1960s. See also pseudepigraph, for falsely attributed authorship.
+
+Sometimes people change their name in such a manner that the new name becomes permanent and is used by all who know the person. This is not an alias or pseudonym, but in fact a new name. In many countries, including common law countries, a name change can be ratified by a court and become a person's new legal name.
+
+For example, in the 1960s, black civil rights campaigner Malcolm Little changed his surname to "X", to represent his unknown African ancestral name that had been lost when his ancestors were brought to North America as slaves. He then changed his name again to Malik El-Shabazz when he converted to Islam.[citation needed] Likewise some Jews adopted Hebrew family names upon immigrating to Israel, dropping surnames that had been in their families for generations. The politician David Ben-Gurion, for example, was born David Grün in Poland. He adopted his Hebrew name in 1910, when he published his first article in a Zionist journal in Jerusalem.[7] Many transgender people also choose to adopt a new name, typically around the time of their social transitioning, to match their desired gender better than their birth name.[according to whom?]
+
+Businesspersons of ethnic minorities in some parts of the world are sometimes advised by an employer to use a pseudonym that is common or acceptable in that area when conducting business, to overcome racial or religious bias.[8]
+
+Criminals may use aliases, fictitious business names, and dummy corporations (corporate shells) to hide their identity, or to impersonate other persons or entities in order to commit fraud. Aliases and fictitious business names used for dummy corporations may become so complex that, in the words of the Washington Post, "getting to the truth requires a walk down a bizarre labyrinth" and multiple government agencies may become involved to uncover the truth.[9]
+
+A pen name, or "nom de plume" (French for "pen name"), is a pseudonym (sometimes a particular form of the real name) adopted by an author (or on the author's behalf by their publishers).
+
+Some female authors used male pen names, in particular in the 19th century, when writing was a male-dominated profession. The Brontë sisters used pen names for their early work, so as not to reveal their gender (see below) and so that local residents would not know that the books related to people of the neighbourhood. The Brontës used their neighbours as inspiration for characters in many of their books. Anne Brontë's The Tenant of Wildfell Hall (1848) was published under the name Acton Bell, while Charlotte Brontë used the name Currer Bell for Jane Eyre (1847) and Shirley (1849), and Emily Brontë adopted Ellis Bell as cover for Wuthering Heights (1847). Other examples from the nineteenth-century are the novelist Mary Ann Evans (George Eliot) and the French writer Amandine Aurore Lucile Dupin (George Sand). Pseudonyms may also be used due to cultural or organization or political prejudices.
+
+On the other hand, some 20th and 21st-century male romance novelists have used female pen names.[10] A few examples are Brindle Chase, Peter O'Donnell (as Madeline Brent), Christopher Wood (as Penny Sutton and Rosie Dixon), and Hugh C. Rae (as Jessica Sterling).[10]
+
+A pen name may be used if a writer's real name is likely to be confused with the name of another writer or notable individual, or if the real name is deemed unsuitable.
+
+Authors who write both fiction and non-fiction, or in different genres, may use different pen names to avoid confusing their readers. For example, the romance writer Nora Roberts writes mystery novels under the name J.D. Robb.
+
+In some cases, an author may become better known by his pen name than his real name. A famous example is Samuel Clemens, writing as Mark Twain. The British mathematician Charles Dodgson wrote fantasy novels as Lewis Carroll and mathematical treatises under his own name.
+
+Some authors, such as Harold Robbins, use several literary pseudonyms.[11]
+
+Some pen names have been used for long periods, even decades, without the author's true identity being discovered, as with Elena Ferrante and Torsten Krol.
+
+Some pen names are not strictly pseudonyms, as they are simply variants of the authors' actual names. The authors C.L. Moore and S.E. Hinton were female authors who used the initialled forms of their full names, Moore being Catherine Lucille Moore, writing in the 1930s male-dominated science fiction genre, and Hinton, (author of The Outsiders) Susan Eloise Hinton. Star Trek writer D.C. Fontana (Dorothy Catherine) wrote using her own abbreviated name and under the pen names Michael Richards and J. Michael Bingham. Author V.C. Andrews intended to publish under her given name, Virginia Andrews, but was told that, due to a production error, her first novel was being released under the name of "V.C. Andrews"; later she learned that her publisher had in fact done this deliberately. Joanne Kathleen Rowling[12] published the Harry Potter series as J.K. Rowling. Rowling also published the Cormoran Strike series, a series of detective novels including The Cuckoo's Calling under the pseudonym "Robert Galbraith".
+
+Winston Churchill wrote as Winston S. Churchill (from his full surname "Spencer-Churchill" which he did not otherwise use) in an attempt to avoid confusion with an American novelist of the same name. The attempt was not wholly successful – the two are still sometimes confused by booksellers.[13][14]
+
+A pen name may be used specifically to hide the identity of the author, as with exposé books about espionage or crime, or explicit erotic fiction. Some prolific authors adopt a pseudonym to disguise the extent of their published output, e. g. Stephen King writing as Richard Bachman. Co-authors may choose to publish under a collective pseudonym, e. g., P. J. Tracy and Perri O'Shaughnessy. Frederic Dannay and Manfred Lee used the name Ellery Queen as a pen name for their collaborative works and as the name of their main character.[citation needed] Asa Earl Carter, a Southern white segregationist affiliated with the KKK, wrote Western books under a fictional Cherokee persona to imply legitimacy and conceal his history.[15]
+
+"Why do authors choose pseudonyms? It is rarely because they actually hope to stay anonymous forever," mused writer and columnist Russell Smith in his review of the Canadian novel Into That Fire by the pseudonymous M.J. Cates.[16]
+
+A famous case in French literature was Romain Gary. Already a well-known writer, he started publishing books as Émile Ajar to test whether his new books would be well received on their own merits, without the aid of his established reputation. They were: Émile Ajar, like Romain Gary before him, was awarded the prestigious Prix Goncourt by a jury unaware that they were the same person. Similarly, TV actor Ronnie Barker submitted comedy material under the name Gerald Wiley.
+
+A collective pseudonym may represent an entire publishing house, or any contributor to a long-running series, especially with juvenile literature. Examples include Watty Piper, Victor Appleton, Erin Hunter, and Kamiru M. Xhan.
+
+Another use of a pseudonym in literature is to present a story as being written by the fictional characters in the story. The series of novels known as A Series Of Unfortunate Events are written by Daniel Handler under the pen name of Lemony Snicket, a character in the series. This applies also to some of the several 18th-century English and American writers who used the name Fidelia.
+
+An anonymity pseudonym or multiple-use name is a name used by many different people to protect anonymity.[17] It is a strategy that has been adopted by many unconnected radical groups and by cultural groups, where the construct of personal identity has been criticised. This has led to the idea of the "open pop star".
+
+Pseudonyms and acronyms are often employed in medical research to protect subjects' identities through a process known as de-identification.
+
+Nicolaus Copernicus put forward his theory of heliocentrism in the manuscript Commentariolus anonymously.[18] Sophie Germain and William Sealy Gosset used pseudonyms to publish their work in the field of mathematics.[19][20] Satoshi Nakamoto is a pseudonym of a still unknown author or authors' group behind a white paper about bitcoin.[21][22][23][24] In the field of physics, one case of usage of pseudonyms is denounced.[25] Ignazio Ciufolini is accused of publishing two papers on the scientific preprint archive arXiv.org under pseudonyms, each criticizing one of the rivals to LAGEOS, what is argued to be a form of ventriloquism.[26] Such conduct is a violation of arXiv terms of use.[27][28][26]
+
+In Ancien Régime France, a nom de guerre ("war name") would be adopted by each new recruit (or assigned to them by the captain of their company) as they enlisted in the French army. These pseudonyms had an official character and were the predecessor of identification numbers: soldiers were identified by their first names, their family names, and their noms de guerre (e. g. Jean Amarault dit Lafidélité). These pseudonyms were usually related to the soldier's place of origin (e. g. Jean Deslandes dit Champigny, for a soldier coming from a town named Champigny), or to a particular physical or personal trait (e. g. Antoine Bonnet dit Prettaboire, for a soldier prêt à boire, ready to drink). In 1716, a nom de guerre was mandatory for every soldier; officers did not adopt noms de guerre as they considered them derogatory. In daily life, these aliases could replace the real family name.[29]
+
+Noms de guerre were adopted for security reasons by members of the World War II French resistance and Polish resistance. Such pseudonyms are often adopted by military special-forces soldiers, such as members of the SAS and similar units of resistance fighters, terrorists, and guerrillas. This practice hides their identities and may protect their families from reprisals; it may also be a form of dissociation from domestic life. Some well-known men who adopted noms de guerre include Carlos, for Ilich Ramírez Sánchez; Willy Brandt, Chancellor of West Germany; and Subcomandante Marcos, spokesman of the Zapatista Army of National Liberation (EZLN).[citation needed] During Lehi's underground fight against the British in Mandatory Palestine, the organization's commander Yitzchak Shamir (later Prime Minister of Israel) adopted the nom de guerre "Michael", in honour of Ireland's Michael Collins.
+
+Revolutionaries and resistance leaders, such as Lenin, Trotsky, Golda Meir, Philippe Leclerc de Hauteclocque, and Josip Broz Tito, often adopted their noms de guerre as their proper names after the struggle. George Grivas, the Greek-Cypriot EOKA militant, adopted the nom de guerre Digenis (Διγενής). In the French Foreign Legion, recruits can adopt a pseudonym to break with their past lives. Mercenaries have long used "noms de guerre", sometimes even multiple identities, depending on country, conflict and circumstance.[citation needed] Some of the most familiar noms de guerre today are the kunya used by Islamic mujahideen. These take the form of a teknonym, either literal or figurative.
+
+Individuals using a computer online may adopt or be required to use a form of pseudonym known as a "handle" (a term deriving from CB slang), "user name", "login name", "avatar", or, sometimes, "screen name", "gamertag" "IGN (In Game (Nick)Name)" or "nickname". On the Internet, pseudonymous remailers use cryptography that achieves persistent pseudonymity, so that two-way communication can be achieved, and reputations can be established, without linking physical identities to their respective pseudonyms. Aliasing is the use of multiple names for the same data location.
+
+More sophisticated cryptographic systems, such as anonymous digital credentials, enable users to communicate pseudonymously (i. e., by identifying themselves by means of pseudonyms). In well-defined abuse cases, a designated authority may be able to revoke the pseudonyms and reveal the individuals' real identity.[citation needed]
+
+Use of pseudonyms is common among professional eSports players, despite the fact that many professional games are played on LAN.[30]
+
+People seeking privacy often use pseudonyms to make appointments and reservations.[31] Those writing to advice columns in newspapers and magazines may use pseudonyms.[32] Steve Wozniak used a pseudonym when attending the University of California, Berkeley after co-founding Apple Computer, because "I knew I wouldn't have time enough to be an A+ student."[33]
+
+When used by an actor, musician, radio disc jockey, model, or other performer or "show business" personality a pseudonym is called a stage name, or, occasionally, a professional name, or screen name.
+
+Members of a marginalized ethnic or religious group have often adopted stage names, typically changing their surname or entire name to mask their original background.
+
+Stage names are also used to create a more marketable name, as in the case of Creighton Tull Chaney, who adopted the pseudonym Lon Chaney, Jr., a reference to his famous father Lon Chaney, Sr.
+
+Chris Curtis of Deep Purple fame was christened as Christopher Crummey ("crumby" is UK slang for poor quality). In this and similar cases a stage name is adopted simply to avoid an unfortunate pun.
+
+Pseudonyms are also used to comply with the rules of performing arts guilds (Screen Actors Guild (SAG), Writers Guild of America, East (WGA), AFTRA, etc.), which do not allow performers to use an existing name, in order to avoid confusion. For example, these rules required film and television actor Michael Fox to add a middle initial and become Michael J. Fox, to avoid being confused with another actor named Michael Fox. This was also true of author and actress Fannie Flagg, who chose this pseudonym; her real name, Patricia Neal, being the name of another well-known actress; and British actor Stewart Granger, whose real name was James Stewart. The film-making team of Joel and Ethan Coen, for instance, share credit for editing under the alias Roderick Jaynes.[34]
+
+Some stage names are used to conceal a person's identity, such as the pseudonym Alan Smithee, which was used by directors in the Directors Guild of America (DGA) to remove their name from a film they feel was edited or modified beyond their artistic satisfaction. In theatre, the pseudonyms George or Georgina Spelvin, and Walter Plinge are used to hide the identity of a performer, usually when he or she is "doubling" (playing more than one role in the same play).
+
+David Agnew was a name used by the BBC to conceal the identity of a scriptwriter, such as for the Doctor Who serial City of Death, which had three writers, including Douglas Adams, who was at the time of writing the show's Script Editor.[35] In another Doctor Who serial, The Brain of Morbius, writer Terrance Dicks demanded the removal of his name from the credits saying it could go out under a "bland pseudonym".[citation needed][36] This ended up as Robin Bland.[36][37]
+
+Musicians and singers can use pseudonyms to allow artists to collaborate with artists on other labels while avoiding the need to gain permission from their own labels, such as the artist Jerry Samuels, who made songs under Napoleon XIV. Rock singer-guitarist George Harrison, for example, played guitar on Cream's song "Badge" using a pseudonym.[38] In classical music, some record companies issued recordings under a nom de disque in the 1950s and 1960s to avoid paying royalties. A number of popular budget LPs of piano music were released under the pseudonym Paul Procopolis.[citation needed] Another example is that Paul McCartney used his fictional name "Bernerd Webb" for Peter and Gordon's song Woman.[39]
+
+Pseudonyms are used as stage names in heavy metal bands, such as Tracii Guns in LA Guns, Axl Rose and Slash in Guns N' Roses, Mick Mars in Mötley Crüe, Dimebag Darrell in Pantera, or C.C. Deville in Poison. Some such names have additional meanings, like that of Brian Hugh Warner, more commonly known as Marilyn Manson: Marilyn coming from Marilyn Monroe and Manson from convicted serial killer Charles Manson. Jacoby Shaddix of Papa Roach went under the name "Coby Dick" during the Infest era. He changed back to his birth name when lovehatetragedy was released.
+
+David Johansen, front man for the hard rock band New York Dolls, recorded and performed pop and lounge music under the pseudonym Buster Poindexter in the late 1980s and early 1990s. The music video for Poindexter's debt single, Hot Hot Hot, opens with a monologue from Johansen where he notes his time with the New York Dolls and explains his desire to create more sophisticated music.
+
+Ross Bagdasarian, Sr., creator of Alvin and the Chipmunks, wrote original songs, arranged, and produced the records under his real name, but performed on them as David Seville. He also wrote songs as Skipper Adams. Danish pop pianist Bent Fabric, whose full name is Bent Fabricius-Bjerre, wrote his biggest instrumental hit "Alley Cat" as Frank Bjorn.
+
+For a time, the musician Prince used an unpronounceable "Love Symbol" as a pseudonym ("Prince" is his actual first name rather than a stage name). He wrote the song "Sugar Walls" for Sheena Easton as "Alexander Nevermind" and "Manic Monday" for The Bangles as "Christopher Tracy". (He also produced albums early in his career as "Jamie Starr").
+
+Many Italian-American singers have used stage names, as their birth names were difficult to pronounce or considered too ethnic for American tastes. Singers changing their names included Dean Martin (born Dino Paul Crocetti), Connie Francis (born Concetta Franconero), Frankie Valli (born Francesco Castelluccio), Tony Bennett (born Anthony Benedetto), and Lady Gaga (born Stefani Germanotta)
+
+In 2009, the British rock band Feeder briefly changed its name to Renegades so it could play a whole show featuring a set list in which 95 per cent of the songs played were from their forthcoming new album of the same name, with none of their singles included. Front man Grant Nicholas felt that if they played as Feeder, there would be uproar over him not playing any of the singles, so used the pseudonym as a hint. A series of small shows were played in 2010, at 250- to 1,000-capacity venues with the plan not to say who the band really are and just announce the shows as if they were a new band.
+
+In many cases, hip-hop and rap artists prefer to use pseudonyms that represents some variation of their name, personality, or interests. Examples include Iggy Azalea (her stage name is a combination of her dog's name, Iggy, and her home street in Mullumbimby, Azalea Street), Ol' Dirty Bastard (known under at least six aliases), Diddy (previously known at various times as Puffy, P. Diddy, and Puff Daddy), Ludacris, Flo Rida (whose stage name is a tribute to his home state, Florida), British-Jamaican hip-hop artist Stefflon Don (real name Stephanie Victoria Allen), LL Cool J, and Chingy. Black metal artists also adopt pseudonyms, usually symbolizing dark values, such as Nocturno Culto, Gaahl, Abbath, and Silenoz. In punk and hardcore punk, singers and band members often replace real names with tougher-sounding stage names such as Sid Vicious (real name John Simon Ritchie) of the late 1970s band Sex Pistols and "Rat" of the early 1980s band The Varukers and the 2000s re-formation of Discharge. The punk rock band The Ramones had every member take the last name of Ramone.[citation needed]
+
+Henry John Deutschendorf Jr., an American singer-songwriter, used the stage name John Denver. The Australian country musician born Robert Lane changed his name to Tex Morton. Reginald Kenneth Dwight legally changed his name in 1972 to Elton John.
+

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+
+
+Binomial nomenclature ("two-term naming system"), also called binominal nomenclature ("two-name naming system") or binary nomenclature, is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, although they can be based on words from other languages. Such a name is called a binomial name (which may be shortened to just "binomial"), a binomen, binominal name or a scientific name; more informally it is also called a Latin name.
+
+The first part of the name – the generic name – identifies the genus to which the species belongs, while the second part – the specific name or specific epithet – identifies the species within the genus. For example, humans belong to the genus Homo and within this genus to the species Homo sapiens. Tyrannosaurus rex is probably the most widely known binomial.[1] The formal introduction of this system of naming species is credited to Carl Linnaeus, effectively beginning with his work Species Plantarum in 1753.[2] But Gaspard Bauhin, in as early as 1622, had introduced in his book Pinax theatri botanici (English, Illustrated exposition of plants) many names of genera that were later adopted by Linnaeus.[3]
+
+The application of binomial nomenclature is now governed by various internationally agreed codes of rules, of which the two most important are the International Code of Zoological Nomenclature (ICZN) for animals and the International Code of Nomenclature for algae, fungi, and plants (ICNafp). Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences, both in the terminology they use and in their precise rules.
+
+In modern usage, the first letter of the first part of the name, the genus, is always capitalized in writing, while that of the second part is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized when a binomial name occurs in normal text (or underlined in handwriting). Thus the binomial name of the annual phlox (named after botanist Thomas Drummond) is now written as Phlox drummondii.
+
+In scientific works, the authority for a binomial name is usually given, at least when it is first mentioned, and the date of publication may be specified.
+
+The name is composed of two word-forming elements: "bi", a Latin prefix for two, and "-nomial", literally translated as "name". The word "binomium" was used in Medieval Latin to signify one of the terms in a two-term binomial expression in mathematics.[4]
+
+Prior to the adoption of the modern binomial system of naming species, a scientific name consisted of a generic name combined with a specific name that was from one to several words long. Together they formed a system of polynomial nomenclature.[5] These names had two separate functions. First, to designate or label the species, and second, to be a diagnosis or description; however these two goals were eventually found to be incompatible.[6] In a simple genus, containing only two species, it was easy to tell them apart with a one-word genus and a one-word specific name; but as more species were discovered, the names necessarily became longer and unwieldy, for instance, Plantago foliis ovato-lanceolatus pubescentibus, spica cylindrica, scapo tereti ("plantain with pubescent ovate-lanceolate leaves, a cylindric spike and a terete scape"), which we know today as Plantago media.
+
+Such "polynomial names" may sometimes look like binomials, but are significantly different. For example, Gerard's herbal (as amended by Johnson) describes various kinds of spiderwort: "The first is called Phalangium ramosum, Branched Spiderwort; the second, Phalangium non ramosum, Unbranched Spiderwort. The other ... is aptly termed Phalangium Ephemerum Virginianum, Soon-Fading Spiderwort of Virginia".[7] The Latin phrases are short descriptions, rather than identifying labels.
+
+The Bauhins, in particular Caspar Bauhin (1560–1624), took some important steps towards the binomial system, by pruning the Latin descriptions, in many cases to two words.[8] The adoption by biologists of a system of strictly binomial nomenclature is due to Swedish botanist and physician Carl Linnaeus (1707–1778).  It was in Linnaeus's 1753 Species Plantarum that he began consistently using a one-word "trivial name" (nomen triviale) after a generic name (genus name) in a system of binomial nomenclature.[9] Trivial names had already appeared in his Critica Botanica (1737) and Philosophia Botanica (1751). This trivial name is what is now known as a specific epithet (ICNafp) or specific name (ICZN).[9] The Bauhins' genus names were retained in many of these, but the descriptive part was reduced to a single word.
+
+Linnaeus's trivial names introduced an important new idea, namely that the function of a name could simply be to give a species a unique label. This meant that the name no longer need be descriptive; for example both parts could be derived from the names of people. Thus Gerard's Phalangium ephemerum virginianum became Tradescantia virginiana, where the genus name honoured John Tradescant the Younger,[note 1] an English botanist and gardener.[10] A bird in the parrot family was named Psittacus alexandri, meaning "Alexander's parrot", after Alexander the Great, whose armies introduced eastern parakeets to Greece.[11] Linnaeus's trivial names were much easier to remember and use than the parallel polynomial names and eventually replaced them.[2]
+
+The value of the binomial nomenclature system derives primarily from its economy, its widespread use, and the uniqueness and stability of names it generally favors:
+
+Binomial nomenclature for species has the effect that when a species is moved from one genus to another, sometimes the specific name or epithet must be changed as well. This may happen because the specific name is already used in the new genus, or to agree in gender with the new genus. Some biologists have argued for the combination of the genus name and specific epithet into a single unambiguous name, or for the use of uninomials (as used in nomenclature of ranks above species).[18]
+
+Because binomials are unique only within a kingdom, it is possible for two or more species to share the same binomial if they occur in different kingdoms. At least 1241 instances of such binomial duplication occur.[19][20]
+
+Nomenclature (including binomial nomenclature) is not the same as classification, although the two are related. Classification is the ordering of items into groups based on similarities or differences; in biological classification, species are one of the kinds of item to be classified.[21] In principle, the names given to species could be completely independent of their classification. This is not the case for binomial names, since the first part of a binomial is the name of the genus into which the species is placed. Above the rank of genus, binomial nomenclature and classification are partly independent; for example, a species retains its binomial name if it is moved from one family to another or from one order to another, unless it better fits a different genus in the same or different family, or it is split from its old genus and placed in a newly created genus. The independence is only partial since the names of families and other higher taxa are usually based on genera.[citation needed]
+
+Taxonomy includes both nomenclature and classification. Its first stages (sometimes called "alpha taxonomy") are concerned with finding, describing and naming species of living or fossil organisms.[22] Binomial nomenclature is thus an important part of taxonomy as it is the system by which species are named. Taxonomists are also concerned with classification, including its principles, procedures and rules.[23]
+
+A complete binomial name is always treated grammatically as if it were a phrase in the Latin language (hence the common use of the term "Latin name" for a binomial name). However, the two parts of a binomial name can each be derived from a number of sources, of which Latin is only one. These include:
+
+The first part of the name, which identifies the genus, must be a word which can be treated as a Latin singular noun in the nominative case. It must be unique within each kingdom, but can be repeated between kingdoms. Thus Huia recurvata is an extinct species of plant, found as fossils in Yunnan, China,[33] whereas Huia masonii is a species of frog found in Java, Indonesia.[34]
+
+The second part of the name, which identifies the species within the genus, is also treated grammatically as a Latin word. It can have one of a number of forms:
+
+Whereas the first part of a binomial name must be unique within a kingdom, the second part is quite commonly used in two or more genera (as is shown by examples of hodgsonii above). The full binomial name must be unique within a kingdom.
+
+From the early 19th century onwards it became ever more apparent that a body of rules was necessary to govern scientific names. In the course of time these became nomenclature codes. The International Code of Zoological Nomenclature (ICZN) governs the naming of animals,[36] the International Code of Nomenclature for algae, fungi, and plants (ICNafp) that of plants (including cyanobacteria), and the International Code of Nomenclature of Bacteria (ICNB) that of bacteria (including Archaea). Virus names are governed by the International Committee on Taxonomy of Viruses (ICTV), a taxonomic code, which determines taxa as well as names. These codes differ in certain ways, e.g.:
+
+Unifying the different codes into a single code, the "BioCode", has been suggested, although implementation is not in sight. (There is also a code in development for a different system of classification which does not use ranks, but instead names clades. This is called the PhyloCode.)
+
+As noted above, there are some differences between the codes in the way in which binomials can be formed; for example the ICZN allows both parts to be the same, while the ICNafp does not. Another difference is in the way in which personal names are used in forming specific names or epithets. The ICNafp sets out precise rules by which a personal name is to be converted to a specific epithet. In particular, names ending in a consonant (but not "er") are treated as first being converted into Latin by adding "-ius" (for a man) or "-ia" (for a woman), and then being made genitive (i.e. meaning "of that person or persons"). This produces specific epithets like lecardii for Lecard (male), wilsoniae for Wilson (female), and brauniarum for the Braun sisters.[41] By contrast the ICZN does not require the intermediate creation of a Latin form of a personal name, allowing the genitive ending to be added directly to the personal name.[42] This explains the difference between the names of  the plant Magnolia hodgsonii and the bird Anthus hodgsoni. Furthermore, the ICNafp requires names not published in the form required by the code to be corrected to conform to it,[43] whereas the ICZN is more protective of the form used by the original author.[44]
+
+By tradition, the binomial names of species are usually typeset in italics; for example, Homo sapiens.[45] Generally, the binomial should be printed in a font style different from that used in the normal text; for example, "Several more Homo sapiens fossils were discovered." When handwritten, a binomial name should be underlined; for example, Homo sapiens.[46]
+
+The first part of the binomial, the genus name, is always written with an initial capital letter. In current usage, the second part is never written with an initial capital.[47][48] Older sources, particularly botanical works published before the 1950s, use a different convention. If the second part of the name is derived from a proper noun, e.g. the name of a person or place, a capital letter was used. Thus the modern form Berberis darwinii was written as Berberis Darwinii. A capital was also used when the name is formed by two nouns in apposition, e.g. Panthera Leo or Centaurea Cyanus.[49][note 3]
+
+When used with a common name, the scientific name often follows in parentheses, although this varies with publication.[51] For example, "The house sparrow (Passer domesticus) is decreasing in Europe."
+
+The binomial name should generally be written in full. The exception to this is when several species from the same genus are being listed or discussed in the same paper or report, or the same species is mentioned repeatedly; in which case the genus is written in full when it is first used, but may then be abbreviated to an initial (and a period/full stop).[52] For example, a list of members of the genus Canis might be written as "Canis lupus, C. aureus, C. simensis". In rare cases, this abbreviated form has spread to more general use; for example, the bacterium Escherichia coli is often referred to as just E. coli, and Tyrannosaurus rex is perhaps even better known simply as T. rex, these two both often appearing in this form in popular writing even where the full genus name has not already been given.
+
+The abbreviation "sp." is used when the actual specific name cannot or need not be specified. The abbreviation "spp." (plural) indicates "several species". These abbreviations are not italicised (or underlined).[53] For example: "Canis sp." means "an unspecified species of the genus Canis", while "Canis spp." means "two or more species of the genus Canis" (the abbreviations "sp." and "spp." can easily be confused with the abbreviations "ssp." (zoology) or "subsp." (botany), plurals "sspp." or "subspp.", referring to one or more subspecies. See trinomen (zoology) and infraspecific name).
+
+The abbreviation "cf." (i.e. confer in Latin) is used to compare individuals/taxa with known/described species. Conventions for use of the "cf." qualifier vary.[54] In paleontology, it is typically used when the identification is not confirmed.[55] For example, "Corvus cf. nasicus"  was used to indicate "a fossil bird similar to the Cuban crow but not certainly identified as this species".[56] In molecular systematics papers, "cf." may be used to indicate one or more undescribed species assumed related to a described species. For example, in a paper describing the phylogeny of small benthic freshwater fish called darters, five undescribed putative species (Ozark, Sheltowee, Wildcat, Ihiyo, and Mamequit darters), notable for brightly colored nuptial males with distinctive color patterns,[57] were referred to as "Etheostoma cf. spectabile" because they had been viewed as related to, but distinct from, Etheostoma spectabile (orangethroat darter).[58] This view was supported in varying degrees by DNA analysis. The somewhat informal use of taxa names with qualifying abbreviations is referred to as open nomenclature and it is not subject to strict usage codes.
+
+In some contexts the dagger symbol ("†") may be used before or after the binomial name to indicate that the species is extinct.
+
+In scholarly texts, at least the first or main use of the binomial name is usually followed by the "authority" – a way of designating the scientist(s) who first published the name. The authority is written in slightly different ways in zoology and botany. For names governed by the ICZN the surname is usually written in full together with the date (normally only the year) of publication. The ICZN recommends that the "original author and date of a name should be cited at least once in each work dealing with the taxon denoted by that name."[59] For names governed by the ICNafp the name is generally reduced to a standard abbreviation and the date omitted. The International Plant Names Index maintains an approved list of botanical author abbreviations. Historically, abbreviations were used in zoology too.
+
+When the original name is changed, e.g. the species is moved to a different genus, both codes use parentheses around the original authority; the ICNafp also requires the person who made the change to be given. In the ICNafp, the original name is then called the basionym. Some examples:
+
+Binomial nomenclature, as described here, is a system for naming species. Implicitly it includes a system for naming genera, since the first part of the name of the species is a genus name. In a classification system based on ranks there are also ways of naming ranks above the level of genus and below the level of species. Ranks above genus (e.g., family, order, class) receive one-part names, which are conventionally not written in italics. Thus the house sparrow, Passer domesticus, belongs to the family Passeridae. Family names are normally based on genus names, although the endings used differ between zoology and botany.
+
+Ranks below species receive three-part names, conventionally written in italics like the names of species. There are significant differences between the ICZN and the ICNafp. In zoology, the only rank below species is subspecies and the name is written simply as three parts (a trinomen). Thus one of the subspecies of the olive-backed pipit is Anthus hodgsoni berezowskii. In botany, there are many ranks below species and although the name itself is written in three parts, a "connecting term" (not part of the name) is needed to show the rank. Thus the American black elder is Sambucus nigra subsp. canadensis; the white-flowered form of the ivy-leaved cyclamen is Cyclamen hederifolium f. albiflorum.

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+A noun can co-occur with an article or an attributive adjective. Verbs and adjectives cannot. In the following, an asterisk (*) in front of an example means that this example is ungrammatical.
+
+A noun (from Latin nōmen, literally 'name')[1] is a word that functions as the name of some specific thing or set of things, such as living creatures, objects, places, actions, qualities, states of existence, or ideas.[2][note 1] However, noun is not a semantic category, so that it cannot be characterized in terms of its meaning. Thus, actions and states of existence can also be expressed by verbs, qualities by adjectives, and places by adverbs. Linguistically, a noun is a member of a large, open part of speech whose members can occur as the main word in the subject of a clause, the object of a verb, or the object of a preposition.[3]
+
+Lexical categories (parts of speech) are defined in terms of the ways in which their members combine with other kinds of expressions.  The syntactic rules for nouns differ from language to language. In English, nouns are those words which can occur with articles and attributive adjectives and can function as the head of a noun phrase. "As far as we know, every language makes a grammatical distinction that looks like a noun verb distinction."[4]
+
+Word classes (parts of speech) were described by Sanskrit grammarians from at least the 5th century BC. In Yāska's Nirukta, the noun (nāma) is one of the four main categories of words defined.[5]
+
+The Ancient Greek equivalent was ónoma (ὄνομα), referred to by Plato in the Cratylus dialog, and later listed as one of the eight parts of speech in The Art of Grammar, attributed to Dionysius Thrax (2nd century BC). The term used in Latin grammar was nōmen. All of these terms for "noun" were also words meaning "name".[6] The English word noun is derived from the Latin term, through the Anglo-Norman noun.
+
+The word classes were defined partly by the grammatical forms that they take. In Sanskrit, Greek and Latin, for example, nouns are categorized by gender and inflected for case and number. Because adjectives share these three grammatical categories, adjectives are placed in the same class as nouns.
+
+Similarly, the Latin nōmen includes both nouns (substantives) and adjectives, as originally did the English word noun, the two types being distinguished as nouns substantive and nouns adjective (or substantive nouns and adjective nouns, or short substantives and adjectives). (The word nominal is now sometimes used to denote a class that includes both nouns and adjectives.)
+
+Many European languages use a cognate of the word substantive as the basic term for noun (for example, Spanish sustantivo, "noun"). Nouns in the dictionaries of such languages are demarked by the abbreviation s. or sb. instead of n., which may be used for proper nouns or neuter nouns instead. In English, some modern authors use the word substantive to refer to a class that includes both nouns (single words) and noun phrases (multiword units, also called noun equivalents).[7] It can also be used as a counterpart to attributive when distinguishing between a noun being used as the head (main word) of a noun phrase and a noun being used as a noun adjunct. For example, the noun knee can be said to be used substantively in my knee hurts, but attributively in the patient needed knee replacement.
+
+Nouns have sometimes been defined in terms of the grammatical categories to which they are subject (classed by gender, inflected for case and number). Such definitions tend to be language-specific, since nouns do not have the same categories in all languages.
+
+Nouns are frequently defined, particularly in informal contexts, in terms of their semantic properties (their meanings). Nouns are described as words that refer to a person, place, thing, event, substance, quality, quantity, etc. However this type of definition has been criticized by contemporary linguists as being uninformative.[8]
+
+There have been offered several examples of English-language nouns which do not have any reference: drought, enjoyment, finesse, behalf (as found in on behalf of), dint (in dint of), and sake (for the sake of).[9][10][11] Moreover, there may be a relationship similar to reference in the case of other parts of speech: the verbs to rain or to mother; many adjectives, like red; and there is little difference between the adverb gleefully and the noun-based phrase with glee.[note 2]
+
+There are placeholder names, such as the legal fiction reasonable person (whose existence is not in question), an experimental artifact, or personifications such as gremlin.
+
+Linguists often prefer to define nouns (and other lexical categories) in terms of their formal properties. These include morphological information, such as what prefixes or suffixes they take, and also their syntax – how they combine with other words and expressions of particular types. Such definitions may nonetheless still be language-specific since syntax as well as morphology varies between languages. For example, in English, it might be noted that nouns are words that can co-occur with definite articles (as stated at the start of this article), but this would not apply in Russian, which has no definite articles.
+
+There have been several attempts, sometimes controversial, to produce a stricter definition of nouns on a semantic basis. Some of these are referenced in the § Further reading section below.
+
+In some languages, genders are assigned to nouns, such as masculine, feminine and neuter. The gender of a noun (as well as its number and case, where applicable) will often entail agreement in words that modify or are related to it. For example, in French, the singular form of the definite article is le with masculine nouns and la with feminines; adjectives and certain verb forms also change (with the addition of -e with feminines). Grammatical gender often correlates with the form of the noun and the inflection pattern it follows; for example, in both Italian and Russian most nouns ending -a are feminine. Gender can also correlate with the sex of the noun's referent, particularly in the case of nouns denoting people (and sometimes animals). Nouns arguably do not have gender in Modern English, although many of them denote people or animals of a specific sex (or social gender), and pronouns that refer to nouns must take the appropriate gender for that noun. (The girl lost her spectacles.)
+
+A proper noun or proper name is a noun representing unique entities (such as India, Pegasus, Jupiter, Confucius, or Pequod), as distinguished from common nouns, which describe a class of entities (such as country, animal, planet, person or ship).[12]
+
+Count nouns or countable nouns are common nouns that can take a plural, can combine with numerals or counting quantifiers (e.g., one, two, several, every, most), and can take an indefinite article such as a or an (in languages which have such articles). Examples of count nouns are chair, nose, and occasion.
+
+Mass nouns or uncountable (or non-count) nouns differ from count nouns in precisely that respect: they cannot take plurals or combine with number words or the above type of quantifiers.  For example, it is not possible to refer to a furniture or three furnitures. This is true even though the pieces of furniture comprising furniture could be counted. Thus the distinction between mass and count nouns should not be made in terms of what sorts of things the nouns refer to, but rather in terms of how the nouns present these entities.[13][14]
+
+Many nouns have both countable and uncountable uses; for example, soda is countable in "give me three sodas", but uncountable in "he likes soda".
+
+Collective nouns are nouns that – even when they are inflected for the singular – refer to groups consisting of more than one individual or entity. Examples include committee, government, and police. In English these nouns may be followed by a singular or a plural verb and referred to by a singular or plural pronoun,  the singular being generally preferred when referring to the body as a unit and the plural often being preferred, especially in British English, when emphasizing the individual members.[15] Examples of acceptable and unacceptable use given by Gowers in Plain Words include:[15]
+
+Concrete nouns refer to physical entities that can, in principle at least (i.e. different schools of philosophy and sciences may question the assumption, but, for the most part, people agree to the existence of something. E.g. a rock, a tree,  universe), be observed by at least one of the senses (for instance, chair, apple, Janet or atom). Abstract nouns, on the other hand, refer to abstract objects; that is, ideas or concepts (such as justice or hatred). While this distinction is sometimes exclusive, some nouns have multiple senses, including both concrete and abstract ones: consider, for example, the noun art, which usually refers to a concept (e.g., Art is an important element of human culture.) but which can refer to a specific artwork in certain contexts (e.g., I put my daughter's art up on the fridge.)
+
+Some abstract nouns developed etymologically by figurative extension from literal roots. These include drawback, fraction, holdout and uptake. Similarly, some nouns have both abstract and concrete senses, with the latter having developed by figurative extension from the former. These include view, filter, structure and key.
+
+In English, many abstract nouns are formed by adding a suffix (-ness, -ity, -ion) to adjectives or verbs. Examples are happiness (from the adjective happy), circulation (from the verb circulate) and serenity (from the adjective serene).
+
+Some languages, such as the Awa language spoken in Papua New Guinea,[16] refer to nouns differently, depending on how ownership is being given for the given noun. This can be broken into two categories: alienable and inalienable. An alienable noun is something that does not belong to a person indefinitely. Inalienable nouns, on the other hand, refer to something that is possessed definitely. Examples of alienable nouns would be a tree or a shirt or roads. Examples of inalienable nouns would be a father or shadow or hair.
+
+The Pingelapese language uses a distinction between nouns.[17] There are several classifier forms: The first is for objects which tend to be pretty large in size and not being a favourite possession (tree or shirt), and the second is for small, controllable, favourite objects like dogs, books or spears. A third form would be set aside for food objects like bananas, oranges or fish. Drinks like water or coconut liquor also have classifier forms. A fifth classifier would be designated for things that are to be chewed but not fully consumed. The only example of this was from the book Papers in Kosraean and Ponapeic: the fruit, pandanus, is chewed for the sweet/bitter juice, but what remains after consuming the juice discarded. The 6th classifier forms are set aside for ways of transportation (bikes, canoes, and boats). The last two classifiers are designated for land and houses.
+
+A noun phrase is a phrase based on a noun, pronoun, or other noun-like words (nominal) optionally accompanied by modifiers such as determiners and adjectives. A noun phrase functions within a clause or sentence in a role such as that of subject, object, or complement of a verb or preposition. For example, in the sentence "The black cat sat on a dear friend of mine", the noun phrase the black cat serves as the subject, and the noun phrase a dear friend of mine serves as the complement of the preposition on.
+
+Nouns and noun phrases can typically be replaced by pronouns, such as he, it, which, and those, in order to avoid repetition or explicit identification, or for other reasons. For example, in the sentence Gareth thought that he was weird, the word he is a pronoun standing in place of the person's name. The word one can replace parts of noun phrases, and it sometimes stands in for a noun.  An example is given below:
+
+But one can also stand in for larger parts of a noun phrase. For example, in the following example, one can stand in for new car.
+
+Nominalization is a process whereby a word that belongs to another part of speech comes to be used as a noun.
+In French and Spanish, for example, adjectives frequently act as nouns referring to people who have the characteristics denoted by the adjective. This sometimes happens in English as well, as in the following examples:
+
+For definitions of nouns based on the concept of "identity criteria":
+
+For more on identity criteria:
+
+For the concept that nouns are "prototypically referential":
+
+For an attempt to relate the concepts of identity criteria and prototypical referentiality:
+
+Understanding nouns in the context of WordNet:

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+
+
+Binomial nomenclature ("two-term naming system"), also called binominal nomenclature ("two-name naming system") or binary nomenclature, is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, although they can be based on words from other languages. Such a name is called a binomial name (which may be shortened to just "binomial"), a binomen, binominal name or a scientific name; more informally it is also called a Latin name.
+
+The first part of the name – the generic name – identifies the genus to which the species belongs, while the second part – the specific name or specific epithet – identifies the species within the genus. For example, humans belong to the genus Homo and within this genus to the species Homo sapiens. Tyrannosaurus rex is probably the most widely known binomial.[1] The formal introduction of this system of naming species is credited to Carl Linnaeus, effectively beginning with his work Species Plantarum in 1753.[2] But Gaspard Bauhin, in as early as 1622, had introduced in his book Pinax theatri botanici (English, Illustrated exposition of plants) many names of genera that were later adopted by Linnaeus.[3]
+
+The application of binomial nomenclature is now governed by various internationally agreed codes of rules, of which the two most important are the International Code of Zoological Nomenclature (ICZN) for animals and the International Code of Nomenclature for algae, fungi, and plants (ICNafp). Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences, both in the terminology they use and in their precise rules.
+
+In modern usage, the first letter of the first part of the name, the genus, is always capitalized in writing, while that of the second part is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized when a binomial name occurs in normal text (or underlined in handwriting). Thus the binomial name of the annual phlox (named after botanist Thomas Drummond) is now written as Phlox drummondii.
+
+In scientific works, the authority for a binomial name is usually given, at least when it is first mentioned, and the date of publication may be specified.
+
+The name is composed of two word-forming elements: "bi", a Latin prefix for two, and "-nomial", literally translated as "name". The word "binomium" was used in Medieval Latin to signify one of the terms in a two-term binomial expression in mathematics.[4]
+
+Prior to the adoption of the modern binomial system of naming species, a scientific name consisted of a generic name combined with a specific name that was from one to several words long. Together they formed a system of polynomial nomenclature.[5] These names had two separate functions. First, to designate or label the species, and second, to be a diagnosis or description; however these two goals were eventually found to be incompatible.[6] In a simple genus, containing only two species, it was easy to tell them apart with a one-word genus and a one-word specific name; but as more species were discovered, the names necessarily became longer and unwieldy, for instance, Plantago foliis ovato-lanceolatus pubescentibus, spica cylindrica, scapo tereti ("plantain with pubescent ovate-lanceolate leaves, a cylindric spike and a terete scape"), which we know today as Plantago media.
+
+Such "polynomial names" may sometimes look like binomials, but are significantly different. For example, Gerard's herbal (as amended by Johnson) describes various kinds of spiderwort: "The first is called Phalangium ramosum, Branched Spiderwort; the second, Phalangium non ramosum, Unbranched Spiderwort. The other ... is aptly termed Phalangium Ephemerum Virginianum, Soon-Fading Spiderwort of Virginia".[7] The Latin phrases are short descriptions, rather than identifying labels.
+
+The Bauhins, in particular Caspar Bauhin (1560–1624), took some important steps towards the binomial system, by pruning the Latin descriptions, in many cases to two words.[8] The adoption by biologists of a system of strictly binomial nomenclature is due to Swedish botanist and physician Carl Linnaeus (1707–1778).  It was in Linnaeus's 1753 Species Plantarum that he began consistently using a one-word "trivial name" (nomen triviale) after a generic name (genus name) in a system of binomial nomenclature.[9] Trivial names had already appeared in his Critica Botanica (1737) and Philosophia Botanica (1751). This trivial name is what is now known as a specific epithet (ICNafp) or specific name (ICZN).[9] The Bauhins' genus names were retained in many of these, but the descriptive part was reduced to a single word.
+
+Linnaeus's trivial names introduced an important new idea, namely that the function of a name could simply be to give a species a unique label. This meant that the name no longer need be descriptive; for example both parts could be derived from the names of people. Thus Gerard's Phalangium ephemerum virginianum became Tradescantia virginiana, where the genus name honoured John Tradescant the Younger,[note 1] an English botanist and gardener.[10] A bird in the parrot family was named Psittacus alexandri, meaning "Alexander's parrot", after Alexander the Great, whose armies introduced eastern parakeets to Greece.[11] Linnaeus's trivial names were much easier to remember and use than the parallel polynomial names and eventually replaced them.[2]
+
+The value of the binomial nomenclature system derives primarily from its economy, its widespread use, and the uniqueness and stability of names it generally favors:
+
+Binomial nomenclature for species has the effect that when a species is moved from one genus to another, sometimes the specific name or epithet must be changed as well. This may happen because the specific name is already used in the new genus, or to agree in gender with the new genus. Some biologists have argued for the combination of the genus name and specific epithet into a single unambiguous name, or for the use of uninomials (as used in nomenclature of ranks above species).[18]
+
+Because binomials are unique only within a kingdom, it is possible for two or more species to share the same binomial if they occur in different kingdoms. At least 1241 instances of such binomial duplication occur.[19][20]
+
+Nomenclature (including binomial nomenclature) is not the same as classification, although the two are related. Classification is the ordering of items into groups based on similarities or differences; in biological classification, species are one of the kinds of item to be classified.[21] In principle, the names given to species could be completely independent of their classification. This is not the case for binomial names, since the first part of a binomial is the name of the genus into which the species is placed. Above the rank of genus, binomial nomenclature and classification are partly independent; for example, a species retains its binomial name if it is moved from one family to another or from one order to another, unless it better fits a different genus in the same or different family, or it is split from its old genus and placed in a newly created genus. The independence is only partial since the names of families and other higher taxa are usually based on genera.[citation needed]
+
+Taxonomy includes both nomenclature and classification. Its first stages (sometimes called "alpha taxonomy") are concerned with finding, describing and naming species of living or fossil organisms.[22] Binomial nomenclature is thus an important part of taxonomy as it is the system by which species are named. Taxonomists are also concerned with classification, including its principles, procedures and rules.[23]
+
+A complete binomial name is always treated grammatically as if it were a phrase in the Latin language (hence the common use of the term "Latin name" for a binomial name). However, the two parts of a binomial name can each be derived from a number of sources, of which Latin is only one. These include:
+
+The first part of the name, which identifies the genus, must be a word which can be treated as a Latin singular noun in the nominative case. It must be unique within each kingdom, but can be repeated between kingdoms. Thus Huia recurvata is an extinct species of plant, found as fossils in Yunnan, China,[33] whereas Huia masonii is a species of frog found in Java, Indonesia.[34]
+
+The second part of the name, which identifies the species within the genus, is also treated grammatically as a Latin word. It can have one of a number of forms:
+
+Whereas the first part of a binomial name must be unique within a kingdom, the second part is quite commonly used in two or more genera (as is shown by examples of hodgsonii above). The full binomial name must be unique within a kingdom.
+
+From the early 19th century onwards it became ever more apparent that a body of rules was necessary to govern scientific names. In the course of time these became nomenclature codes. The International Code of Zoological Nomenclature (ICZN) governs the naming of animals,[36] the International Code of Nomenclature for algae, fungi, and plants (ICNafp) that of plants (including cyanobacteria), and the International Code of Nomenclature of Bacteria (ICNB) that of bacteria (including Archaea). Virus names are governed by the International Committee on Taxonomy of Viruses (ICTV), a taxonomic code, which determines taxa as well as names. These codes differ in certain ways, e.g.:
+
+Unifying the different codes into a single code, the "BioCode", has been suggested, although implementation is not in sight. (There is also a code in development for a different system of classification which does not use ranks, but instead names clades. This is called the PhyloCode.)
+
+As noted above, there are some differences between the codes in the way in which binomials can be formed; for example the ICZN allows both parts to be the same, while the ICNafp does not. Another difference is in the way in which personal names are used in forming specific names or epithets. The ICNafp sets out precise rules by which a personal name is to be converted to a specific epithet. In particular, names ending in a consonant (but not "er") are treated as first being converted into Latin by adding "-ius" (for a man) or "-ia" (for a woman), and then being made genitive (i.e. meaning "of that person or persons"). This produces specific epithets like lecardii for Lecard (male), wilsoniae for Wilson (female), and brauniarum for the Braun sisters.[41] By contrast the ICZN does not require the intermediate creation of a Latin form of a personal name, allowing the genitive ending to be added directly to the personal name.[42] This explains the difference between the names of  the plant Magnolia hodgsonii and the bird Anthus hodgsoni. Furthermore, the ICNafp requires names not published in the form required by the code to be corrected to conform to it,[43] whereas the ICZN is more protective of the form used by the original author.[44]
+
+By tradition, the binomial names of species are usually typeset in italics; for example, Homo sapiens.[45] Generally, the binomial should be printed in a font style different from that used in the normal text; for example, "Several more Homo sapiens fossils were discovered." When handwritten, a binomial name should be underlined; for example, Homo sapiens.[46]
+
+The first part of the binomial, the genus name, is always written with an initial capital letter. In current usage, the second part is never written with an initial capital.[47][48] Older sources, particularly botanical works published before the 1950s, use a different convention. If the second part of the name is derived from a proper noun, e.g. the name of a person or place, a capital letter was used. Thus the modern form Berberis darwinii was written as Berberis Darwinii. A capital was also used when the name is formed by two nouns in apposition, e.g. Panthera Leo or Centaurea Cyanus.[49][note 3]
+
+When used with a common name, the scientific name often follows in parentheses, although this varies with publication.[51] For example, "The house sparrow (Passer domesticus) is decreasing in Europe."
+
+The binomial name should generally be written in full. The exception to this is when several species from the same genus are being listed or discussed in the same paper or report, or the same species is mentioned repeatedly; in which case the genus is written in full when it is first used, but may then be abbreviated to an initial (and a period/full stop).[52] For example, a list of members of the genus Canis might be written as "Canis lupus, C. aureus, C. simensis". In rare cases, this abbreviated form has spread to more general use; for example, the bacterium Escherichia coli is often referred to as just E. coli, and Tyrannosaurus rex is perhaps even better known simply as T. rex, these two both often appearing in this form in popular writing even where the full genus name has not already been given.
+
+The abbreviation "sp." is used when the actual specific name cannot or need not be specified. The abbreviation "spp." (plural) indicates "several species". These abbreviations are not italicised (or underlined).[53] For example: "Canis sp." means "an unspecified species of the genus Canis", while "Canis spp." means "two or more species of the genus Canis" (the abbreviations "sp." and "spp." can easily be confused with the abbreviations "ssp." (zoology) or "subsp." (botany), plurals "sspp." or "subspp.", referring to one or more subspecies. See trinomen (zoology) and infraspecific name).
+
+The abbreviation "cf." (i.e. confer in Latin) is used to compare individuals/taxa with known/described species. Conventions for use of the "cf." qualifier vary.[54] In paleontology, it is typically used when the identification is not confirmed.[55] For example, "Corvus cf. nasicus"  was used to indicate "a fossil bird similar to the Cuban crow but not certainly identified as this species".[56] In molecular systematics papers, "cf." may be used to indicate one or more undescribed species assumed related to a described species. For example, in a paper describing the phylogeny of small benthic freshwater fish called darters, five undescribed putative species (Ozark, Sheltowee, Wildcat, Ihiyo, and Mamequit darters), notable for brightly colored nuptial males with distinctive color patterns,[57] were referred to as "Etheostoma cf. spectabile" because they had been viewed as related to, but distinct from, Etheostoma spectabile (orangethroat darter).[58] This view was supported in varying degrees by DNA analysis. The somewhat informal use of taxa names with qualifying abbreviations is referred to as open nomenclature and it is not subject to strict usage codes.
+
+In some contexts the dagger symbol ("†") may be used before or after the binomial name to indicate that the species is extinct.
+
+In scholarly texts, at least the first or main use of the binomial name is usually followed by the "authority" – a way of designating the scientist(s) who first published the name. The authority is written in slightly different ways in zoology and botany. For names governed by the ICZN the surname is usually written in full together with the date (normally only the year) of publication. The ICZN recommends that the "original author and date of a name should be cited at least once in each work dealing with the taxon denoted by that name."[59] For names governed by the ICNafp the name is generally reduced to a standard abbreviation and the date omitted. The International Plant Names Index maintains an approved list of botanical author abbreviations. Historically, abbreviations were used in zoology too.
+
+When the original name is changed, e.g. the species is moved to a different genus, both codes use parentheses around the original authority; the ICNafp also requires the person who made the change to be given. In the ICNafp, the original name is then called the basionym. Some examples:
+
+Binomial nomenclature, as described here, is a system for naming species. Implicitly it includes a system for naming genera, since the first part of the name of the species is a genus name. In a classification system based on ranks there are also ways of naming ranks above the level of genus and below the level of species. Ranks above genus (e.g., family, order, class) receive one-part names, which are conventionally not written in italics. Thus the house sparrow, Passer domesticus, belongs to the family Passeridae. Family names are normally based on genus names, although the endings used differ between zoology and botany.
+
+Ranks below species receive three-part names, conventionally written in italics like the names of species. There are significant differences between the ICZN and the ICNafp. In zoology, the only rank below species is subspecies and the name is written simply as three parts (a trinomen). Thus one of the subspecies of the olive-backed pipit is Anthus hodgsoni berezowskii. In botany, there are many ranks below species and although the name itself is written in three parts, a "connecting term" (not part of the name) is needed to show the rank. Thus the American black elder is Sambucus nigra subsp. canadensis; the white-flowered form of the ivy-leaved cyclamen is Cyclamen hederifolium f. albiflorum.

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+
+
+In biology, taxonomy (from Ancient Greek  τάξις (taxis), meaning 'arrangement', and  -νομία (-nomia), meaning 'method') is the science of naming, defining (circumscribing) and classifying groups of biological organisms on the basis of shared characteristics. Organisms are grouped together into taxa (singular: taxon) and these groups are given a taxonomic rank; groups of a given rank can be aggregated to form a super-group of higher rank, thus creating a taxonomic hierarchy. The principal ranks in modern use are domain, kingdom, phylum (division is sometimes used in botany in place of phylum), class, order, family, genus, and species. The Swedish botanist Carl Linnaeus is regarded as the founder of the current system of taxonomy, as he developed a system known as Linnaean taxonomy for categorizing organisms and binomial nomenclature for naming organisms.
+
+With the advent of such fields of study as phylogenetics, cladistics, and systematics, the Linnaean system has progressed to a system of modern biological classification based on the evolutionary relationships between organisms, both living and extinct.
+
+The exact definition of taxonomy varies from source to source, but the core of the discipline remains: the conception, naming, and classification of groups of organisms.[1] As points of reference, recent definitions of taxonomy are presented below:
+
+The varied definitions either place taxonomy as a sub-area of systematics (definition 2), invert that relationship (definition 6), or appear to consider the two terms synonymous. There is some disagreement as to whether biological nomenclature is considered a part of taxonomy (definitions 1 and 2), or a part of systematics outside taxonomy.[8] For example, definition 6 is paired with the following definition of systematics that places nomenclature outside taxonomy:[6]
+
+A whole set of terms including taxonomy, systematic biology, systematics, biosystematics, scientific classification, biological classification, and phylogenetics have at times had overlapping meanings – sometimes the same, sometimes slightly different, but always related and intersecting.[1][9] The broadest meaning of "taxonomy" is used here. The term itself was introduced in 1813 by de Candolle, in his Théorie élémentaire de la botanique.[10]
+
+A taxonomic revision or taxonomic review is a novel analysis of the variation patterns in a particular taxon. This analysis may be executed on the basis of any combination of the various available kinds of characters, such as morphological, anatomical, palynological, biochemical and genetic. A monograph or complete revision is a revision that is comprehensive for a taxon for the information given at a particular time, and for the entire world. Other (partial) revisions may be restricted in the sense that they may only use some of the available character sets or have a limited spatial scope. A revision results in a conformation of or new insights in the relationships between the subtaxa within the taxon under study, which may result in a change in the classification of these subtaxa, the identification of new subtaxa, or the merger of previous subtaxa.[11]
+
+The term "alpha taxonomy" is primarily used today to refer to the discipline of finding, describing, and naming taxa, particularly species.[12] In earlier literature, the term had a different meaning, referring to morphological taxonomy, and the products of research through the end of the 19th century.[13]
+
+William Bertram Turrill introduced the term "alpha taxonomy" in a series of papers published in 1935 and 1937 in which he discussed the philosophy and possible future directions of the discipline of taxonomy.[14]
+
+… there is an increasing desire amongst taxonomists to consider their problems from wider viewpoints, to investigate the possibilities of closer co-operation with their cytological, ecological and genetics colleagues and to acknowledge that some revision or expansion, perhaps of a drastic nature, of their aims and methods, may be desirable … Turrill (1935) has suggested that while accepting the older invaluable taxonomy, based on structure, and conveniently designated "alpha", it is possible to glimpse a far-distant taxonomy built upon as wide a basis of morphological and physiological facts as possible, and one in which "place is found for all observational and experimental data relating, even if indirectly, to the constitution, subdivision, origin, and behaviour of species and other taxonomic groups". Ideals can, it may be said, never be completely realized. They have, however, a great value of acting as permanent stimulants, and if we have some, even vague, ideal of an "omega" taxonomy we may progress a little way down the Greek alphabet. Some of us please ourselves by thinking we are now groping in a "beta" taxonomy.[14]
+
+Turrill thus explicitly excludes from alpha taxonomy various areas of study that he includes within taxonomy as a whole, such as ecology, physiology, genetics, and cytology. He further excludes phylogenetic reconstruction from alpha taxonomy (pp. 365–366).
+
+Later authors have used the term in a different sense, to mean the delimitation of species (not subspecies or taxa of other ranks), using whatever investigative techniques are available, and including sophisticated computational or laboratory techniques.[15][12] Thus, Ernst Mayr in 1968 defined "beta taxonomy" as the classification of ranks higher than species.[16]
+
+An understanding of the biological meaning of variation and of the evolutionary origin of groups of related species is even more important for the second stage of taxonomic activity, the sorting of species into groups of relatives ("taxa") and their arrangement in a hierarchy of higher categories. This activity is what the term classification denotes; it is also referred to as "beta taxonomy".
+
+How species should be defined in a particular group of organisms gives rise to practical and theoretical problems that are referred to as the species problem. The scientific work of deciding how to define species has been called microtaxonomy.[17][18][12] By extension, macrotaxonomy is the study of groups at the higher taxonomic ranks subgenus and above.[12]
+
+While some descriptions of taxonomic history attempt to date taxonomy to ancient civilizations, a truly scientific attempt to classify organisms did not occur until the 18th century. Earlier works were primarily descriptive and focused on plants that were useful in agriculture or medicine. There are a number of stages in this scientific thinking. Early taxonomy was based on arbitrary criteria, the so-called "artificial systems", including Linnaeus's system of sexual classification. Later came systems based on a more complete consideration of the characteristics of taxa, referred to as "natural systems", such as those of de Jussieu (1789), de Candolle (1813) and Bentham and Hooker (1862–1863). These were pre-evolutionary in thinking. The publication of Charles Darwin's On the Origin of Species (1859) led to new ways of thinking about classification based on evolutionary relationships. This was the concept of phyletic systems, from 1883 onwards. This approach was typified by those of Eichler (1883) and Engler (1886–1892). The advent of molecular genetics and statistical methodology allowed the creation of the modern era of "phylogenetic systems" based on cladistics, rather than morphology alone.[19][page needed][20][page needed][21][page needed]
+
+Naming and classifying our surroundings has probably been taking place as long as mankind has been able to communicate. It would always have been important to know the names of poisonous and edible plants and animals in order to communicate this information to other members of the family or group. Medicinal plant illustrations show up in Egyptian wall paintings from c. 1500 BC, indicating that the uses of different species were understood and that a basic taxonomy was in place.[22]
+
+Organisms were first classified by Aristotle (Greece, 384–322 BC) during his stay on the Island of Lesbos.[23][24][25] He classified beings by their parts, or in modern terms attributes, such as having live birth, having four legs, laying eggs, having blood, or being warm-bodied.[26] He divided all living things into two groups: plants and animals.[24] Some of his groups of animals, such as Anhaima (animals without blood, translated as invertebrates) and Enhaima (animals with blood, roughly the vertebrates), as well as groups like the sharks and cetaceans, are still commonly used today.[27] His student Theophrastus (Greece, 370–285 BC) carried on this tradition, mentioning some 500 plants and their uses in his Historia Plantarum. Again, several plant groups currently still recognized can be traced back to Theophrastus, such as Cornus, Crocus, and Narcissus.[24]
+
+Taxonomy in the Middle Ages was largely based on the Aristotelian system,[26] with additions concerning the philosophical and existential order of creatures. This included concepts such as the Great chain of being in the Western scholastic tradition,[26] again deriving ultimately from Aristotle. Aristotelian system did not classify plants or fungi, due to the lack of microscope at the time,[25] as his ideas were based on arranging the complete world in a single continuum, as per the scala naturae (the Natural Ladder).[24] This, as well, was taken into consideration in the Great chain of being.[24] Advances were made by scholars such as Procopius, Timotheos of Gaza, Demetrios Pepagomenos, and Thomas Aquinas. Medieval thinkers used abstract philosophical and logical categorizations more suited to abstract philosophy than to pragmatic taxonomy.[24]
+
+During the Renaissance, the Age of Reason, and the Enlightenment, categorizing organisms became more prevalent,[24]
+and taxonomic works became ambitious enough to replace the ancient texts. This is sometimes credited to the development of sophisticated optical lenses, which allowed the morphology of organisms to be studied in much greater detail. One of the earliest authors to take advantage of this leap in technology was the Italian physician Andrea Cesalpino (1519–1603), who has been called "the first taxonomist".[28] His magnum opus De Plantis came out in 1583, and described more than 1500 plant species.[29][30] Two large plant families that he first recognized are still in use today: the Asteraceae and Brassicaceae.[31] Then in the 17th century John Ray (England, 1627–1705) wrote many important taxonomic works.[25] Arguably his greatest accomplishment was Methodus Plantarum Nova (1682),[32] in which he published details of over 18,000 plant species. At the time, his classifications were perhaps the most complex yet produced by any taxonomist, as he based his taxa on many combined characters. The next major taxonomic works were produced by Joseph Pitton de Tournefort (France, 1656–1708).[33] His work from 1700, Institutiones Rei Herbariae, included more than 9000 species in 698 genera, which directly influenced Linnaeus, as it was the text he used as a young student.[22]
+
+The Swedish botanist Carl Linnaeus (1707–1778)[26] ushered in a new era of taxonomy. With his major works Systema Naturae 1st Edition in 1735,[34] Species Plantarum in 1753,[35] and Systema Naturae 10th Edition,[36] he revolutionized modern taxonomy. His works implemented a standardized binomial naming system for animal and plant species,[37] which proved to be an elegant solution to a chaotic and disorganized taxonomic literature. He not only introduced the standard of class, order, genus, and species, but also made it possible to identify plants and animals from his book, by using the smaller parts of the flower.[37] Thus the Linnaean system was born, and is still used in essentially the same way today as it was in the 18th century.[37] Currently, plant and animal taxonomists regard Linnaeus' work as the "starting point" for valid names (at 1753 and 1758 respectively).[38] Names published before these dates are referred to as "pre-Linnaean", and not considered valid (with the exception of spiders published in Svenska Spindlar[39]). Even taxonomic names published by Linnaeus himself before these dates are considered pre-Linnaean.[22]
+
+Whereas Linnaeus aimed simply to create readily identifiable taxa, the idea of the Linnaean taxonomy as translating into a sort of dendrogram of the animal and plant kingdoms was formulated toward the end of the 18th century, well before On the Origin of Species was published.[25] Among early works exploring the idea of a transmutation of species were Erasmus Darwin's 1796 Zoönomia and Jean-Baptiste Lamarck's Philosophie Zoologique of 1809.[12] The idea was popularized in the Anglophone world by the speculative but widely read Vestiges of the Natural History of Creation, published anonymously by Robert Chambers in 1844.[40]
+
+With Darwin's theory, a general acceptance quickly appeared that a classification should reflect the Darwinian principle of common descent.[41] Tree of life representations became popular in scientific works, with known fossil groups incorporated. One of the first modern groups tied to fossil ancestors was birds.[42] Using the then newly discovered fossils of Archaeopteryx and Hesperornis, Thomas Henry Huxley pronounced that they had evolved from dinosaurs, a group formally named by Richard Owen in 1842.[43][44] The resulting description, that of dinosaurs "giving rise to" or being "the ancestors of" birds, is the essential hallmark of evolutionary taxonomic thinking. As more and more fossil groups were found and recognized in the late 19th and early 20th centuries, palaeontologists worked to understand the history of animals through the ages by linking together known groups.[45] With the modern evolutionary synthesis of the early 1940s, an essentially modern understanding of the evolution of the major groups was in place. As evolutionary taxonomy is based on Linnaean taxonomic ranks, the two terms are largely interchangeable in modern use.[46]
+
+The cladistic method has emerged since the 1960s.[41] In 1958, Julian Huxley used the term clade.[12] Later, in 1960, Cain and Harrison introduced the term cladistic.[12] The salient feature is arranging taxa in a hierarchical evolutionary tree, ignoring ranks.[41] A taxon is called monophyletic, if it includes all the descendants of an ancestral form.[47][48] Groups that have descendant groups removed from them are termed paraphyletic,[47] while groups representing more than one branch from the tree of life are called polyphyletic.[47][48] The International Code of Phylogenetic Nomenclature or PhyloCode is intended to regulate the formal naming of clades.[49][50] Linnaean ranks will be optional under the PhyloCode, which is intended to coexist with the current, rank-based codes.[50]
+
+Well before Linnaeus, plants and animals were considered separate Kingdoms.[51] Linnaeus used this as the top rank, dividing the physical world into the plant, animal and mineral kingdoms. As advances in microscopy made classification of microorganisms possible, the number of kingdoms increased, five- and six-kingdom systems being the most common.
+
+Domains are a relatively new grouping. First proposed in 1977, Carl Woese's three-domain system was not generally accepted until later.[52] One main characteristic of the three-domain method is the separation of Archaea and Bacteria, previously grouped into the single kingdom Bacteria (a kingdom also sometimes called Monera),[51] with the Eukaryota for all organisms whose cells contain a nucleus.[53] A small number of scientists include a sixth kingdom, Archaea, but do not accept the domain method.[51]
+
+Thomas Cavalier-Smith, who has published extensively on the classification of protists, has recently proposed that the Neomura, the clade that groups together the Archaea and Eucarya, would have evolved from Bacteria, more precisely from Actinobacteria. His 2004 classification treated the archaeobacteria as part of a subkingdom of the kingdom Bacteria, i.e., he rejected the three-domain system entirely.[54] Stefan Luketa in 2012 proposed a five "dominion" system, adding Prionobiota (acellular and without nucleic acid) and Virusobiota (acellular but with nucleic acid) to the traditional three domains.[55]
+
+Partial classifications exist for many individual groups of organisms and are revised and replaced as new information becomes available; however, comprehensive, published treatments of most or all life are rarer; recent examples are that of Adl et al., 2012 and 2019,[63][64] which covers eukaryotes only with an emphasis on protists, and Ruggiero et al., 2015,[65] covering both eukaryotes and prokaryotes to the rank of Order, although both exclude fossil representatives.[65] A separate compilation (Ruggiero, 2014)[66] covers extant taxa to the rank of family. Other, database-driven treatments include the Encyclopedia of Life, the Global Biodiversity Information Facility, the NCBI taxonomy database, the Interim Register of Marine and Nonmarine Genera, the Open Tree of Life, and the Catalogue of Life. The Paleobiology Database is a resource for fossils.
+
+Biological taxonomy is a sub-discipline of biology, and is generally practiced by biologists known as "taxonomists", though enthusiastic naturalists are also frequently involved in the publication of new taxa.[67] Because taxonomy aims to describe and organize life, the work conducted by taxonomists is essential for the study of biodiversity and the resulting field of conservation biology.[68][69]
+
+Biological classification is a critical component of the taxonomic process. As a result, it informs the user as to what the relatives of the taxon are hypothesized to be. Biological classification uses taxonomic ranks, including among others (in order from most inclusive to least inclusive): Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species, and Strain.[70][note 1]
+
+The "definition" of a taxon is encapsulated by its description or its diagnosis or by both combined. There are no set rules governing the definition of taxa, but the naming and publication of new taxa is governed by sets of rules.[8] In zoology, the nomenclature for the more commonly used ranks (superfamily to subspecies), is regulated by the International Code of Zoological Nomenclature (ICZN Code).[71] In the fields of phycology, mycology, and botany, the naming of taxa is governed by the International Code of Nomenclature for algae, fungi, and plants (ICN).[72]
+
+The initial description of a taxon involves five main requirements:[73]
+
+However, often much more information is included, like the geographic range of the taxon, ecological notes, chemistry, behavior, etc. How researchers arrive at their taxa varies: depending on the available data, and resources, methods vary from simple quantitative or qualitative comparisons of striking features, to elaborate computer analyses of large amounts of DNA sequence data.[74]
+
+An "authority" may be placed after a scientific name.[75] The authority is the name of the scientist or scientists who first validly published the name.[75] For example, in 1758 Linnaeus gave the Asian elephant the scientific name Elephas maximus, so the name is sometimes written as "Elephas maximus Linnaeus, 1758".[76] The names of authors are frequently abbreviated: the abbreviation L., for Linnaeus, is commonly used. In botany, there is, in fact, a regulated list of standard abbreviations (see list of botanists by author abbreviation).[77] The system for assigning authorities differs slightly between botany and zoology.[8] However, it is standard that if the genus of a species has been changed since the original description, the original authority's name is placed in parentheses.[78]
+
+In phenetics, also known as taximetrics, or numerical taxonomy, organisms are classified based on overall similarity, regardless of their phylogeny or evolutionary relationships.[12] It results in a measure of evolutionary "distance" between taxa. Phenetic methods have become relatively rare in modern times, largely superseded by cladistic analyses, as phenetic methods do not distinguish common ancestral (or plesiomorphic) traits from new common (or apomorphic) traits.[79] However, certain phenetic methods, such as neighbor joining, have found their way into cladistics, as a reasonable approximation of phylogeny when more advanced methods (such as Bayesian inference) are too computationally expensive.[80]
+
+Modern taxonomy uses database technologies to search and catalogue classifications and their documentation.[81] While there is no commonly used database, there are comprehensive databases such as the Catalogue of Life, which attempts to list every documented species.[82] The catalogue listed 1.64 million species for all kingdoms as of April 2016, claiming coverage of more than three quarters of the estimated species known to modern science.[83]

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+A monk  (/mʌŋk/, from Greek: μοναχός,  monachos, "single, solitary" via Latin monachus)[1][2] is a person who practices religious asceticism by monastic  living, either alone or with any number of other monks. A monk may be a person who decides to dedicate his life to serving all other living beings, or to be an ascetic who voluntarily chooses to leave mainstream society and live his or her life in prayer and contemplation. The concept is ancient and can be seen in many religions and in philosophy.
+
+In the Greek language the term can apply to women, but in modern English it is mainly in use for men. The word nun is typically used for female monastics.
+
+Although the term monachos is of Christian origin, in the English language monk tends to be used loosely also for both male and female ascetics from other religious or philosophical backgrounds.  However, being generic, it is not interchangeable with terms that denote particular kinds of monk, such as cenobite, hermit, anchorite, hesychast, or solitary.
+
+Traditions of Christian monasticism exist in major Christian denominations, with religious orders being present in Catholicism, Lutheranism, Oriental Orthodoxy, Eastern Orthodoxy, Reformed Christianity, Anglicanism and Methodism. Indian religions, including Hinduism, Buddhism and Jainism also have monastic traditions as well.
+
+In Theravada Buddhism, bhikkhu is the term for monk. Their disciplinary code is called the patimokkha, which is part of the larger Vinaya. They live lives of mendicancy, and go on a morning almsround (Pali: pindapata) every day. The local people give food for the monks to eat, though the monks are not permitted to positively ask for anything. The monks live in monasteries, and have an important function in traditional Asian society. Young boys can be ordained as samaneras. Both bhikkhus and samaneras eat only in the morning, and are not supposed to lead a luxurious life. Their rules forbid the use of money, although this rule is nowadays not kept by all monks. The monks are part of the Sangha, the third of the Triple Gem of Buddha, Dhamma, Sangha.
+
+In Mahayana Buddhism, the term 'Sangha' strictly speaking refers to those who have achieved certain levels of understanding. They are therefore called 'community of the excellent ones' (Standard Tibetan: mchog kyi tshogs); however, these in turn need not be monks (i.e., hold such vows). Several Mahayana orders accept female practitioners as monks, instead of using the normal title of "nun", and they are considered equal to male ascetics in all respects.
+
+The Bhikkhus are only allowed 4 items (other than their robes): a razor, a needle, an alms bowl and a water strainer.[citation needed]
+
+In Vajrayana Buddhism, monkhood is part of the system of 'vows of individual liberation'; these vows are taken in order to develop one's own personal ethical discipline. The monks and nuns form the (ordinary) sangha. As for the Vajrayana vows of individual liberation, there are four steps: A lay person may take the 5 vows called 'approaching virtue' (in Tibetan 'genyen' < dge snyan>). The next step is to enter the monastic way of life (Tib. rabjung) which includes wearing monk's or nun's robes. After that, one can become a 'novice' (Pali samanera, Tib. getshül); the last and final step is to take all vows of the 'fully ordained monk' (gelong). This term 'gelong' (Tib. < dge long>, in the female form gelongma) is the translation of Skt. bikshu (for women bikshuni) which is the equivalent of the Pali term bhikkhuni; bhikkhu is the word used in Theravada Buddhism (Sri Lanka, Burma, Thailand).
+
+Chinese Buddhist monks have been traditionally and stereotypically linked with the practice of the Chinese martial arts or Kung fu, and monks are frequently important characters in martial arts films.  This association is focused around the Shaolin Monastery.  The Buddhist monk Bodhidharma, traditionally credited as the founder of Zen Buddhism in China, is also claimed to have introduced Kalaripayattu (which later evolved into Kung Fu) to the country. This latter claim has however been a source of much controversy (see Bodhidharma, the martial arts, and the disputed India connection) One more feature about the Chinese Buddhist monks is that they practice the burning marks on their scalp, finger or part of the skin on their anterior side of the forearm with incense as a sign of ordination.
+
+In Thailand and Burma, it is common for boys to spend some time living as a monk in a monastery. Most stay for only a few years and then leave, but a number continue on in the ascetic life for the rest of their lives.
+
+In Mongolia during the 1920s, there were about 110,000 monks, including children, who made up about one-third of the male population,[3] many of whom were killed in the purges of Choibalsan.
+
+Within Catholicism, a monk is a member of a religious order who lives a communal life in a monastery, abbey, or priory under a monastic rule of life (such as the Rule of St. Benedict). St. Benedict of Nursia, (480-543 or 547 AD) is considered to be the founder of western monasticism. He authored the Rule of St. Benedict, which is the foundation for the Order of St. Benedict and all of its reform groups such as the Cistercians and the Trappists. He founded the great Benedictine monastery, Monte Cassino, in 529.
+
+The religious vows taken in the West were first developed by St. Benedict.  These vows were three in number: obedience, conversion of life, and stability.  Obedience calls for the monk to obey Christ, as represented by the superior person of the monastery, which is an abbot or prior.  Conversion of life means, generally, that the monk convert himself to the way of a monk, which is death to self and to the world and life to God and to his work. A Christian monk is to be an instrument of God's work. Stability entails that the monk commit himself to the monastery for the remainder of his life, and so, upon death, will be buried at its cemetery.  The vow of stability is unique to Benedictines.
+
+The solemn vows in other religious communities were eventually established as vows of obedience, poverty, and chastity. Poverty requires that they renounce any ownership of property or assets, except for items that were allowed to them by their superior (such as a religious habit, shoes, a cloak, etc.), and to live meekly, sharing whatever they might have with the poor.  Chastity requires that since they were willing to dedicate their lives to God, they sacrificed the love between men and women and would not marry. Also, they give up any act of sexual conduct.
+
+To become a monk, one first must become a postulant, during which time the man lives at the monastery to evaluate whether he is called to become a monk. As a postulant, the man is not bound by any vows, and is free to leave the monastery at any time. If the postulant and the community agree that the postulant should become a monk, the man is received as a novice, at which time he is given his religious habit, and begins to participate more fully in the life of the monastery. Following a period as a novice, usually six months to a year, the novice professes temporary vows, which can be renewed for a period of years. After a few years, the monk professes permanent vows, which are binding for life.
+
+The monastic life generally consists of prayer in the form of the Liturgy of the Hours (also known as the Divine Office) and divine reading (lectio divina) and manual labor. Among most religious orders, monks live in simple, austere rooms called cells and come together daily to celebrate the Conventual Mass and to recite the Liturgy of the Hours. In most communities, the monks take their meals together in the refectory. While there is no vow of silence, many communities have a period of silence lasting from evening until the next morning and some others restrict talking to only when it is necessary for the monks to perform their work and during weekly recreation.
+
+Monks who have been or will be ordained into Holy Orders as priests or deacons are referred to as choir monks, as they have the obligation to recite the entire Divine Office daily in choir. Those monks who are not ordained into Holy Orders are referred to as lay brothers. In most monastic communities today, little distinction exists between the lay brothers and the choir monks. However, historically, the roles of the two groups of monks within the monastery differed. The work of the choir monks was considered to be prayer, chanting the seven hours of the Divine Office and celebrating the Mass daily whereas the lay brothers provided for the material needs of the community by growing food, preparing meals, maintaining the monastery and the grounds. This distinction arose historically because generally those monks who could read Latin typically became choir monks, while those monks who were illiterate or could not read Latin became lay brothers. Since the lay brothers could not recite the Divine Office in Latin, they would instead pray easily memorizable prayers such as the Our Father or the Hail Mary as many as 150 times per day. Since the Second Vatican Council, the distinction between choir monks and lay brothers has been deemphasized, as the council allowed the Divine Office to be said in the vernacular language, effectively opening participation to all of the monks.
+
+Within western monasticism, it is important to differentiate between monks and friars. Monks generally live a contemplative life of prayer confined within a monastery while friars usually engage in an active ministry of service to the outside community. The monastic orders include all Benedictines (the Order of Saint Benedict and its later reforms including the Cistercians and the Trappists) and the Carthusians, who live according to their own Statutes, and not according to the Rule of St. Benedict proper. Orders of friars include the Franciscans, Dominicans, Carmelites, and Augustinians. Although the Canons Regular, such as the Norbertines, live in community, they are neither monks nor friars as they are characterized by their clerical state and not by any monastic vows.
+
+Loccum Abbey and Amelungsborn Abbey have the longest traditions as Lutheran monasteries; after the Reformation, many monasteries and convents were received into the Lutheran Church and continued religious life, existing to this day.[4]
+
+Since the 19th and 20th century, there has been a renewal in the monastic life among Lutheranism. Lutheran religious orders in the Franciscan, Benedictine and other traditions exist, with some Lutheran monasteries having third orders and accepting oblates.[5][6]
+
+In American Lutheran traditions, "The Congregation of the Servants of Christ" was established at St. Augustine's House in Oxford, Michigan, in 1958 when some other men joined Father Arthur Kreinheder in observing the monastic life and offices of prayer. These men and others came and went over the years. The community has always remained small; at times the only member was Father Arthur.[7] During the 35 years of its existence over 25 men tested their vocations to monastic life by living at the house for some time, from a few months to many years, but at Father Arthur's death in 1989 only one permanent resident remained. At the beginning of 2006, there was 2 permanent professed members and 2 long-term guests. Strong ties remain with this community and their brothers in Sweden (Östanbäck monastery) and in Germany (Priory of St. Wigbert).[8]
+
+There is also the Order of Lutheran Franciscans, a religious community of friars and sisters within the tradition of the Evangelical Lutheran Church in America.
+
+Monastic life in England came to an abrupt end when King Henry VIII broke from the Catholic Church and made himself the head of the Church of England. He initiated the Dissolution of the Monasteries, during which all of the monasteries within England were destroyed. A large number of monks were executed, others fled to continental European monasteries where they were able to continue their monastic life.
+
+Shortly after the beginning of the Anglo-Catholic Movement in the Church of England, there was felt to be a need for a restoration of the monastic life. In the 1840s, the then Anglican priest and future Catholic Cardinal John Henry Newman established a community of men at Littlemore near Oxford. From then on, there have been established many communities of monks, friars and other religious communities for men in the Anglican Communion. There are Anglican Benedictines, Franciscans, Cistercians, and in the Episcopal Church in the United States, Dominicans. There are also uniquely Anglican monastic orders such as the Society of Saint John the Evangelist and the Community of the Resurrection at Mirfield.
+
+Some Anglican religious communities are contemplative, some active, but a distinguishing feature of the monastic life among Anglicans is that most practice the so-called "mixed life". Anglican monks recite the Divine Office in choir daily, either the full eight services of the Breviary or the four offices found in the Book of Common Prayer and celebrate the Eucharist daily. Many orders take on external works such as service to the poor, giving religious retreats, or other active ministries within their immediate communities. Like Catholic monks, Anglican monks also take the monastic vows of poverty, chastity, and obedience.
+
+In the early 20th century when the Oxford Movement was at its height, the Anglican Communion had hundreds[citation needed] of orders and communities and thousands of religious followers. However, since the 1960s there has been a sharp falling off in the numbers of religious in many parts of the Anglican Communion. Many once large and international communities have been reduced to a single convent or monastery composed of elderly men or women. In the last few decades of the 20th century, novices have for most communities been few and far between. Some orders and communities have already become extinct.
+
+There are however, still several thousand Anglican monks working today in approximately 200 communities around the world. The most surprising growth has been in the Melanesian countries of the Solomon Islands, Vanuatu and Papua New Guinea. The Melanesian Brotherhood, founded at Tabalia, Guadalcanal, in 1925 by Ini Kopuria, is now the largest Anglican community in the world with over 450 brothers in the Solomon Islands, Vanuatu, Papua New Guinea, the Philippines and the United Kingdom.
+
+The Saint Brigid of Kildare Monastery is a double monastery of the United Methodist Church rooted in the Benedictine tradition, being located in Collegeville, Minnesota.[9] Besides monastic orders, the Order of Saint Luke is a dispersed religious order within Methodism, though being ecumenical, it accepts believers of other Christian denominations.
+
+The Emmanuel Sisters is a convent of the Presbyterian Church in Cameroon that was founded by Rev Mother Magdaline Marie Handy.[10] These nuns are engaged in prayer, teaching, and healthcare.[10]
+
+In Eastern Orthodoxy monasticism holds a very special and important place: "Angels are a light for monks, monks are a light for laymen" (St. John Klimakos). Orthodox monastics separate themselves from the world in order to pray unceasingly for the world. They do not, in general, have as their primary purpose the running of social services, but instead are concerned with attaining theosis, or union with God. However, care for the poor and needy has always been an obligation of monasticism,[citation needed] so not all monasteries are "cloistered". The level of contact will vary from community to community. Hermits, on the other hand, have little or no contact with the outside world.
+
+Orthodox monasticism does not have religious orders as are found in the West, nor do they have Rules in the same sense as the Rule of St. Benedict. Rather, Eastern monastics study and draw inspiration from the writings of the Desert Fathers as well as other Church Fathers; probably the most influential of which are the Greater Asketikon and Lesser Asketikon of St. Basil the Great and the Philokalia, which was compiled by St. Nikodemos of the Holy Mountain and St. Makarios of Corinth. Hesychasm is of primary importance in the ascetical theology of the Orthodox Church.
+
+Most communities are self-supporting, and the monastic’s daily life is usually divided into three parts: (a) communal worship in the catholicon (the monastery's main church); (b) hard manual labour; and (c) private prayer, spiritual study, and rest when necessary. Meals are usually taken in common in a sizable dining hall known as a trapeza (refectory), at elongated refectory tables. Food is usually simple and is eaten in silence while one of the brethren reads aloud from the spiritual writings of the Holy Fathers. The monastic lifestyle takes a great deal of serious commitment. Within the cenobitic community, all monks conform to a common way of living based on the traditions of that particular monastery. In struggling to attain this conformity, the monastic comes to realize his own shortcomings and is guided by his spiritual father in how to deal honestly with them. For this same reason, bishops are almost always chosen from the ranks of monks.
+
+Eastern monasticism is found in three distinct forms: anchoritic (a solitary living in isolation), cenobitic (a community living and worshiping together under the direct rule of an abbot or abbess), and the "middle way" between the two, known as the skete (a community of individuals living separately but in close proximity to one another, who come together only on Sundays and feast days, working and praying the rest of the time in solitude, but under the direction of an elder). One normally enters a cenobitic community first, and only after testing and spiritual growth would one go on to the skete or, for the most advanced, become a solitary anchorite. However, one is not necessarily expected to join a skete or become a solitary; most monastics remain in the cenobium the whole of their lives.
+
+In general, Orthodox monastics have little or no contact with the outside world, including their own families. The purpose of the monastic life is union with God, the means is through leaving the world (i.e., the life of the passions). After tonsure, Orthodox monks and nuns are never permitted to cut their hair. The hair of the head and the beard remain uncut as a symbol of the vows they have taken, reminiscent of the Nazarites from the Old Testament. The tonsure of monks is the token of a consecrated life, and symbolizes the cutting off of their self-will.
+
+The process of becoming a monk is intentionally slow, as the vows taken are considered to entail a lifelong commitment to God, and are not to be entered into lightly. In Orthodox monasticism after completing the novitiate, there are three ranks of monasticism. There is only one monastic habit in the Eastern Church (with certain slight regional variations), and it is the same for both monks and nuns. Each successive grade is given a portion of the habit, the full habit being worn only by those in the highest grade, known for that reason as the "Great Schema", or "Great Habit".
+
+The various profession rites are normally performed by the Abbot, but if the abbot has not been ordained a priest, or if the monastic community is a convent, a hieromonk will perform the service. The abbot or hieromonk who performs a tonsure must be of at least the rank he is tonsuring into. In other words, only a hieromonk who has been tonsured into the Great Schema may himself tonsure a Schemamonk. A bishop, however, may tonsure into any rank, regardless of his own.
+
+Novice (Church Slavonic: Poslushnik), lit. "one under obedience"—Those wishing to join a monastery begin their lives as novices. After coming to the monastery and living as a guest for not less than three days, the revered abbot or abbess may bless the candidate to become a novice. There is no formal ceremony for the clothing of a novice, he or she simply receives permission to wear the clothing of a novice. In the Eastern monastic tradition, novices may or may not dress in the black inner cassock (Greek: Anterion, Eisorasson; Church Slavonic: Podriasnik) and wear the soft monastic hat (Greek: Skoufos, Church Slavonic: Skufia), depending on the tradition of the local community, and in accordance to the abbot’s directives. The inner-cassock and the skoufos are the first part of the Orthodox monastic habit. In some communities, the novice also wears the leather belt. He is also given a prayer rope and instructed in the use of the Jesus Prayer. If a novice chooses to leave during the period of the novitiate, no penalty is incurred. He may also be asked to leave at any time if his behaviour does not conform to the monastic life, or if the superior discerns that he is not called to monasticism. When the abbot or abbess deems the novice ready, he is asked if he wishes to join the monastery. Some, out of humility, will choose to remain novices all their lives. Every stage of the monastic life must be entered into voluntarily.
+
+Rassophore (Church Slavonic: Ryassofor), lit. "Robe-bearer"—If the novice continues on to become a monk, he is clothed in the first degree of monasticism at a formal service known as the Tonsure. Although there are no formal vows made at this point, the candidate is normally required to affirm his commitment to persevere in the monastic life. The abbot will then perform the tonsure, cutting a small amount of hair from four spots on the head, forming a cross. He is then given the outer cassock (Greek: Rasson, Exorasson, or Mandorasson; Church Slavonic: Ryassa)—an outer robe with wide sleeves, something like the cowl used in the West, but without a hood—from which the name of Rassophore is derived. He is also given a brimless hat with a veil, known as a klobuk, and a leather belt is fastened around his waist. His habit is usually black, signifying that he is now dead to the world, and he receives a new name. Although the Rassophore does not make formal vows, he is still morally obligated to continue in the monastic estate for the rest of his life. Some will remain Rassophores permanently without going on to the higher degrees.
+
+Stavrophore (Church Slavonic: Krestonosets), lit. "Cross-bearer"—The next level for Eastern monastics takes place some years after the first tonsure when the abbot feels the monk has reached an appropriate level of discipline, dedication, and humility. This degree is also known as the Little Schema, and is considered to be a "betrothal" to the Great Schema. At this stage, the monk makes formal vows of stability, chastity, obedience and poverty. Then he is tonsured and clothed in the habit, which in addition to that worn by the Rassophore, includes the paramandyas (Church Slavonic: paraman), a piece of square cloth worn on the back, embroidered with the instruments of the Passion (see picture above), and connected by ties to a wooden cross worn over the heart. The paramandyas represents the yoke of Christ. Because of this addition he is now called Stavrophore, or Cross-bearer. He is also given a wooden hand cross (or "profession cross"), which he should keep in his icon corner, and a beeswax candle, symbolic of monastic vigilance the sacrificing of himself for God. He will be buried holding the cross, and the candle will be burned at his funeral. In the Slavic practice, the Stavrophore also wears the monastic mantle. The rasson (outer robe) worn by the Stavrophore is more ample than that worn by the Rassophore. The abbot increases the Stavrophore monk’s prayer rule, allows a more strict personal ascetic practice, and gives the monk more responsibility.
+
+Great Schema (Greek: Megaloschemos, Church Slavonic: Skhimnik)—Monks whose abbot feels they have reached a high level of spiritual excellence reach the final stage, called the Great Schema. The tonsure of a Schemamonk follows the same format as the Stavrophore, and he makes the same vows and is tonsured in the same manner. But in addition to all the garments worn by the Stavrophore, he is given the Analavos (Church Slavonic: Analav) which is the article of monastic vesture emblematic of the Great Schema. For this reason, the analavos itself is sometimes called the "Great Schema". The analavos comes down in the front and the back, somewhat like the scapular in Western monasticism, although the two garments are probably not related. It is often intricately embroidered with the instruments of the Passion and the Trisagion (the angelic hymn). The Greek form does not have a hood, the Slavic form has a hood and lappets on the shoulders, so that the garment forms a large cross covering the monk's shoulders, chest, and back. Another piece added is the Polystavrion or "Many Crosses", which consists of a cord with a number of small crosses plaited into it.  The polystavrion forms a yoke around the monk and serves to hold the analavos in place, and reminds the monastic that he is bound to Christ and that his arms are no longer fit for worldly activities, but that he must labor only for the Kingdom of Heaven.  Among the Greeks, the mantle is added at this stage.  The paramandyas of the Megaloschemos is larger than that of the Stavrophore, and if he wears the klobuk, it is of a distinctive thimble shape, called a koukoulion, the veil of which is usually embroidered with crosses.  In some monastic traditions the Great Schema is only given to monks and nuns on their death bed, while in others they may be elevated after as little as 25 years of service.
+
+Eastern Orthodox monks are addressed as "Father" even if they are not priests; but when conversing among themselves, monks will often address one another as "Brother".  Novices are always referred to as "Brother". Among the Greeks, old monks are often called Gheronda, or "Elder", out of respect for their dedication.  In the Slavic tradition, the title of Elder (Church Slavonic: Starets) is normally reserved for those who are of an advanced spiritual life, and who serve as guides to others.
+
+For the Orthodox, Mother is the correct term for nuns who have been tonsured Stavrophore or higher. Novices and Rassophores are addressed as "Sister".  Nuns live identical ascetic lives to their male counterparts and are therefore also called monachai (the feminine plural of monachos), and their community is likewise called a monastery.
+
+Many (but not all) Orthodox seminaries are attached to monasteries, combining academic preparation for ordination with participation in the community's life of prayer, and hopefully benefiting from the example and wise counsel of the monks.  Bishops are required by the sacred canons of the Orthodox Church to be chosen from among the monastic clergy. The requirement is specifically that they be monastics, not simply celibate (see clerical celibacy).  Monks who have been ordained to the priesthood are called hieromonks (priest-monks); monks who have been ordained to the diaconate are called hierodeacons (deacon-monks).  A Schemamonk who is a priest is called a Hieroschemamonk.  Most monks are not ordained; a community will normally only present as many candidates for ordination to the bishop as the liturgical needs of the community require.
+
+Hinduism has many monastic orders, including the Dashanami Sampradaya ("Tradition of Ten Names") orders established by Adi Shankara as well as Vaishnava orders.
+
+Madhvaacharya (Madhvacharya), the Dwaita philosopher, established ashta matha (Eight Monasteries). He appointed a monk (called swamiji or swamigalu in local parlance) for each matha or monastery who has the right to worship Madhvacharya's murti of Lord Krishna by rotation. Each matha's swamiji gets a chance to worship after fourteen years. This ritual is called Paryaya and has been used also outside his sampradaya, e.g. in Gaudiya Vaisnava Radharamana temple in Vrindavan.
+
+Similar in appearance to Buddhist monks, brahmacari monks from the International Society for Krishna Consciousness (ISKCON), or Hare Krishnas as they are popularly known, are the best known Vaishnava monks outside India. They are a common sight in many places around the world. Their appearance—simple saffron dhoti, shaved head with sikha, Tulasi neckbeads and tilaka markings—and social customs (sadhana) date back many thousands of years to the Vedic era with its varnasrama society. This social scheme includes both monastic and lay stages meant for various persons in various stages of life as per their characteristics (guna) and work (karma).
+
+ISKCON started as a predominantly monastic group but nowadays the majority of members live as lay persons. Many of them, however, spent some time as monks. New persons joining ISKCON as full-time members (living in its centers) first undergo a three-month Bhakta training, which includes learning the basics of brahmacari (monastic) life. After that they can decide if they prefer to continue as monks or as married Grihasthas.
+
+Brahmacari older than fifty years (as per ISKCON rule) can become sannyasi. Sannyasa, a life of full dedication to spiritual pursuits, is the highest stage of life in the varnasrama society. It is permanent and one cannot give it up. A Sannyasi is given the title Swami. Older grihastha with grown-up children are traditionally expected to accept vanaprastha (celibate retired) life.
+
+The role of monastic orders in Indian and now also Western society has to some extent been adapted over the years in accordance with ever-changing social structures.
+
+One of the most intense forms of Asceticism can be found in Jainism, one of the world's oldest religions. Jainism encourages fasting, yoga practices, meditation in difficult postures, and other austerities.[11] According to Jains, one's highest goal should be attaining Nirvana or Moksha (i.e., liberation from samsara, the cycle of birth and rebirth). For this, a soul has to be without attachment or self-indulgence. This can be achieved only by the monks and nuns who take five great vows: of non-violence, of truth, of non-stealing, of non-possession and of celibacy.
+
+Most of the austerities and ascetic practices can be traced back to Vardhaman Mahavira, the twenty-fourth "fordmaker" or Tirthankara. The Acaranga Sutra, or Book of Good Conduct, is a sacred book within Jainism that discusses the ascetic code of conduct. Other texts that provide insight into conduct of ascetics include Yogashastra by Acharya Hemachandra and Niyamasara by Acharya Kundakunda. Other illustrious Jain works on ascetic conduct are Oghanijjutti, Pindanijjutti, Cheda Sutta, and Nisiha Suttafee.
+
+Full Jain monk in either Svetambara or Digambara tradition[12] can belong to one of these ranks:
+
+These three are mentioned is the three lines of the Namokar Mantra. In the Digambara tradition, a junior monk can be a:
+
+The Svetambar Terapanthi sect has a new rank of junior monks who are called samana. The nuns are called Aryikas in Digambar tradition and Sadhvi in the Svetambar tradition.
+
+As per the Jain vows, the monks and nuns renounce all relations and possessions. Jain ascetics practice complete non-violence. Ahimsa is the first and foremost vow of a Jain ascetic. They do not hurt any living being, be it an insect or a human. They carry a special broom to sweep away any insects that may cross their path. Some Jain monks wear a cloth over the mouth to prevent accidental harm to airborne germs and insects. They also do not use electricity as it involves violence. Furthermore, they do not use any devices or machines.
+
+As they are without possession and attachment, they travel from city to city, often crossing forests and deserts, and always barefoot. Jain ascetics do not stay in a single place for more than two months to prevent themselves from becoming attached to any location. However, during four months of monsoon (rainy season) known as chaturmaas, they continue to stay in a single place to avoid killing the life forms that thrive during the rains.
+Jain monks and nuns practice complete celibacy. They do not touch or share a sitting platform with a person of opposite sex.
+
+Jain ascetics follow a strict vegetarian diet without root vegetables. Shvetambara monks do not cook food but solicit alms from householders. Digambara monks have only a single meal a day. Neither group will beg for food, but a Jain ascetic may accept a meal from a householder, provided that the latter is pure of mind and body and offers the food of his own volition and in the prescribed manner. During such an encounter, the monk remains standing and eats only a measured amount. Fasting (i.e., abstinence from food and sometimes water) is a routine feature of Jain asceticism. Fasts last for a day or longer, up to a month. Some monks avoid (or limit) medicine or hospitalization due to their careful attention to body.
+
+Other austerities include meditation in seated or standing posture near river banks in the cold wind, or meditation atop hills and mountains, especially at noon when the sun is at its fiercest. Such austerities are undertaken according to the physical and mental limits of the individual ascetic. Jain ascetics are (almost) completely without possessions. Some Jains (Shvetambara monks and nuns) own only unstitched white robes (an upper and lower garment) and a bowl used for eating and collecting alms. Male Digambara monks do not wear any clothes and carry nothing with them except a soft broom made of shed peacock feathers (pinchi) and eat from their hands. They sleep on the floor without blankets and sit on special wooden platforms.
+
+Every day is spent either in study of scriptures or meditation or teaching to lay people. They stand aloof from worldly matters. Many Jain ascetics take a final vow of Santhara or Sallekhana (i.e., a peaceful and detached death where medicines, food, and water are abandoned). This is done when death is imminent or when a monk feels that he is unable to adhere to his vows on account of advanced age or terminal disease.
+
+Quotes on ascetic practices from the Akaranga Sutra as Hermann Jacobi translated it:[13][14]
+
+A monk or a nun wandering from village to village should look forward for four cubits, and seeing animals they should move on by walking on his toes or heels or the sides of his feet. If there be some bypath, they should choose it, and not go straight on; then they may circumspectly wander from village to village.
+
+I shall become a Sramana who owns no house, no property, no sons, no cattle, who eats what others give him; I shall commit no sinful action; Master, I renounce to accept anything that has not been given.' Having taken such vows, (a mendicant) should not, on entering a village or scot-free town, &c., take himself, or induce others to take, or allow others to take, what has not been given.

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+A monk  (/mʌŋk/, from Greek: μοναχός,  monachos, "single, solitary" via Latin monachus)[1][2] is a person who practices religious asceticism by monastic  living, either alone or with any number of other monks. A monk may be a person who decides to dedicate his life to serving all other living beings, or to be an ascetic who voluntarily chooses to leave mainstream society and live his or her life in prayer and contemplation. The concept is ancient and can be seen in many religions and in philosophy.
+
+In the Greek language the term can apply to women, but in modern English it is mainly in use for men. The word nun is typically used for female monastics.
+
+Although the term monachos is of Christian origin, in the English language monk tends to be used loosely also for both male and female ascetics from other religious or philosophical backgrounds.  However, being generic, it is not interchangeable with terms that denote particular kinds of monk, such as cenobite, hermit, anchorite, hesychast, or solitary.
+
+Traditions of Christian monasticism exist in major Christian denominations, with religious orders being present in Catholicism, Lutheranism, Oriental Orthodoxy, Eastern Orthodoxy, Reformed Christianity, Anglicanism and Methodism. Indian religions, including Hinduism, Buddhism and Jainism also have monastic traditions as well.
+
+In Theravada Buddhism, bhikkhu is the term for monk. Their disciplinary code is called the patimokkha, which is part of the larger Vinaya. They live lives of mendicancy, and go on a morning almsround (Pali: pindapata) every day. The local people give food for the monks to eat, though the monks are not permitted to positively ask for anything. The monks live in monasteries, and have an important function in traditional Asian society. Young boys can be ordained as samaneras. Both bhikkhus and samaneras eat only in the morning, and are not supposed to lead a luxurious life. Their rules forbid the use of money, although this rule is nowadays not kept by all monks. The monks are part of the Sangha, the third of the Triple Gem of Buddha, Dhamma, Sangha.
+
+In Mahayana Buddhism, the term 'Sangha' strictly speaking refers to those who have achieved certain levels of understanding. They are therefore called 'community of the excellent ones' (Standard Tibetan: mchog kyi tshogs); however, these in turn need not be monks (i.e., hold such vows). Several Mahayana orders accept female practitioners as monks, instead of using the normal title of "nun", and they are considered equal to male ascetics in all respects.
+
+The Bhikkhus are only allowed 4 items (other than their robes): a razor, a needle, an alms bowl and a water strainer.[citation needed]
+
+In Vajrayana Buddhism, monkhood is part of the system of 'vows of individual liberation'; these vows are taken in order to develop one's own personal ethical discipline. The monks and nuns form the (ordinary) sangha. As for the Vajrayana vows of individual liberation, there are four steps: A lay person may take the 5 vows called 'approaching virtue' (in Tibetan 'genyen' < dge snyan>). The next step is to enter the monastic way of life (Tib. rabjung) which includes wearing monk's or nun's robes. After that, one can become a 'novice' (Pali samanera, Tib. getshül); the last and final step is to take all vows of the 'fully ordained monk' (gelong). This term 'gelong' (Tib. < dge long>, in the female form gelongma) is the translation of Skt. bikshu (for women bikshuni) which is the equivalent of the Pali term bhikkhuni; bhikkhu is the word used in Theravada Buddhism (Sri Lanka, Burma, Thailand).
+
+Chinese Buddhist monks have been traditionally and stereotypically linked with the practice of the Chinese martial arts or Kung fu, and monks are frequently important characters in martial arts films.  This association is focused around the Shaolin Monastery.  The Buddhist monk Bodhidharma, traditionally credited as the founder of Zen Buddhism in China, is also claimed to have introduced Kalaripayattu (which later evolved into Kung Fu) to the country. This latter claim has however been a source of much controversy (see Bodhidharma, the martial arts, and the disputed India connection) One more feature about the Chinese Buddhist monks is that they practice the burning marks on their scalp, finger or part of the skin on their anterior side of the forearm with incense as a sign of ordination.
+
+In Thailand and Burma, it is common for boys to spend some time living as a monk in a monastery. Most stay for only a few years and then leave, but a number continue on in the ascetic life for the rest of their lives.
+
+In Mongolia during the 1920s, there were about 110,000 monks, including children, who made up about one-third of the male population,[3] many of whom were killed in the purges of Choibalsan.
+
+Within Catholicism, a monk is a member of a religious order who lives a communal life in a monastery, abbey, or priory under a monastic rule of life (such as the Rule of St. Benedict). St. Benedict of Nursia, (480-543 or 547 AD) is considered to be the founder of western monasticism. He authored the Rule of St. Benedict, which is the foundation for the Order of St. Benedict and all of its reform groups such as the Cistercians and the Trappists. He founded the great Benedictine monastery, Monte Cassino, in 529.
+
+The religious vows taken in the West were first developed by St. Benedict.  These vows were three in number: obedience, conversion of life, and stability.  Obedience calls for the monk to obey Christ, as represented by the superior person of the monastery, which is an abbot or prior.  Conversion of life means, generally, that the monk convert himself to the way of a monk, which is death to self and to the world and life to God and to his work. A Christian monk is to be an instrument of God's work. Stability entails that the monk commit himself to the monastery for the remainder of his life, and so, upon death, will be buried at its cemetery.  The vow of stability is unique to Benedictines.
+
+The solemn vows in other religious communities were eventually established as vows of obedience, poverty, and chastity. Poverty requires that they renounce any ownership of property or assets, except for items that were allowed to them by their superior (such as a religious habit, shoes, a cloak, etc.), and to live meekly, sharing whatever they might have with the poor.  Chastity requires that since they were willing to dedicate their lives to God, they sacrificed the love between men and women and would not marry. Also, they give up any act of sexual conduct.
+
+To become a monk, one first must become a postulant, during which time the man lives at the monastery to evaluate whether he is called to become a monk. As a postulant, the man is not bound by any vows, and is free to leave the monastery at any time. If the postulant and the community agree that the postulant should become a monk, the man is received as a novice, at which time he is given his religious habit, and begins to participate more fully in the life of the monastery. Following a period as a novice, usually six months to a year, the novice professes temporary vows, which can be renewed for a period of years. After a few years, the monk professes permanent vows, which are binding for life.
+
+The monastic life generally consists of prayer in the form of the Liturgy of the Hours (also known as the Divine Office) and divine reading (lectio divina) and manual labor. Among most religious orders, monks live in simple, austere rooms called cells and come together daily to celebrate the Conventual Mass and to recite the Liturgy of the Hours. In most communities, the monks take their meals together in the refectory. While there is no vow of silence, many communities have a period of silence lasting from evening until the next morning and some others restrict talking to only when it is necessary for the monks to perform their work and during weekly recreation.
+
+Monks who have been or will be ordained into Holy Orders as priests or deacons are referred to as choir monks, as they have the obligation to recite the entire Divine Office daily in choir. Those monks who are not ordained into Holy Orders are referred to as lay brothers. In most monastic communities today, little distinction exists between the lay brothers and the choir monks. However, historically, the roles of the two groups of monks within the monastery differed. The work of the choir monks was considered to be prayer, chanting the seven hours of the Divine Office and celebrating the Mass daily whereas the lay brothers provided for the material needs of the community by growing food, preparing meals, maintaining the monastery and the grounds. This distinction arose historically because generally those monks who could read Latin typically became choir monks, while those monks who were illiterate or could not read Latin became lay brothers. Since the lay brothers could not recite the Divine Office in Latin, they would instead pray easily memorizable prayers such as the Our Father or the Hail Mary as many as 150 times per day. Since the Second Vatican Council, the distinction between choir monks and lay brothers has been deemphasized, as the council allowed the Divine Office to be said in the vernacular language, effectively opening participation to all of the monks.
+
+Within western monasticism, it is important to differentiate between monks and friars. Monks generally live a contemplative life of prayer confined within a monastery while friars usually engage in an active ministry of service to the outside community. The monastic orders include all Benedictines (the Order of Saint Benedict and its later reforms including the Cistercians and the Trappists) and the Carthusians, who live according to their own Statutes, and not according to the Rule of St. Benedict proper. Orders of friars include the Franciscans, Dominicans, Carmelites, and Augustinians. Although the Canons Regular, such as the Norbertines, live in community, they are neither monks nor friars as they are characterized by their clerical state and not by any monastic vows.
+
+Loccum Abbey and Amelungsborn Abbey have the longest traditions as Lutheran monasteries; after the Reformation, many monasteries and convents were received into the Lutheran Church and continued religious life, existing to this day.[4]
+
+Since the 19th and 20th century, there has been a renewal in the monastic life among Lutheranism. Lutheran religious orders in the Franciscan, Benedictine and other traditions exist, with some Lutheran monasteries having third orders and accepting oblates.[5][6]
+
+In American Lutheran traditions, "The Congregation of the Servants of Christ" was established at St. Augustine's House in Oxford, Michigan, in 1958 when some other men joined Father Arthur Kreinheder in observing the monastic life and offices of prayer. These men and others came and went over the years. The community has always remained small; at times the only member was Father Arthur.[7] During the 35 years of its existence over 25 men tested their vocations to monastic life by living at the house for some time, from a few months to many years, but at Father Arthur's death in 1989 only one permanent resident remained. At the beginning of 2006, there was 2 permanent professed members and 2 long-term guests. Strong ties remain with this community and their brothers in Sweden (Östanbäck monastery) and in Germany (Priory of St. Wigbert).[8]
+
+There is also the Order of Lutheran Franciscans, a religious community of friars and sisters within the tradition of the Evangelical Lutheran Church in America.
+
+Monastic life in England came to an abrupt end when King Henry VIII broke from the Catholic Church and made himself the head of the Church of England. He initiated the Dissolution of the Monasteries, during which all of the monasteries within England were destroyed. A large number of monks were executed, others fled to continental European monasteries where they were able to continue their monastic life.
+
+Shortly after the beginning of the Anglo-Catholic Movement in the Church of England, there was felt to be a need for a restoration of the monastic life. In the 1840s, the then Anglican priest and future Catholic Cardinal John Henry Newman established a community of men at Littlemore near Oxford. From then on, there have been established many communities of monks, friars and other religious communities for men in the Anglican Communion. There are Anglican Benedictines, Franciscans, Cistercians, and in the Episcopal Church in the United States, Dominicans. There are also uniquely Anglican monastic orders such as the Society of Saint John the Evangelist and the Community of the Resurrection at Mirfield.
+
+Some Anglican religious communities are contemplative, some active, but a distinguishing feature of the monastic life among Anglicans is that most practice the so-called "mixed life". Anglican monks recite the Divine Office in choir daily, either the full eight services of the Breviary or the four offices found in the Book of Common Prayer and celebrate the Eucharist daily. Many orders take on external works such as service to the poor, giving religious retreats, or other active ministries within their immediate communities. Like Catholic monks, Anglican monks also take the monastic vows of poverty, chastity, and obedience.
+
+In the early 20th century when the Oxford Movement was at its height, the Anglican Communion had hundreds[citation needed] of orders and communities and thousands of religious followers. However, since the 1960s there has been a sharp falling off in the numbers of religious in many parts of the Anglican Communion. Many once large and international communities have been reduced to a single convent or monastery composed of elderly men or women. In the last few decades of the 20th century, novices have for most communities been few and far between. Some orders and communities have already become extinct.
+
+There are however, still several thousand Anglican monks working today in approximately 200 communities around the world. The most surprising growth has been in the Melanesian countries of the Solomon Islands, Vanuatu and Papua New Guinea. The Melanesian Brotherhood, founded at Tabalia, Guadalcanal, in 1925 by Ini Kopuria, is now the largest Anglican community in the world with over 450 brothers in the Solomon Islands, Vanuatu, Papua New Guinea, the Philippines and the United Kingdom.
+
+The Saint Brigid of Kildare Monastery is a double monastery of the United Methodist Church rooted in the Benedictine tradition, being located in Collegeville, Minnesota.[9] Besides monastic orders, the Order of Saint Luke is a dispersed religious order within Methodism, though being ecumenical, it accepts believers of other Christian denominations.
+
+The Emmanuel Sisters is a convent of the Presbyterian Church in Cameroon that was founded by Rev Mother Magdaline Marie Handy.[10] These nuns are engaged in prayer, teaching, and healthcare.[10]
+
+In Eastern Orthodoxy monasticism holds a very special and important place: "Angels are a light for monks, monks are a light for laymen" (St. John Klimakos). Orthodox monastics separate themselves from the world in order to pray unceasingly for the world. They do not, in general, have as their primary purpose the running of social services, but instead are concerned with attaining theosis, or union with God. However, care for the poor and needy has always been an obligation of monasticism,[citation needed] so not all monasteries are "cloistered". The level of contact will vary from community to community. Hermits, on the other hand, have little or no contact with the outside world.
+
+Orthodox monasticism does not have religious orders as are found in the West, nor do they have Rules in the same sense as the Rule of St. Benedict. Rather, Eastern monastics study and draw inspiration from the writings of the Desert Fathers as well as other Church Fathers; probably the most influential of which are the Greater Asketikon and Lesser Asketikon of St. Basil the Great and the Philokalia, which was compiled by St. Nikodemos of the Holy Mountain and St. Makarios of Corinth. Hesychasm is of primary importance in the ascetical theology of the Orthodox Church.
+
+Most communities are self-supporting, and the monastic’s daily life is usually divided into three parts: (a) communal worship in the catholicon (the monastery's main church); (b) hard manual labour; and (c) private prayer, spiritual study, and rest when necessary. Meals are usually taken in common in a sizable dining hall known as a trapeza (refectory), at elongated refectory tables. Food is usually simple and is eaten in silence while one of the brethren reads aloud from the spiritual writings of the Holy Fathers. The monastic lifestyle takes a great deal of serious commitment. Within the cenobitic community, all monks conform to a common way of living based on the traditions of that particular monastery. In struggling to attain this conformity, the monastic comes to realize his own shortcomings and is guided by his spiritual father in how to deal honestly with them. For this same reason, bishops are almost always chosen from the ranks of monks.
+
+Eastern monasticism is found in three distinct forms: anchoritic (a solitary living in isolation), cenobitic (a community living and worshiping together under the direct rule of an abbot or abbess), and the "middle way" between the two, known as the skete (a community of individuals living separately but in close proximity to one another, who come together only on Sundays and feast days, working and praying the rest of the time in solitude, but under the direction of an elder). One normally enters a cenobitic community first, and only after testing and spiritual growth would one go on to the skete or, for the most advanced, become a solitary anchorite. However, one is not necessarily expected to join a skete or become a solitary; most monastics remain in the cenobium the whole of their lives.
+
+In general, Orthodox monastics have little or no contact with the outside world, including their own families. The purpose of the monastic life is union with God, the means is through leaving the world (i.e., the life of the passions). After tonsure, Orthodox monks and nuns are never permitted to cut their hair. The hair of the head and the beard remain uncut as a symbol of the vows they have taken, reminiscent of the Nazarites from the Old Testament. The tonsure of monks is the token of a consecrated life, and symbolizes the cutting off of their self-will.
+
+The process of becoming a monk is intentionally slow, as the vows taken are considered to entail a lifelong commitment to God, and are not to be entered into lightly. In Orthodox monasticism after completing the novitiate, there are three ranks of monasticism. There is only one monastic habit in the Eastern Church (with certain slight regional variations), and it is the same for both monks and nuns. Each successive grade is given a portion of the habit, the full habit being worn only by those in the highest grade, known for that reason as the "Great Schema", or "Great Habit".
+
+The various profession rites are normally performed by the Abbot, but if the abbot has not been ordained a priest, or if the monastic community is a convent, a hieromonk will perform the service. The abbot or hieromonk who performs a tonsure must be of at least the rank he is tonsuring into. In other words, only a hieromonk who has been tonsured into the Great Schema may himself tonsure a Schemamonk. A bishop, however, may tonsure into any rank, regardless of his own.
+
+Novice (Church Slavonic: Poslushnik), lit. "one under obedience"—Those wishing to join a monastery begin their lives as novices. After coming to the monastery and living as a guest for not less than three days, the revered abbot or abbess may bless the candidate to become a novice. There is no formal ceremony for the clothing of a novice, he or she simply receives permission to wear the clothing of a novice. In the Eastern monastic tradition, novices may or may not dress in the black inner cassock (Greek: Anterion, Eisorasson; Church Slavonic: Podriasnik) and wear the soft monastic hat (Greek: Skoufos, Church Slavonic: Skufia), depending on the tradition of the local community, and in accordance to the abbot’s directives. The inner-cassock and the skoufos are the first part of the Orthodox monastic habit. In some communities, the novice also wears the leather belt. He is also given a prayer rope and instructed in the use of the Jesus Prayer. If a novice chooses to leave during the period of the novitiate, no penalty is incurred. He may also be asked to leave at any time if his behaviour does not conform to the monastic life, or if the superior discerns that he is not called to monasticism. When the abbot or abbess deems the novice ready, he is asked if he wishes to join the monastery. Some, out of humility, will choose to remain novices all their lives. Every stage of the monastic life must be entered into voluntarily.
+
+Rassophore (Church Slavonic: Ryassofor), lit. "Robe-bearer"—If the novice continues on to become a monk, he is clothed in the first degree of monasticism at a formal service known as the Tonsure. Although there are no formal vows made at this point, the candidate is normally required to affirm his commitment to persevere in the monastic life. The abbot will then perform the tonsure, cutting a small amount of hair from four spots on the head, forming a cross. He is then given the outer cassock (Greek: Rasson, Exorasson, or Mandorasson; Church Slavonic: Ryassa)—an outer robe with wide sleeves, something like the cowl used in the West, but without a hood—from which the name of Rassophore is derived. He is also given a brimless hat with a veil, known as a klobuk, and a leather belt is fastened around his waist. His habit is usually black, signifying that he is now dead to the world, and he receives a new name. Although the Rassophore does not make formal vows, he is still morally obligated to continue in the monastic estate for the rest of his life. Some will remain Rassophores permanently without going on to the higher degrees.
+
+Stavrophore (Church Slavonic: Krestonosets), lit. "Cross-bearer"—The next level for Eastern monastics takes place some years after the first tonsure when the abbot feels the monk has reached an appropriate level of discipline, dedication, and humility. This degree is also known as the Little Schema, and is considered to be a "betrothal" to the Great Schema. At this stage, the monk makes formal vows of stability, chastity, obedience and poverty. Then he is tonsured and clothed in the habit, which in addition to that worn by the Rassophore, includes the paramandyas (Church Slavonic: paraman), a piece of square cloth worn on the back, embroidered with the instruments of the Passion (see picture above), and connected by ties to a wooden cross worn over the heart. The paramandyas represents the yoke of Christ. Because of this addition he is now called Stavrophore, or Cross-bearer. He is also given a wooden hand cross (or "profession cross"), which he should keep in his icon corner, and a beeswax candle, symbolic of monastic vigilance the sacrificing of himself for God. He will be buried holding the cross, and the candle will be burned at his funeral. In the Slavic practice, the Stavrophore also wears the monastic mantle. The rasson (outer robe) worn by the Stavrophore is more ample than that worn by the Rassophore. The abbot increases the Stavrophore monk’s prayer rule, allows a more strict personal ascetic practice, and gives the monk more responsibility.
+
+Great Schema (Greek: Megaloschemos, Church Slavonic: Skhimnik)—Monks whose abbot feels they have reached a high level of spiritual excellence reach the final stage, called the Great Schema. The tonsure of a Schemamonk follows the same format as the Stavrophore, and he makes the same vows and is tonsured in the same manner. But in addition to all the garments worn by the Stavrophore, he is given the Analavos (Church Slavonic: Analav) which is the article of monastic vesture emblematic of the Great Schema. For this reason, the analavos itself is sometimes called the "Great Schema". The analavos comes down in the front and the back, somewhat like the scapular in Western monasticism, although the two garments are probably not related. It is often intricately embroidered with the instruments of the Passion and the Trisagion (the angelic hymn). The Greek form does not have a hood, the Slavic form has a hood and lappets on the shoulders, so that the garment forms a large cross covering the monk's shoulders, chest, and back. Another piece added is the Polystavrion or "Many Crosses", which consists of a cord with a number of small crosses plaited into it.  The polystavrion forms a yoke around the monk and serves to hold the analavos in place, and reminds the monastic that he is bound to Christ and that his arms are no longer fit for worldly activities, but that he must labor only for the Kingdom of Heaven.  Among the Greeks, the mantle is added at this stage.  The paramandyas of the Megaloschemos is larger than that of the Stavrophore, and if he wears the klobuk, it is of a distinctive thimble shape, called a koukoulion, the veil of which is usually embroidered with crosses.  In some monastic traditions the Great Schema is only given to monks and nuns on their death bed, while in others they may be elevated after as little as 25 years of service.
+
+Eastern Orthodox monks are addressed as "Father" even if they are not priests; but when conversing among themselves, monks will often address one another as "Brother".  Novices are always referred to as "Brother". Among the Greeks, old monks are often called Gheronda, or "Elder", out of respect for their dedication.  In the Slavic tradition, the title of Elder (Church Slavonic: Starets) is normally reserved for those who are of an advanced spiritual life, and who serve as guides to others.
+
+For the Orthodox, Mother is the correct term for nuns who have been tonsured Stavrophore or higher. Novices and Rassophores are addressed as "Sister".  Nuns live identical ascetic lives to their male counterparts and are therefore also called monachai (the feminine plural of monachos), and their community is likewise called a monastery.
+
+Many (but not all) Orthodox seminaries are attached to monasteries, combining academic preparation for ordination with participation in the community's life of prayer, and hopefully benefiting from the example and wise counsel of the monks.  Bishops are required by the sacred canons of the Orthodox Church to be chosen from among the monastic clergy. The requirement is specifically that they be monastics, not simply celibate (see clerical celibacy).  Monks who have been ordained to the priesthood are called hieromonks (priest-monks); monks who have been ordained to the diaconate are called hierodeacons (deacon-monks).  A Schemamonk who is a priest is called a Hieroschemamonk.  Most monks are not ordained; a community will normally only present as many candidates for ordination to the bishop as the liturgical needs of the community require.
+
+Hinduism has many monastic orders, including the Dashanami Sampradaya ("Tradition of Ten Names") orders established by Adi Shankara as well as Vaishnava orders.
+
+Madhvaacharya (Madhvacharya), the Dwaita philosopher, established ashta matha (Eight Monasteries). He appointed a monk (called swamiji or swamigalu in local parlance) for each matha or monastery who has the right to worship Madhvacharya's murti of Lord Krishna by rotation. Each matha's swamiji gets a chance to worship after fourteen years. This ritual is called Paryaya and has been used also outside his sampradaya, e.g. in Gaudiya Vaisnava Radharamana temple in Vrindavan.
+
+Similar in appearance to Buddhist monks, brahmacari monks from the International Society for Krishna Consciousness (ISKCON), or Hare Krishnas as they are popularly known, are the best known Vaishnava monks outside India. They are a common sight in many places around the world. Their appearance—simple saffron dhoti, shaved head with sikha, Tulasi neckbeads and tilaka markings—and social customs (sadhana) date back many thousands of years to the Vedic era with its varnasrama society. This social scheme includes both monastic and lay stages meant for various persons in various stages of life as per their characteristics (guna) and work (karma).
+
+ISKCON started as a predominantly monastic group but nowadays the majority of members live as lay persons. Many of them, however, spent some time as monks. New persons joining ISKCON as full-time members (living in its centers) first undergo a three-month Bhakta training, which includes learning the basics of brahmacari (monastic) life. After that they can decide if they prefer to continue as monks or as married Grihasthas.
+
+Brahmacari older than fifty years (as per ISKCON rule) can become sannyasi. Sannyasa, a life of full dedication to spiritual pursuits, is the highest stage of life in the varnasrama society. It is permanent and one cannot give it up. A Sannyasi is given the title Swami. Older grihastha with grown-up children are traditionally expected to accept vanaprastha (celibate retired) life.
+
+The role of monastic orders in Indian and now also Western society has to some extent been adapted over the years in accordance with ever-changing social structures.
+
+One of the most intense forms of Asceticism can be found in Jainism, one of the world's oldest religions. Jainism encourages fasting, yoga practices, meditation in difficult postures, and other austerities.[11] According to Jains, one's highest goal should be attaining Nirvana or Moksha (i.e., liberation from samsara, the cycle of birth and rebirth). For this, a soul has to be without attachment or self-indulgence. This can be achieved only by the monks and nuns who take five great vows: of non-violence, of truth, of non-stealing, of non-possession and of celibacy.
+
+Most of the austerities and ascetic practices can be traced back to Vardhaman Mahavira, the twenty-fourth "fordmaker" or Tirthankara. The Acaranga Sutra, or Book of Good Conduct, is a sacred book within Jainism that discusses the ascetic code of conduct. Other texts that provide insight into conduct of ascetics include Yogashastra by Acharya Hemachandra and Niyamasara by Acharya Kundakunda. Other illustrious Jain works on ascetic conduct are Oghanijjutti, Pindanijjutti, Cheda Sutta, and Nisiha Suttafee.
+
+Full Jain monk in either Svetambara or Digambara tradition[12] can belong to one of these ranks:
+
+These three are mentioned is the three lines of the Namokar Mantra. In the Digambara tradition, a junior monk can be a:
+
+The Svetambar Terapanthi sect has a new rank of junior monks who are called samana. The nuns are called Aryikas in Digambar tradition and Sadhvi in the Svetambar tradition.
+
+As per the Jain vows, the monks and nuns renounce all relations and possessions. Jain ascetics practice complete non-violence. Ahimsa is the first and foremost vow of a Jain ascetic. They do not hurt any living being, be it an insect or a human. They carry a special broom to sweep away any insects that may cross their path. Some Jain monks wear a cloth over the mouth to prevent accidental harm to airborne germs and insects. They also do not use electricity as it involves violence. Furthermore, they do not use any devices or machines.
+
+As they are without possession and attachment, they travel from city to city, often crossing forests and deserts, and always barefoot. Jain ascetics do not stay in a single place for more than two months to prevent themselves from becoming attached to any location. However, during four months of monsoon (rainy season) known as chaturmaas, they continue to stay in a single place to avoid killing the life forms that thrive during the rains.
+Jain monks and nuns practice complete celibacy. They do not touch or share a sitting platform with a person of opposite sex.
+
+Jain ascetics follow a strict vegetarian diet without root vegetables. Shvetambara monks do not cook food but solicit alms from householders. Digambara monks have only a single meal a day. Neither group will beg for food, but a Jain ascetic may accept a meal from a householder, provided that the latter is pure of mind and body and offers the food of his own volition and in the prescribed manner. During such an encounter, the monk remains standing and eats only a measured amount. Fasting (i.e., abstinence from food and sometimes water) is a routine feature of Jain asceticism. Fasts last for a day or longer, up to a month. Some monks avoid (or limit) medicine or hospitalization due to their careful attention to body.
+
+Other austerities include meditation in seated or standing posture near river banks in the cold wind, or meditation atop hills and mountains, especially at noon when the sun is at its fiercest. Such austerities are undertaken according to the physical and mental limits of the individual ascetic. Jain ascetics are (almost) completely without possessions. Some Jains (Shvetambara monks and nuns) own only unstitched white robes (an upper and lower garment) and a bowl used for eating and collecting alms. Male Digambara monks do not wear any clothes and carry nothing with them except a soft broom made of shed peacock feathers (pinchi) and eat from their hands. They sleep on the floor without blankets and sit on special wooden platforms.
+
+Every day is spent either in study of scriptures or meditation or teaching to lay people. They stand aloof from worldly matters. Many Jain ascetics take a final vow of Santhara or Sallekhana (i.e., a peaceful and detached death where medicines, food, and water are abandoned). This is done when death is imminent or when a monk feels that he is unable to adhere to his vows on account of advanced age or terminal disease.
+
+Quotes on ascetic practices from the Akaranga Sutra as Hermann Jacobi translated it:[13][14]
+
+A monk or a nun wandering from village to village should look forward for four cubits, and seeing animals they should move on by walking on his toes or heels or the sides of his feet. If there be some bypath, they should choose it, and not go straight on; then they may circumspectly wander from village to village.
+
+I shall become a Sramana who owns no house, no property, no sons, no cattle, who eats what others give him; I shall commit no sinful action; Master, I renounce to accept anything that has not been given.' Having taken such vows, (a mendicant) should not, on entering a village or scot-free town, &c., take himself, or induce others to take, or allow others to take, what has not been given.

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+
+
+Asteroids are minor planets, especially of the inner Solar System. Larger asteroids have also been called planetoids. These terms have historically been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered that were found to have volatile-rich surfaces similar to comets, these came to be distinguished from the objects found in the main asteroid belt.[1]
+
+In this article, the term "asteroid" refers to the minor planets of the inner Solar System, including those co-orbital with Jupiter.
+
+Millions of asteroids exist, many the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets.[2] The vast majority of known asteroids orbit within the main asteroid belt located between the orbits of Mars and Jupiter, or are co-orbital with Jupiter (the Jupiter trojans). However, other orbital families exist with significant populations, including the near-Earth objects. Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, and S-type. These were named after and are generally identified with carbon-rich, metallic, and silicate (stony) compositions, respectively. The sizes of asteroids varies greatly; the largest, Ceres, is almost 1,000 km (600 mi) across and massive enough to qualify as a dwarf planet.
+
+Asteroids are somewhat arbitrarily differentiated from comets and meteoroids. In the case of comets, the difference is one of composition: while asteroids are mainly composed of mineral and rock, comets are primarily composed of dust and ice. Furthermore, asteroids formed closer to the sun, preventing the development of cometary ice.[3] The difference between asteroids and meteoroids is mainly one of size: meteoroids have a diameter of one meter or less, whereas asteroids have a diameter of greater than one meter.[4] Finally, meteoroids can be composed of either cometary or asteroidal materials.[5]
+
+Only one asteroid, 4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the naked eye for a short time.[6] As of March 2020[update], the Minor Planet Center had data on 930,000 minor planets in the inner and outer Solar System, of which about 545,000 had enough information to be given numbered designations.[7]
+
+The United Nations declared 30 June as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908.[8][9]
+
+In April 2018, the B612 Foundation reported "It is 100 percent certain we'll be hit [by a devastating asteroid], but we're not 100 percent sure when."[10] Also in 2018, physicist Stephen Hawking,
+in his final book Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet.[11][12][13] In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, and has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.[14][15][16][17][18] According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched.[19]
+
+The first asteroid to be discovered, Ceres, was originally considered to be a new planet.[a] This was followed by the discovery of other similar bodies, which, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though readily distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid",[b] coined in Greek as ἀστεροειδής, or asteroeidēs, meaning 'star-like, star-shaped', and derived from the Ancient Greek ἀστήρ astēr 'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" (not always qualified as "minor") were still used interchangeably.[c]
+
+Discovery timeline:[23]
+
+Asteroid discovery methods have dramatically improved over the past two centuries.
+
+In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law, partly because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law.[26] This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, be spotted. The expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers.
+
+The first object, Ceres, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily. He discovered a new star-like object in Taurus and followed the displacement of this object during several nights. Later that year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, which was found to be between the planets Mars and Jupiter. Piazzi named it after Ceres, the Roman goddess of agriculture.[26]
+
+Three other asteroids (2 Pallas, 3 Juno, and 4 Vesta) were discovered over the next few years, with Vesta found in 1807. After eight more years of fruitless searches, most astronomers assumed that there were no more and abandoned any further searches.[citation needed]
+
+However, Karl Ludwig Hencke persisted, and began searching for more asteroids in 1830. Fifteen years later, he found 5 Astraea, the first new asteroid in 38 years. He also found 6 Hebe less than two years later. After this, other astronomers joined in the search and at least one new asteroid was discovered every year after that (except the wartime year 1945). Notable asteroid hunters of this early era were J.R. Hind, A. de Gasparis, R. Luther, H.M.S. Goldschmidt, J. Chacornac, J. Ferguson, N.R. Pogson, E.W. Tempel, J.C. Watson, C.H.F. Peters, A. Borrelly, J. Palisa, the Henry brothers and A. Charlois.
+
+In 1891, Max Wolf pioneered the use of astrophotography to detect asteroids, which appeared as short streaks on long-exposure photographic plates. This dramatically increased the rate of detection compared with earlier visual methods: Wolf alone discovered 248 asteroids, beginning with 323 Brucia, whereas only slightly more than 300 had been discovered up to that point. It was known that there were many more, but most astronomers did not bother with them, some calling them "vermin of the skies",[27] a phrase variously attributed to E. Suess[28] and E. Weiss.[29] Even a century later, only a few thousand asteroids were identified, numbered and named.
+
+Until 1998, asteroids were discovered by a four-step process. First, a region of the sky was photographed by a wide-field telescope, or astrograph. Pairs of photographs were taken, typically one hour apart. Multiple pairs could be taken over a series of days. Second, the two films or plates of the same region were viewed under a stereoscope. Any body in orbit around the Sun would move slightly between the pair of films. Under the stereoscope, the image of the body would seem to float slightly above the background of stars. Third, once a moving body was identified, its location would be measured precisely using a digitizing microscope. The location would be measured relative to known star locations.[30]
+
+These first three steps do not constitute asteroid discovery: the observer has only found an apparition, which gets a provisional designation, made up of the year of discovery, a letter representing the half-month of discovery, and finally a letter and a number indicating the discovery's sequential number (example: 1998 FJ74).
+
+The last step of discovery is to send the locations and time of observations to the Minor Planet Center, where computer programs determine whether an apparition ties together earlier apparitions into a single orbit. If so, the object receives a catalogue number and the observer of the first apparition with a calculated orbit is declared the discoverer, and granted the honor of naming the object subject to the approval of the International Astronomical Union.
+
+There is increasing interest in identifying asteroids whose orbits cross Earth's, and that could, given enough time, collide with Earth (see Earth-crosser asteroids). The three most important groups of near-Earth asteroids are the Apollos, Amors, and Atens. Various asteroid deflection strategies have been proposed, as early as the 1960s.
+
+The near-Earth asteroid 433 Eros had been discovered as long ago as 1898, and the 1930s brought a flurry of similar objects. In order of discovery, these were: 1221 Amor, 1862 Apollo, 2101 Adonis, and finally 69230 Hermes, which approached within 0.005 AU of Earth in 1937. Astronomers began to realize the possibilities of Earth impact.
+
+Two events in later decades increased the alarm: the increasing acceptance of the Alvarez hypothesis that an impact event resulted in the Cretaceous–Paleogene extinction, and the 1994 observation of Comet Shoemaker-Levy 9 crashing into Jupiter. The U.S. military also declassified the information that its military satellites, built to detect nuclear explosions, had detected hundreds of upper-atmosphere impacts by objects ranging from one to ten meters across.
+
+All these considerations helped spur the launch of highly efficient surveys that consist of charge-coupled device (CCD) cameras and computers directly connected to telescopes. As of 2011[update], it was estimated that 89% to 96% of near-Earth asteroids one kilometer or larger in diameter had been discovered.[31] A list of teams using such systems includes:[32]
+[33]
+
+As of 29 October 2018[update], the LINEAR system alone has discovered 147,132 asteroids.[34] Among all the surveys, 19,266 near-Earth asteroids have been discovered[35] including almost 900 more than 1 km (0.6 mi) in diameter.[36]
+
+Traditionally, small bodies orbiting the Sun were classified as comets, asteroids, or meteoroids, with anything smaller than one meter across being called a meteoroid. Beech and Steel's 1995 paper proposed a meteoroid definition including size limits.[37][38] The term "asteroid", from the Greek word for "star-like", never had a formal definition, with the broader term minor planet being preferred by the International Astronomical Union.
+
+However, following the discovery of asteroids below ten meters in size, Rubin and Grossman's 2010 paper revised the previous definition of meteoroid to objects between 10 µm and 1 meter in size in order to maintain the distinction between asteroids and meteoroids.[4] The smallest asteroids discovered (based on absolute magnitude H) are 2008 TS26 with {{{1}}} and 2011 CQ1 with {{{1}}} both with an estimated size of about 1 meter.[39]
+
+In 2006, the term "small Solar System body" was also introduced to cover both most minor planets and comets.[40][d] Other languages prefer "planetoid" (Greek for "planet-like"), and this term is occasionally used in English especially for larger minor planets such as the dwarf planets as well as an alternative for asteroids since they are not star-like.[41] The word "planetesimal" has a similar meaning, but refers specifically to the small building blocks of the planets that existed when the Solar System was forming. The term "planetule" was coined by the geologist William Daniel Conybeare to describe minor planets,[42] but is not in common use. The three largest objects in the asteroid belt, Ceres, Pallas, and Vesta, grew to the stage of protoplanets. Ceres is a dwarf planet, the only one in the inner Solar System.
+
+When found, asteroids were seen as a class of objects distinct from comets, and there was no unified term for the two until "small Solar System body" was coined in 2006. The main difference between an asteroid and a comet is that a comet shows a coma due to sublimation of near surface ices by solar radiation. A few objects have ended up being dual-listed because they were first classified as minor planets but later showed evidence of cometary activity. Conversely, some (perhaps all) comets are eventually depleted of their surface volatile ices and become asteroid-like. A further distinction is that comets typically have more eccentric orbits than most asteroids; most "asteroids" with notably eccentric orbits are probably dormant or extinct comets.[43]
+
+For almost two centuries, from the discovery of Ceres in 1801 until the discovery of the first centaur, Chiron in 1977, all known asteroids spent most of their time at or within the orbit of Jupiter, though a few such as Hidalgo ventured far beyond Jupiter for part of their orbit. Those located between the orbits of Mars and Jupiter were known for many years simply as The Asteroids.[44] When astronomers started finding more small bodies that permanently resided further out than Jupiter, now called centaurs, they numbered them among the traditional asteroids, though there was debate over whether they should be considered asteroids or as a new type of object. Then, when the first trans-Neptunian object (other than Pluto), Albion, was discovered in 1992, and especially when large numbers of similar objects started turning up, new terms were invented to sidestep the issue: Kuiper-belt object, trans-Neptunian object, scattered-disc object, and so on. These inhabit the cold outer reaches of the Solar System where ices remain solid and comet-like bodies are not expected to exhibit much cometary activity; if centaurs or trans-Neptunian objects were to venture close to the Sun, their volatile ices would sublimate, and traditional approaches would classify them as comets and not asteroids.
+
+The innermost of these are the Kuiper-belt objects, called "objects" partly to avoid the need to classify them as asteroids or comets.[45] They are thought to be predominantly comet-like in composition, though some may be more akin to asteroids.[46] Furthermore, most do not have the highly eccentric orbits associated with comets, and the ones so far discovered are larger than traditional comet nuclei. (The much more distant Oort cloud is hypothesized to be the main reservoir of dormant comets.) Other recent observations, such as the analysis of the cometary dust collected by the Stardust probe, are increasingly blurring the distinction between comets and asteroids,[47] suggesting "a continuum between asteroids and comets" rather than a sharp dividing line.[48]
+
+The minor planets beyond Jupiter's orbit are sometimes also called "asteroids", especially in popular presentations.[e] However, it is becoming increasingly common for the term "asteroid" to be restricted to minor planets of the inner Solar System.[45] Therefore, this article will restrict itself for the most part to the classical asteroids: objects of the asteroid belt, Jupiter trojans, and near-Earth objects.
+
+When the IAU introduced the class small Solar System bodies in 2006 to include most objects previously classified as minor planets and comets, they created the class of dwarf planets for the largest minor planets – those that have enough mass to have become ellipsoidal under their own gravity. According to the IAU, "the term 'minor planet' may still be used, but generally the term 'Small Solar System Body' will be preferred."[49] Currently only the largest object in the asteroid belt, Ceres, at about 975 km (606 mi) across, has been placed in the dwarf planet category.
+
+It is thought that planetesimals in the asteroid belt evolved much like the rest of the solar nebula until Jupiter neared its current mass, at which point excitation from orbital resonances with Jupiter ejected over 99% of planetesimals in the belt. Simulations and a discontinuity in spin rate and spectral properties suggest that asteroids larger than approximately 120 km (75 mi) in diameter accreted during that early era, whereas smaller bodies are fragments from collisions between asteroids during or after the Jovian disruption.[51] Ceres and Vesta grew large enough to melt and differentiate, with heavy metallic elements sinking to the core, leaving rocky minerals in the crust.[52]
+
+In the Nice model, many Kuiper-belt objects are captured in the outer asteroid belt, at distances greater than 2.6 AU. Most were later ejected by Jupiter, but those that remained may be the D-type asteroids, and possibly include Ceres.[53]
+
+Various dynamical groups of asteroids have been discovered orbiting in the inner Solar System. Their orbits are perturbed by the gravity of other bodies in the Solar System and by the Yarkovsky effect. Significant populations include:
+
+The majority of known asteroids orbit within the asteroid belt between the orbits of Mars and Jupiter, generally in relatively low-eccentricity (i.e. not very elongated) orbits. This belt is now estimated to contain between 1.1 and 1.9 million asteroids larger than 1 km (0.6 mi) in diameter,[54] and millions of smaller ones. These asteroids may be remnants of the protoplanetary disk, and in this region the accretion of planetesimals into planets during the formative period of the Solar System was prevented by large gravitational perturbations by Jupiter.
+
+Trojans are populations that share an orbit with a larger planet or moon, but do not collide with it because they orbit in one of the two Lagrangian points of stability, L4 and L5, which lie 60° ahead of and behind the larger body.
+The most significant population of trojans are the Jupiter trojans. Although fewer Jupiter trojans have been discovered (As of 2010[update]), it is thought that they are as numerous as the asteroids in the asteroid belt. Trojans have been found in the orbits of other planets, including Venus, Earth, Mars, Uranus, and Neptune.
+
+Near-Earth asteroids, or NEAs, are asteroids that have orbits that pass close to that of Earth. Asteroids that actually cross Earth's orbital path are known as Earth-crossers. As of June 2016[update], 14,464 near-Earth asteroids are known[31] and the number over one kilometer in diameter is estimated to be 900–1,000.
+
+Asteroids vary greatly in size, from almost 1000 km for the largest down to rocks just 1 meter across.[f] The three largest are very much like miniature planets: they are roughly spherical, have at least partly differentiated interiors,[55] and are thought to be surviving protoplanets. The vast majority, however, are much smaller and are irregularly shaped; they are thought to be either battered planetesimals or fragments of larger bodies.
+
+The dwarf planet Ceres is by far the largest asteroid, with a diameter of 940 km (580 mi). The next largest are 4 Vesta and 2 Pallas, both with diameters of just over 500 km (300 mi). Vesta is the only main-belt asteroid that can, on occasion, be visible to the naked eye. On some rare occasions, a near-Earth asteroid may briefly become visible without technical aid; see 99942 Apophis.
+
+The mass of all the objects of the asteroid belt, lying between the orbits of Mars and Jupiter, is estimated to be in the range of (2.8–3.2)×1021 kg, about 4% of the mass of the Moon. Of this, Ceres comprises 0.938×1021 kg, about a third of the total. Adding in the next three most massive objects, Vesta (9%), Pallas (7%), and Hygiea (3%), brings this figure up to half, whereas the three most-massive asteroids after that, 511 Davida (1.2%), 704 Interamnia (1.0%), and 52 Europa (0.9%), constitute only another 3%. The number of asteroids increases rapidly as their individual masses decrease.
+
+The number of asteroids decreases markedly with size. Although this generally follows a power law, there are 'bumps' at 5 km and 100 km, where more asteroids than expected from a logarithmic distribution are found.[56]
+
+Although their location in the asteroid belt excludes them from planet status, the three largest objects, Ceres, Vesta, and Pallas, are intact protoplanets that share many characteristics common to planets, and are atypical compared to the majority of irregularly shaped asteroids. The fourth largest asteroid, Hygiea, appears nearly spherical although it may have an undifferentiated interior[citation needed], like the majority of asteroids. Between them, the four largest asteroids constitute half the mass of the asteroid belt.
+
+Ceres is the only asteroid with a fully ellipsoidal shape and hence the only one that is a dwarf planet.[40] It has a much higher absolute magnitude than the other asteroids, of around 3.32,[57] and may possess a surface layer of ice.[58] Like the planets, Ceres is differentiated: it has a crust, a mantle and a core.[58] No meteorites from Ceres have been found on Earth.
+
+Vesta, too, has a differentiated interior, though it formed inside the Solar System's frost line, and so is devoid of water;[59][60] its composition is mainly of basaltic rock with minerals such as olivine.[61] Aside from the large crater at its southern pole, Rheasilvia, Vesta also has an ellipsoidal shape. Vesta is the parent body of the Vestian family and other V-type asteroids, and is the source of the HED meteorites, which constitute 5% of all meteorites on Earth.
+
+Pallas is unusual in that, like Uranus, it rotates on its side, with its axis of rotation tilted at high angles to its orbital plane.[62] Its composition is similar to that of Ceres: high in carbon and silicon, and perhaps partially differentiated.[63] Pallas is the parent body of the Palladian family of asteroids.
+
+Hygiea is the largest carbonaceous asteroid[64] and, unlike the other largest asteroids, lies relatively close to the plane of the ecliptic.[65] It is the largest member and presumed parent body of the Hygiean family of asteroids. Because there is no sufficiently large crater on the surface to be the source of that family, as there is on Vesta, it is thought that Hygiea may have been completely disrupted in the collision that formed the Hygiean family, and recoalesced after losing a bit less than 2% of its mass. Observations taken with the Very Large Telescope's SPHERE imager in 2017 and 2018, and announced in late 2019, revealed that Hygiea has a nearly spherical shape, which is at consistent both with it being in hydrostatic equilibrium (and thus a dwarf planet), or formerly being in hydrostatic equilibrium, or with being disrupted and recoalescing.[66][67]
+
+Measurements of the rotation rates of large asteroids in the asteroid belt show that there is an upper limit. Very few asteroids with a diameter larger than 100 meters have a rotation period smaller than 2.2 hours.[70] For asteroids rotating faster than approximately this rate, the inertial force at the surface is greater than the gravitational force, so any loose surface material would be flung out. However, a solid object should be able to rotate much more rapidly. This suggests that most asteroids with a diameter over 100 meters are rubble piles formed through accumulation of debris after collisions between asteroids.[71]
+
+The physical composition of asteroids is varied and in most cases poorly understood. Ceres appears to be composed of a rocky core covered by an icy mantle, where Vesta is thought to have a nickel-iron core, olivine mantle, and basaltic crust.[72] 10 Hygiea, however, which appears to have a uniformly primitive composition of carbonaceous chondrite, is thought to be the largest undifferentiated asteroid. Most of the smaller asteroids are thought to be piles of rubble held together loosely by gravity, though the largest are probably solid. Some asteroids have moons or are co-orbiting binaries: Rubble piles, moons, binaries, and scattered asteroid families are thought to be the results of collisions that disrupted a parent asteroid, or, possibly, a planet.[73]
+
+Asteroids contain traces of amino acids and other organic compounds, and some speculate that asteroid impacts may have seeded the early Earth with the chemicals necessary to initiate life, or may have even brought life itself to Earth (also see panspermia).[74][75] In August 2011, a report, based on NASA studies with meteorites found on Earth, was published suggesting DNA and RNA components (adenine, guanine and related organic molecules) may have been formed on asteroids and comets in outer space.[76][77][78]
+
+Composition is calculated from three primary sources: albedo, surface spectrum, and density. The last can only be determined accurately by observing the orbits of moons the asteroid might have. So far, every asteroid with moons has turned out to be a rubble pile, a loose conglomeration of rock and metal that may be half empty space by volume. The investigated asteroids are as large as 280 km in diameter, and include 121 Hermione (268×186×183 km), and 87 Sylvia (384×262×232 km). Only half a dozen asteroids are larger than 87 Sylvia, though none of them have moons; however, some smaller asteroids are thought to be more massive, suggesting they may not have been disrupted, and indeed 511 Davida, the same size as Sylvia to within measurement error, is estimated to be two and a half times as massive, though this is highly uncertain. The fact that such large asteroids as Sylvia can be rubble piles, presumably due to disruptive impacts, has important consequences for the formation of the Solar System: Computer simulations of collisions involving solid bodies show them destroying each other as often as merging, but colliding rubble piles are more likely to merge. This means that the cores of the planets could have formed relatively quickly.[79]
+
+On 7 October 2009, the presence of water ice was confirmed on the surface of 24 Themis using NASA's Infrared Telescope Facility. The surface of the asteroid appears completely covered in ice. As this ice layer is sublimating, it may be getting replenished by a reservoir of ice under the surface. Organic compounds were also detected on the surface.[80][81][82][83] Scientists hypothesize that some of the first water brought to Earth was delivered by asteroid impacts after the collision that produced the Moon. The presence of ice on 24 Themis supports this theory.[82]
+
+In October 2013, water was detected on an extrasolar body for the first time, on an asteroid orbiting the white dwarf GD 61.[84] On 22 January 2014, European Space Agency (ESA) scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt.[85] The detection was made by using the far-infrared abilities of the Herschel Space Observatory.[86] The finding is unexpected because comets, not asteroids, are typically considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids."[86]
+
+In May 2016, significant asteroid data arising from the Wide-field Infrared Survey Explorer and NEOWISE missions have been questioned.[87][88][89] Although the early original criticism had not undergone peer review,[90] a more recent peer-reviewed study was subsequently published.[91][18]
+
+In November 2019, scientists reported detecting, for the first time, sugar molecules, including ribose, in meteorites, suggesting that chemical processes on asteroids can produce some fundamentally essential bio-ingredients important to life, and supporting the notion of an RNA world prior to a DNA-based origin of life on Earth, and possibly, as well, the notion of panspermia.[92][93]
+
+Most asteroids outside the "big four" (Ceres, Pallas, Vesta, and Hygiea) are likely to be broadly similar in appearance, if irregular in shape. 50 km (31 mi) 253 Mathilde is a rubble pile saturated with craters with diameters the size of the asteroid's radius, and Earth-based observations of 300 km (186 mi) 511 Davida, one of the largest asteroids after the big four, reveal a similarly angular profile, suggesting it is also saturated with radius-size craters.[94] Medium-sized asteroids such as Mathilde and 243 Ida that have been observed up close also reveal a deep regolith covering the surface. Of the big four, Pallas and Hygiea are practically unknown. Vesta has compression fractures encircling a radius-size crater at its south pole but is otherwise a spheroid. Ceres seems quite different in the glimpses Hubble has provided, with surface features that are unlikely to be due to simple craters and impact basins, but details will be expanded with the Dawn spacecraft, which entered Ceres orbit on 6 March 2015.[95]
+
+Asteroids become darker and redder with age due to space weathering.[96] However evidence suggests most of the color change occurs rapidly, in the first hundred thousands years, limiting the usefulness of spectral measurement for determining the age of asteroids.[97]
+
+Asteroids are commonly categorized according to two criteria: the characteristics of their orbits, and features of their reflectance spectrum.
+
+Many asteroids have been placed in groups and families based on their orbital characteristics. Apart from the broadest divisions, it is customary to name a group of asteroids after the first member of that group to be discovered. Groups are relatively loose dynamical associations, whereas families are tighter and result from the catastrophic break-up of a large parent asteroid sometime in the past.[98] Families are more common and easier to identify within the main asteroid belt, but several small families have been reported among the Jupiter trojans.[99] Main belt families were first recognized by Kiyotsugu Hirayama in 1918 and are often called Hirayama families in his honor.
+
+About 30–35% of the bodies in the asteroid belt belong to dynamical families each thought to have a common origin in a past collision between asteroids. A family has also been associated with the plutoid dwarf planet Haumea.
+
+Some asteroids have unusual horseshoe orbits that are co-orbital with Earth or some other planet. Examples are 3753 Cruithne and 2002 AA29. The first instance of this type of orbital arrangement was discovered between Saturn's moons Epimetheus and Janus.
+
+Sometimes these horseshoe objects temporarily become quasi-satellites for a few decades or a few hundred years, before returning to their earlier status. Both Earth and Venus are known to have quasi-satellites.
+
+Such objects, if associated with Earth or Venus or even hypothetically Mercury, are a special class of Aten asteroids. However, such objects could be associated with outer planets as well.
+
+In 1975, an asteroid taxonomic system based on color, albedo, and spectral shape was developed by Chapman, Morrison, and Zellner.[100] These properties are thought to correspond to the composition of the asteroid's surface material. The original classification system had three categories: C-types for dark carbonaceous objects (75% of known asteroids), S-types for stony (silicaceous) objects (17% of known asteroids) and U for those that did not fit into either C or S. This classification has since been expanded to include many other asteroid types. The number of types continues to grow as more asteroids are studied.
+
+The two most widely used taxonomies now used are the Tholen classification and SMASS classification. The former was proposed in 1984 by David J. Tholen, and was based on data collected from an eight-color asteroid survey performed in the 1980s. This resulted in 14 asteroid categories.[101] In 2002, the Small Main-Belt Asteroid Spectroscopic Survey resulted in a modified version of the Tholen taxonomy with 24 different types. Both systems have three broad categories of C, S, and X asteroids, where X consists of mostly metallic asteroids, such as the M-type. There are also several smaller classes.[102]
+
+The proportion of known asteroids falling into the various spectral types does not necessarily reflect the proportion of all asteroids that are of that type; some types are easier to detect than others, biasing the totals.
+
+Originally, spectral designations were based on inferences of an asteroid's composition.[103] However, the correspondence between spectral class and composition is not always very good, and a variety of classifications are in use. This has led to significant confusion. Although asteroids of different spectral classifications are likely to be composed of different materials, there are no assurances that asteroids within the same taxonomic class are composed of the same (or similar) materials.
+
+A newly discovered asteroid is given a provisional designation (such as 2002 AT4) consisting of the year of discovery and an alphanumeric code indicating the half-month of discovery and the sequence within that half-month. Once an asteroid's orbit has been confirmed, it is given a number, and later may also be given a name (e.g. 433 Eros). The formal naming convention uses parentheses around the number – e.g. (433) Eros – but dropping the parentheses is quite common. Informally, it is common to drop the number altogether, or to drop it after the first mention when a name is repeated in running text.[104] In addition, names can be proposed by the asteroid's discoverer, within guidelines established by the International Astronomical Union.[105]
+
+The first asteroids to be discovered were assigned iconic symbols like the ones traditionally used to designate the planets. By 1855 there were two dozen asteroid symbols, which often occurred in multiple variants.[106]
+
+In 1851,[111] after the fifteenth asteroid (Eunomia) had been discovered, Johann Franz Encke made a major change in the upcoming 1854 edition of the Berliner Astronomisches Jahrbuch (BAJ, Berlin Astronomical Yearbook). He introduced a disk (circle), a traditional symbol for a star, as the generic symbol for an asteroid. The circle was then numbered in order of discovery to indicate a specific asteroid (although he assigned ① to the fifth, Astraea, while continuing to designate the first four only with their existing iconic symbols). The numbered-circle convention was quickly adopted by astronomers, and the next asteroid to be discovered (16 Psyche, in 1852) was the first to be designated in that way at the time of its discovery. However, Psyche was given an iconic symbol as well, as were a few other asteroids discovered over the next few years (see chart above). 20 Massalia was the first asteroid that was not assigned an iconic symbol, and no iconic symbols were created after the 1855 discovery of 37 Fides.[h] That year Astraea's number was increased to ⑤, but the first four asteroids, Ceres to Vesta, were not listed by their numbers until the 1867 edition. The circle was soon abbreviated to a pair of parentheses, which were easier to typeset and sometimes omitted altogether over the next few decades, leading to the modern convention.[107]
+
+Until the age of space travel, objects in the asteroid belt were merely pinpricks of light in even the largest telescopes and their shapes and terrain remained a mystery. The best modern ground-based telescopes and the Earth-orbiting Hubble Space Telescope can resolve a small amount of detail on the surfaces of the largest asteroids, but even these mostly remain little more than fuzzy blobs. Limited information about the shapes and compositions of asteroids can be inferred from their light curves (their variation in brightness as they rotate) and their spectral properties, and asteroid sizes can be estimated by timing the lengths of star occulations (when an asteroid passes directly in front of a star). Radar imaging can yield good information about asteroid shapes and orbital and rotational parameters, especially for near-Earth asteroids. In terms of delta-v and propellant requirements, NEOs are more easily accessible than the Moon.[112]
+
+The first close-up photographs of asteroid-like objects were taken in 1971, when the Mariner 9 probe imaged Phobos and Deimos, the two small moons of Mars, which are probably captured asteroids. These images revealed the irregular, potato-like shapes of most asteroids, as did later images from the Voyager probes of the small moons of the gas giants.
+
+The first true asteroid to be photographed in close-up was 951 Gaspra in 1991, followed in 1993 by 243 Ida and its moon Dactyl, all of which were imaged by the Galileo probe en route to Jupiter.
+
+The first dedicated asteroid probe was NEAR Shoemaker, which photographed 253 Mathilde in 1997, before entering into orbit around 433 Eros, finally landing on its surface in 2001.
+
+Other asteroids briefly visited by spacecraft en route to other destinations include 9969 Braille (by Deep Space 1 in 1999), and 5535 Annefrank (by Stardust in 2002).
+
+From September to November 2005, the Japanese Hayabusa probe studied 25143 Itokawa in detail and was plagued with difficulties, but returned samples of its surface to Earth on 13 June 2010.
+
+The European Rosetta probe (launched in 2004) flew by 2867 Šteins in 2008 and 21 Lutetia, the third-largest asteroid visited to date, in 2010.
+
+In September 2007, NASA launched the Dawn spacecraft, which orbited 4 Vesta from July 2011 to September 2012, and has been orbiting the dwarf planet 1 Ceres since 2015. 4 Vesta is the second-largest asteroid visited to date.
+
+On 13 December 2012, China's lunar orbiter Chang'e 2 flew within 3.2 km (2 mi) of the asteroid 4179 Toutatis on an extended mission.
+
+The Japan Aerospace Exploration Agency (JAXA) launched the Hayabusa2 probe in December 2014, and plans to return samples from 162173 Ryugu in December 2020.
+
+In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, and has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.[14][15][16][18]
+
+In September 2016, NASA launched the OSIRIS-REx sample return mission to asteroid 101955 Bennu, which it reached in December 2018. As of June 2019[update], the probe is in orbit around the asteroid.[113]
+
+In early 2013, NASA announced the planning stages of a mission to capture a near-Earth asteroid and move it into lunar orbit where it could possibly be visited by astronauts and later impacted into the Moon.[114] On 19 June 2014, NASA reported that asteroid 2011 MD was a prime candidate for capture by a robotic mission, perhaps in the early 2020s.[115]
+
+It has been suggested that asteroids might be used as a source of materials that may be rare or exhausted on Earth (asteroid mining), or materials for constructing space habitats (see Colonization of the asteroids). Materials that are heavy and expensive to launch from Earth may someday be mined from asteroids and used for space manufacturing and construction.
+
+In the U.S. Discovery program the Psyche spacecraft proposal to 16 Psyche and Lucy spacecraft to Jupiter trojans made it to the semi-finalist stage of mission selection.
+
+In January 2017, Lucy and Psyche mission were both selected as NASA's Discovery Program missions 13 and 14 respectively.[116]
+
+Location of Ceres (within asteroid belt) compared to other bodies of the Solar System
+
+Distances of selected bodies of the Solar System from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively, hence long bars denote high orbital eccentricity. The radius of the Sun is 0.7 million km, and the radius of Jupiter (the largest planet) is 0.07 million km, both too small to resolve on this image.
+
+Asteroids and the asteroid belt are a staple of science fiction stories. Asteroids play several potential roles in science fiction: as places human beings might colonize, resources for extracting minerals, hazards encountered by spacecraft traveling between two other points, and as a threat to life on Earth or other inhabited planets, dwarf planets, and natural satellites by potential impact.
+
+951 Gaspra is the first asteroid to be imaged in close-up, imaged by Galileo on 29 October 1991 (enhanced color)
+
+Several views of 433 Eros in natural color, imaged by NEAR on 12 February 2000
+
+Vesta imaged by Dawn on 9 July 2011
+
+Ceres imaged by Dawn on 4 February 2015
+
+"We include Trojans (bodies captured in Jupiter's 4th and 5th Lagrange points), Centaurs (bodies in orbit between Jupiter and Neptune), and trans-Neptunian objects (orbiting beyond Neptune) in our definition of "asteroid" as used on this site, even though they may more correctly be called "minor planets" instead of asteroids."[citation needed]
+
+Further information about asteroids
+
+Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Observable universe → UniverseEach arrow (→) may be read as "within" or "part of".

en/4170.html.txt

@@ -0,0 +1,29 @@
+North is one of the four compass points or cardinal directions. It is the opposite of south and is perpendicular to east and west. North is a noun, adjective, or adverb indicating direction or geography.
+
+The word north is related to the Old High German nord,[1] both descending from the Proto-Indo-European unit *ner-, meaning "left; below" as north is to left when facing the rising sun.[2] Similarly, the other cardinal directions are also related to the sun's position.[3][4][5]
+
+The Latin word borealis comes from the Greek boreas "north wind, north", which, according to Ovid, was personified as the son of the river-god Strymon, the father of Calais and Zetes. Septentrionalis is from septentriones, "the seven plow oxen", a name of Ursa Maior. The Greek ἀρκτικός (arktikós) is named for the same constellation, and is the source of the English word Arctic.
+
+Other languages have other derivations. For example, in Lezgian, kefer can mean both "disbelief" and "north", since to the north of the Muslim Lezgian homeland there are areas formerly inhabited by non-Muslim Caucasian and Turkic peoples. In many languages of Mesoamerica, north also means "up". In Hungarian, the word for north is észak, which is derived from éjszaka ("night"), since above the Tropic of Cancer, the Sun never shines from the north, except inside the Arctic Circle during the summer midnight sun.
+
+The direction north is quite often associated with colder climates because most of the world's land at high latitudes is located in the Northern Hemisphere. The Arctic Circle passes through the Arctic Ocean, Norway, Sweden, Finland, Russia, the United States (Alaska), Canada (Yukon, Northwest Territories and Nunavut), Denmark (Greenland) and Iceland (where it passes through the small offshore island of Grímsey).
+
+By convention, the top side of a map is often north.
+
+To go north using a compass for navigation, set a bearing or azimuth of 0° or 360°.
+
+North is specifically the direction that, in Western culture, is considered the fundamental direction:
+
+Magnetic north is of interest because it is the direction indicated as north on a properly functioning (but uncorrected) magnetic compass.  The difference between it and true north is called the magnetic declination (or simply the declination where the context is clear).  For many purposes and physical circumstances, the error in direction that results from ignoring the distinction is tolerable; in others a mental or instrument compensation, based on assumed knowledge of the applicable declination, can solve all the problems. But simple generalizations on the subject should be treated as unsound, and as likely to reflect popular misconceptions about terrestrial magnetism.
+
+Maps intended for usage in orienteering by compass will clearly indicate the local declination for easy correction to true north. Maps may also indicate grid north, which is a navigational term referring to the direction northwards along the grid lines of a map projection.
+
+The visible rotation of the night sky around the visible celestial pole provides a vivid metaphor of that direction corresponding to "up".  Thus the choice of the north as corresponding to "up" in the northern hemisphere, or of south in that role in the southern, is, prior to worldwide communication, anything but an arbitrary one - at least for night-time astronomers.[7] (Note: the southern hemisphere lacks a prominent visible analog to  the northern Pole Star.)  On the contrary, Chinese and Islamic cultures considered south as the proper "top" end for  maps.[8] In the cultures of Polynesia, where navigation played an important role, winds - prevailing local or ancestral - can define cardinal points.[9]
+
+In Western culture:
+
+While the choice of north over south as prime direction reflects quite arbitrary historical factors,[which?] east and west are not nearly as natural alternatives as first glance might suggest.  Their folk definitions are, respectively, "where the sun rises" and "where it sets".  Except on the Equator, however, these definitions, taken together, would imply that
+
+Reasonably accurate folk astronomy, such as is usually attributed to Stone Age peoples or later Celts, would arrive at east and west by noting the directions of rising and setting (preferably more than once each) and choosing as prime direction one of the two mutually opposite directions that lie halfway between those two.  The true folk-astronomical definitions of east and west are "the directions, a right angle from the prime direction, that are closest to the rising and setting, respectively, of the sun (or moon).
+
+Being the "default" direction on the compass, north is referred to frequently in Western popular culture.  Some examples include:

en/4172.html.txt

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+
+
+Reportedly haunted locations:
+
+Michel de Nostredame (depending on the source, 14 or 21 December 1503 – 1 or 2 July 1566), usually Latinised as Nostradamus,[a] was a French astrologer, physician and reputed seer, who is best known for his book Les Prophéties, a collection of 942 poetic quatrains[b] allegedly predicting future events. The book was first published in 1555 and has rarely been out of print since his death.
+
+Nostradamus's family was originally Jewish, but had converted to Catholic Christianity before he was born. He studied at the University of Avignon, but was forced to leave after just over a year when the university closed due to an outbreak of the plague. He worked as an apothecary for several years before entering the University of Montpellier, hoping to earn a doctorate, but was almost immediately expelled after his work as an apothecary (a manual trade forbidden by university statutes) was discovered. He first married in 1531, but his wife and two children died in 1534 during another plague outbreak. He fought alongside doctors against the plague before remarrying to Anne Ponsarde, with whom he had six children. He wrote an almanac for 1550 and, as a result of its success, continued writing them for future years as he began working as an astrologer for various wealthy patrons. Catherine de' Medici became one of his foremost supporters. His Les Prophéties, published in 1555, relied heavily on historical and literary precedent, and initially received mixed reception. He suffered from severe gout toward the end of his life, which eventually developed into edema. He died on 2 July 1566. Many popular authors have retold apocryphal legends about his life.
+
+In the years since the publication of his Les Prophéties, Nostradamus has attracted many supporters, who, along with much of the popular press, credit him with having accurately predicted many major world events.[6][7] Most academic sources reject the notion that Nostradamus had any genuine supernatural prophetic abilities and maintain that the associations made between world events and Nostradamus's quatrains are the result of misinterpretations or mistranslations (sometimes deliberate).[8] These academics argue that Nostradamus's predictions are characteristically vague, meaning they could be applied to virtually anything, and are useless for determining whether their author had any real prophetic powers. They also point out that English translations of his quatrains are almost always of extremely poor quality, based on later manuscripts, produced by authors with little knowledge of sixteenth-century French, and often deliberately mistranslated to make the prophecies fit whatever events the translator believed they were supposed to have predicted.
+
+Nostradamus was born on either 14 or 21 December 1503 in Saint-Rémy-de-Provence, Provence, France,[9] where his claimed birthplace still exists, and baptized Michel.[9] He was one of at least nine children of notary Jaume (or Jacques) de Nostredame and Reynière, granddaughter of Pierre de Saint-Rémy who worked as a physician in Saint-Rémy.[9] Jaume's family had originally been Jewish, but his father, Cresquas, a grain and money dealer based in Avignon, had converted to Catholicism around 1459–60, taking the Christian name "Pierre" and the surname "Nostredame" (Our Lady), the saint on whose day his conversion was solemnised.[9] The earliest ancestor who can be identified on the paternal side is Astruge of Carcassonne, who died about 1420. Michel's known siblings included Delphine, Jean (c. 1507–77), Pierre, Hector, Louis, Bertrand, Jean II (born 1522) and Antoine (born 1523).[10][11][12]
+Little else is known about his childhood, although there is a persistent tradition that he was educated by his maternal great-grandfather Jean de St. Rémy[13] — a tradition which is somewhat undermined by the fact that the latter disappears from the historical record after 1504 when the child was only one year old.[14]
+
+At the age of 14[6] Nostradamus entered the University of Avignon to study for his baccalaureate. After little more than a year (when he would have studied the regular trivium of grammar, rhetoric and logic rather than the later quadrivium of geometry, arithmetic, music, and astronomy/astrology), he was forced to leave Avignon when the university closed its doors during an outbreak of the plague. After leaving Avignon, Nostradamus, by his own account, traveled the countryside for eight years from 1521 researching herbal remedies. In 1529, after some years as an apothecary, he entered the University of Montpellier to study for a doctorate in medicine. He was expelled shortly afterwards by the student procurator, Guillaume Rondelet, when it was discovered that he had been an apothecary, a "manual trade" expressly banned by the university statutes, and had been slandering doctors.[15] The expulsion document, BIU Montpellier, Register S 2 folio 87, still exists in the faculty library.[16] However, some of his publishers and correspondents would later call him "Doctor". After his expulsion, Nostradamus continued working, presumably still as an apothecary, and became famous for creating a "rose pill" that purportedly protected against the plague.[17]
+
+In 1531 Nostradamus was invited by Jules-César Scaliger, a leading Renaissance scholar, to come to Agen.[18] There he married a woman of uncertain name (possibly Henriette d'Encausse), who bore him two children.[19] In 1534 his wife and children died, presumably from the plague. After their deaths, he continued to travel, passing through France and possibly Italy.[20]
+
+On his return in 1545, he assisted the prominent physician Louis Serre in his fight against a major plague outbreak in Marseille, and then tackled further outbreaks of disease on his own in Salon-de-Provence and in the regional capital, Aix-en-Provence. Finally, in 1547, he settled in Salon-de-Provence in the house which exists today, where he married a rich widow named Anne Ponsarde, with whom he had six children—three daughters and three sons.[21]  Between 1556 and 1567 he and his wife acquired a one-thirteenth share in a huge canal project, organised by Adam de Craponne, to create the Canal de Craponne to irrigate the largely waterless Salon-de-Provence and the nearby Désert de la Crau from the river Durance.[22]
+
+After another visit to Italy, Nostradamus began to move away from medicine and toward the "occult", although evidence suggests that he remained a Catholic and was opposed to the Protestant Reformation.[23] But it seems he could have dabbled in horoscopes, necromancy, scrying, and good luck charms such as the hawthorn rod.[24][25] Following popular trends, he wrote an almanac for 1550, for the first time in print Latinising his name to Nostradamus. He was so encouraged by the almanac's success that he decided to write one or more annually. Taken together, they are known to have contained at least 6,338 prophecies,[26][27] as well as at least eleven annual calendars, all of them starting on 1 January and not, as is sometimes supposed, in March. It was mainly in response to the almanacs that the nobility and other prominent persons from far away soon started asking for horoscopes and "psychic" advice from him, though he generally expected his clients to supply the birth charts on which these would be based, rather than calculating them himself as a professional astrologer would have done. When obliged to attempt this himself on the basis of the published tables of the day, he frequently made errors and failed to adjust the figures for his clients' place or time of birth.[28][29][c][30]
+
+He then began his project of writing a book of one thousand mainly French quatrains, which constitute the largely undated prophecies for which he is most famous today. Feeling vulnerable to opposition on religious grounds,[31] however, he devised a method of obscuring his meaning by using "Virgilianised" syntax, word games and a mixture of other languages such as Greek, Italian, Latin, and Provençal.[32] For technical reasons connected with their publication in three installments (the publisher of the third and last installment seems to have been unwilling to start it in the middle of a "Century," or book of 100 verses), the last fifty-eight quatrains of the seventh "Century" have not survived in any extant edition.
+
+The quatrains, published in a book titled Les Prophéties (The Prophecies), received a mixed reaction when they were published. Some people thought Nostradamus was a servant of evil, a fake, or insane, while many of the elite evidently thought otherwise. Catherine de' Medici, wife of King Henry II of France, was one of Nostradamus's greatest admirers. After reading his almanacs for 1555, which hinted at unnamed threats to the royal family, she summoned him to Paris to explain them and to draw up horoscopes for her children. At the time, he feared that he would be beheaded,[33] but by the time of his death in 1566, Queen Catherine had made him Counselor and Physician-in-Ordinary to her son, the young King Charles IX of France.
+
+Some accounts of Nostradamus's life state that he was afraid of being persecuted for heresy by the Inquisition, but neither prophecy nor astrology fell in this bracket, and he would have been in danger only if he had practised magic to support them. In 1538 he came into conflict with the Church in Agen after an Inquisitor visited the area looking for anti-Catholic views.[34] His brief imprisonment at Marignane in late 1561 was solely because he had violated a recent royal decree by publishing his 1562 almanac without the prior permission of a bishop.[35]
+
+By 1566, Nostradamus's gout, which had plagued him painfully for many years and made movement very difficult, turned into edema. In late June he summoned his lawyer to draw up an extensive will bequeathing his property plus 3,444 crowns (around US$300,000 today), minus a few debts, to his wife pending her remarriage, in trust for her sons pending their twenty-fifth birthdays and her daughters pending their marriages. This was followed by a much shorter codicil.[36] On the evening of 1 July, he is alleged to have told his secretary Jean de Chavigny, "You will not find me alive at sunrise." The next morning he was reportedly found dead, lying on the floor next to his bed and a bench (Presage 141 [originally 152] for November 1567, as posthumously edited by Chavigny to fit what happened).[37][27] He was buried in the local Franciscan chapel in Salon (part of it now incorporated into the restaurant La Brocherie) but re-interred during the French Revolution in the Collégiale Saint-Laurent, where his tomb remains to this day.[38]
+
+In The Prophecies Nostradamus compiled his collection of major, long-term predictions. The first installment was published in 1555 and contained 353 quatrains. The third edition, with three hundred new quatrains, was reportedly printed in 1558, but now survives as only part of the omnibus edition that was published after his death in 1568. This version contains one unrhymed and 941 rhymed quatrains, grouped into nine sets of 100 and one of 42, called "Centuries".
+
+Given printing practices at the time (which included type-setting from dictation), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same. Certainly there is no warrant for assuming—as would-be "code-breakers" are prone to do—that either the spellings or the punctuation of any edition are Nostradamus's originals.[5]
+
+The Almanacs, by far the most popular of his works,[39] were published annually from 1550 until his death. He often published two or three in a year, entitled either Almanachs (detailed predictions), Prognostications or Presages (more generalised predictions).
+
+Nostradamus was not only a diviner, but a professional healer. It is known that he wrote at least two books on medical science. One was an extremely free translation (or rather a paraphrase) of The Protreptic of Galen (Paraphrase de C. GALIEN, sus l'Exhortation de Menodote aux estudes des bonnes Artz, mesmement Medicine), and in his so-called Traité des fardemens (basically a medical cookbook containing, once again, materials borrowed mainly from others), he included a description of the methods he used to treat the plague, including bloodletting, none of which apparently worked.[40] The same book also describes the preparation of cosmetics.
+
+A manuscript normally known as the Orus Apollo also exists in the Lyon municipal library, where upwards of 2,000 original documents relating to Nostradamus are stored under the aegis of Michel Chomarat. It is a purported translation of an ancient Greek work on Egyptian hieroglyphs based on later Latin versions, all of them unfortunately ignorant of the true meanings of the ancient Egyptian script, which was not correctly deciphered until Champollion in the 19th century.[41]
+
+Since his death, only the Prophecies have continued to be popular, but in this case they have been quite extraordinarily so. Over two hundred editions of them have appeared in that time, together with over 2,000 commentaries. Their persistence in popular culture seems to be partly because their vagueness and lack of dating make it easy to quote them selectively after every major dramatic event and retrospectively claim them as "hits".[42]
+
+Nostradamus claimed to base his published predictions on judicial astrology—the astrological 'judgment', or assessment, of the 'quality' (and thus potential) of events such as births, weddings, coronations etc.—but was heavily criticised by professional astrologers of the day such as Laurens Videl[44] for incompetence and for assuming that "comparative horoscopy" (the comparison of future planetary configurations with those accompanying known past events) could actually predict what would happen in the future.[45]
+
+Research suggests that much of his prophetic work paraphrases collections of ancient end-of-the-world prophecies (mainly Bible-based), supplemented with references to historical events and anthologies of omen reports, and then projects those into the future in part with the aid of comparative horoscopy. Hence the many predictions involving ancient figures such as Sulla, Gaius Marius, Nero, and others, as well as his descriptions of "battles in the clouds" and "frogs falling from the sky".[46] Astrology itself is mentioned only twice in Nostradamus's Preface and 41 times in the Centuries themselves, but more frequently in his dedicatory Letter to King Henry II. In the last quatrain of his sixth century he specifically attacks astrologers.
+
+His historical sources include easily identifiable passages from Livy, Suetonius' The Twelve Caesars, Plutarch and other classical historians, as well as from medieval chroniclers such as Geoffrey of Villehardouin and Jean Froissart. Many of his astrological references are taken almost word for word from Richard Roussat's Livre de l'estat et mutations des temps of 1549–50.
+
+One of his major prophetic sources was evidently the Mirabilis Liber of 1522, which contained a range of prophecies by Pseudo-Methodius, the Tiburtine Sibyl, Joachim of Fiore, Savonarola and others (his Preface contains 24 biblical quotations, all but two in the order used by Savonarola). This book had enjoyed considerable success in the 1520s, when it went through half a dozen editions, but did not sustain its influence, perhaps owing to its mostly Latin text, Gothic script and many difficult abbreviations. Nostradamus was one of the first to re-paraphrase these prophecies in French, which may explain why they are credited to him. Modern views of plagiarism did not apply in the 16th century; authors frequently copied and paraphrased passages without acknowledgement, especially from the classics. The latest research suggests that he may in fact have used bibliomancy for this—randomly selecting a book of history or prophecy and taking his cue from whatever page it happened to fall open at.[6]
+
+Further material was gleaned from the De honesta disciplina of 1504 by Petrus Crinitus,[47] which included extracts from Michael Psellos's De daemonibus, and the De Mysteriis Aegyptiorum (Concerning the mysteries of Egypt), a book on Chaldean and Assyrian magic by Iamblichus, a 4th-century Neo-Platonist. Latin versions of both had recently been published in Lyon, and extracts from both are paraphrased (in the second case almost literally) in his first two verses, the first of which is appended to this article. While it is true that Nostradamus claimed in 1555 to have burned all of the occult works in his library, no one can say exactly what books were destroyed in this fire.
+
+Only in the 17th century did people start to notice his reliance on earlier, mainly classical sources.[d]
+
+Nostradamus's reliance on historical precedent is reflected in the fact that he explicitly rejected the label "prophet" (i.e. a person having prophetic powers of his own) on several occasions:[48]
+
+Although, my son, I have used the word prophet, I would not attribute to myself a title of such lofty sublimity.
+
+Not that I would attribute to myself either the name or the role of a prophet.
+
+[S]ome of [the prophets] predicted great and marvelous things to come: [though] for me, I in no way attribute to myself such a title here.
+
+Not that I am foolish enough to claim to be a prophet.
+
+Given this reliance on literary sources, it is unlikely that Nostradamus used any particular methods for entering a trance state, other than contemplation, meditation and incubation.[51] His sole description of this process is contained in letter 41 of his collected Latin correspondence.[52] The popular legend that he attempted the ancient methods of flame gazing, water gazing or both simultaneously is based on a naive reading of his first two verses, which merely liken his efforts to those of the Delphic and Branchidic oracles. The first of these is reproduced at the bottom of this article and the second can be seen by visiting the relevant facsimile site (see External Links). In his dedication to King Henry II, Nostradamus describes "emptying my soul, mind and heart of all care, worry and unease through mental calm and tranquility", but his frequent references to the "bronze tripod" of the Delphic rite are usually preceded by the words "as though" (compare, once again, External References to the original texts).
+
+Most of the quatrains deal with disasters, such as plagues, earthquakes, wars, floods, invasions, murders, droughts, and battles—all undated and based on foreshadowings by the Mirabilis Liber. Some quatrains cover these disasters in overall terms; others concern a single person or small group of people. Some cover a single town, others several towns in several countries.[53] A major, underlying theme is an impending invasion of Europe by Muslim forces from farther east and south headed by the expected Antichrist, directly reflecting the then-current Ottoman invasions and the earlier Saracen equivalents, as well as the prior expectations of the Mirabilis Liber.[54] All of this is presented in the context of the supposedly imminent end of the world—even though this is not in fact mentioned[55]—a conviction that sparked numerous collections of end-time prophecies at the time, including an unpublished collection by Christopher Columbus.[56] [57] Views on Nostradamus have varied widely throughout history.[58] Academic views such as those of Jacques Halbronn regard Nostradamus's Prophecies as antedated forgeries written by later hands with a political axe to grind.[58]
+
+Many of Nostradamus's supporters believe his prophecies are genuine.[58] Owing to the subjective nature of these interpretations, however, no two of them completely agree on what Nostradamus predicted, whether for the past or for the future.[58] Many supporters, however, do agree, for example, that he predicted the Great Fire of London, the French Revolution, the rises of Napoleon and Adolf Hitler,[59][e] both world wars, and the nuclear destruction of Hiroshima and Nagasaki.[58][30] Popular authors frequently claim that he predicted whatever major event had just happened at the time of each book's publication, such as the Apollo moon landings in 1969, the Space Shuttle Challenger disaster in 1986, the death of Diana, Princess of Wales in 1997, and the September 11 attacks on the World Trade Center in 2001.[30][60] This 'movable feast' aspect appears to be characteristic of the genre.[58]
+
+Possibly the first of these books to become popular in English was Henry C. Roberts' The Complete Prophecies of Nostradamus of 1947, reprinted at least seven times during the next forty years, which contained both transcriptions and translations, with brief commentaries. This was followed in 1961 (reprinted in 1982) by Edgar Leoni's Nostradamus and His Prophecies. After that came Erika Cheetham's The Prophecies of Nostradamus, incorporating a reprint of the posthumous 1568 edition, which was reprinted, revised and republished several times from 1973 onwards, latterly as The Final Prophecies of Nostradamus. This served as the basis for the documentary The Man Who Saw Tomorrow and both did indeed mention possible generalised future attacks on New York (via nuclear weapons), though not specifically on the World Trade Center or on any particular date.[61]
+
+A two-part translation of Jean-Charles de Fontbrune's Nostradamus: historien et prophète was published in 1980, and John Hogue has published a number of books on Nostradamus from about 1987, including Nostradamus and the Millennium: Predictions of the Future, Nostradamus: The Complete Prophecies (1999) and Nostradamus: A Life and Myth (2003). In 1992 one commentator who claimed to be able to contact Nostradamus under hypnosis even had him "interpreting" his own verse X.6 (a prediction specifically about floods in southern France around the city of Nîmes and people taking refuge in its collosse, or Colosseum, a Roman amphitheatre now known as the Arènes) as a prediction of an undated attack on the Pentagon, despite the historical seer's clear statement in his dedicatory letter to King Henri II that his prophecies were about Europe, North Africa and part of Asia Minor.[62]
+
+With the exception of Roberts, these books and their many popular imitators were almost unanimous not merely about Nostradamus's powers of prophecy but also in inventing intriguing aspects of his purported biography: that he had been a descendant of the Israelite tribe of Issachar; he had been educated by his grandfathers, who had both been physicians to the court of Good King René of Provence; he had attended Montpellier University in 1525 to gain his first degree; after returning there in 1529, he had successfully taken his medical doctorate; he had gone on to lecture in the Medical Faculty there, until his views became too unpopular; he had supported the heliocentric view of the universe; he had travelled to the Habsburg Netherlands, where he had composed prophecies at the abbey of Orval; in the course of his travels, he had performed a variety of prodigies, including identifying future Pope, Sixtus V, who was then only a seminary monk. He is credited with having successfully cured the Plague at Aix-en-Provence and elsewhere; he had engaged in scrying, using either a magic mirror or a bowl of water; he had been joined by his secretary Chavigny at Easter 1554; having published the first installment of his Prophéties, he had been summoned by Queen Catherine de' Medici to Paris in 1556 to discuss with her his prophecy at quatrain I.35 that her husband King Henri II would be killed in a duel; he had examined the royal children at Blois; he had bequeathed to his son a "lost book" of his own prophetic paintings;[f] he had been buried standing up; and he had been found, when dug up at the French Revolution, to be wearing a medallion bearing the exact date of his disinterment.[63] This was first recorded by Samuel Pepys as early as 1667, long before the French Revolution. Pepys records in his celebrated diary a legend that, before his death, Nostradamus made the townsfolk swear that his grave would never be disturbed; but that 60 years later his body was exhumed, whereupon a brass plaque was found on his chest correctly stating the date and time when his grave would be opened and cursing the exhumers.[64]
+
+In 2000, Li Hongzhi claimed that the 1999 prophecy at X.72 was a prediction of the Chinese Falun Gong persecution which began in July 1999, leading to an increased interest in Nostradamus among Falun Gong members.[65]
+
+From the 1980s onward, however, an academic reaction set in, especially in France. The publication in 1983 of Nostradamus's private correspondence[66] and, during succeeding years, of the original editions of 1555 and 1557 discovered by Chomarat and Benazra, together with the unearthing of much original archival material[38][67] revealed that much that was claimed about Nostradamus did not fit the documented facts. The academics[38][63][67][68] revealed that not one of the claims just listed was backed up by any known contemporary documentary evidence. Most of them had evidently been based on unsourced rumours relayed as fact by much later commentators, such as Jaubert (1656), Guynaud (1693) and Bareste (1840), on modern misunderstandings of the 16th-century French texts, or on pure invention. Even the often-advanced suggestion that quatrain I.35 had successfully prophesied King Henry II's death did not actually appear in print for the first time until 1614, 55 years after the event.[69][70]
+
+Skeptics such as James Randi suggest that his reputation as a prophet is largely manufactured by modern-day supporters who fit his words to events that have either already occurred or are so imminent as to be inevitable, a process sometimes known as "retroactive clairvoyance" (postdiction). No Nostradamus quatrain is known to have been interpreted as predicting a specific event before it occurred, other than in vague, general terms that could equally apply to any number of other events.[71] This even applies to quatrains that contain specific dates, such as III.77, which predicts "in 1727, in October, the king of Persia [shall be] captured by those of Egypt"—a prophecy that has, as ever, been interpreted retrospectively in the light of later events, in this case as though it presaged the known peace treaty between the Ottoman Empire and Persia of that year;[72] Egypt was also an important Ottoman territory at this time.[73] Similarly, Nostradamus's notorious "1999" prophecy at X.72 (see Nostradamus in popular culture) describes no event that commentators have succeeded in identifying either before or since, other than by twisting the words to fit whichever of the many contradictory happenings they claim as "hits".[74]  Moreover, no quatrain suggests, as is often claimed by books and films on the alleged Mayan Prophecy, that the world would end in December 2012.[75] In his preface to the Prophecies, Nostradamus himself stated that his prophecies extend 'from now to the year 3797'[76]—an extraordinary date which, given that the preface was written in 1555, may have more than a little to do with the fact that 2242 (3797–1555) had recently been proposed by his major astrological source Richard Roussat as a possible date for the end of the world.[77][78]
+
+Additionally, scholars have pointed out that almost all English translations of Nostradamus's quatrains are of extremely poor quality, seem to display little or no knowledge of 16th-century French, are tendentious, and are sometimes intentionally altered in order to make them fit whatever events the translator believed they were supposed to refer (or vice versa).[79][68][80] None of them were based on the original editions: Roberts had based his writings on that of 1672, Cheetham and Hogue on the posthumous edition of 1568. Even Leoni accepted on page 115 that he had never seen an original edition, and on earlier pages, he indicated that much of his biographical material was unsourced.[81]
+
+None of this research and criticism was originally known to most of the English-language commentators, by dint of the dates when they were writing and, to some extent, the language in which it was written.[82] Hogue was in a position to take advantage of it, but it was only in 2003 that he accepted that some of his earlier biographical material had in fact been apocryphal. Meanwhile, some of the more recent sources listed (Lemesurier, Gruber, Wilson) have been particularly scathing about later attempts by some lesser-known authors and Internet enthusiasts to extract alleged hidden meanings from the texts, whether with the aid of anagrams, numerical codes, graphs or otherwise.[58]
+
+The prophecies retold and expanded by Nostradamus figured largely in popular culture in the 20th and 21st centuries. As well as being the subject of hundreds of books (both fiction and nonfiction), Nostradamus's life has been depicted in several films and videos, and his life and writings continue to be a subject of media interest.
+
+There have also been several well-known Internet hoaxes, where quatrains in the style of Nostradamus have been circulated by e-mail as the real thing. The best-known examples concern the collapse of the World Trade Center in the 11 September attacks.[83]
+
+With the arrival of the year 2012, Nostradamus's prophecies started to be co-opted (especially by the History Channel) as evidence suggesting that the end of the world was imminent, notwithstanding the fact that his book never mentions the end of the world, let alone the year 2012.[84]

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+The Milky Way[a] is the galaxy that contains our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. The term Milky Way is a translation of the Latin via lactea, from the Greek γαλαξίας κύκλος (galaxías kýklos, "milky circle").[19][20][21] From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within. Galileo Galilei first resolved the band of light into individual stars with his telescope in 1610. Until the early 1920s, most astronomers thought that the Milky Way contained all the stars in the Universe.[22] Following the 1920 Great Debate between the astronomers Harlow Shapley and Heber Curtis,[23] observations by Edwin Hubble showed that the Milky Way is just one of many galaxies.
+
+The Milky Way is a barred spiral galaxy with an estimated visible diameter between 170,000 and 200,000 light-years (ly).[24][25][26][27] It is estimated to contain 100–400 billion stars[28][29] and at least that number of planets.[30][31] The dark matter halo around the Milky Way may span as much as 2 million light years.[5] The Solar System is located at a radius of about 27,000 light-years from the Galactic Center,[15] on the inner edge of the Orion Arm, one of the spiral-shaped concentrations of gas and dust. The stars in the innermost 10,000 light-years form a bulge and one or more bars that radiate from the bulge. The galactic center is an intense radio source known as Sagittarius A*, a supermassive black hole of 4.100 (± 0.034) million solar masses.
+
+Stars and gases at a wide range of distances from the Galactic Center orbit at approximately 220 kilometers per second. The constant rotation speed contradicts the laws of Keplerian dynamics and suggests that much (about 90%)[32][33] of the mass of the Milky Way is invisible to telescopes, neither emitting nor absorbing electromagnetic radiation. This conjectural mass has been termed "dark matter".[34] The rotational period is about 240 million years at the radius of the Sun.[16] The Milky Way as a whole is moving at a velocity of approximately 600 km per second with respect to extragalactic frames of reference. The oldest stars in the Milky Way are nearly as old as the Universe itself and thus probably formed shortly after the Dark Ages of the Big Bang.[35]
+
+The Milky Way has several satellite galaxies and is part of the Local Group of galaxies, which form part of the Virgo Supercluster, which is itself a component of the Laniakea Supercluster.[36][37]
+
+The Milky Way is visible from Earth as a hazy band of white light, some 30° wide, arching across the night sky.[38] In night sky observing, although all the individual naked-eye stars in the entire sky are part of the Milky Way Galaxy, the term "Milky Way" is limited to this band of light.[39][40] The light originates from the accumulation of unresolved stars and other material located in the direction of the galactic plane. Dark regions within the band, such as the Great Rift and the Coalsack, are areas where interstellar dust blocks light from distant stars. The area of sky that the Milky Way obscures is called the Zone of Avoidance.
+
+The Milky Way has a relatively low surface brightness. Its visibility can be greatly reduced by background light, such as light pollution or moonlight. The sky needs to be darker than about 20.2 magnitude per square arcsecond in order for the Milky Way to be visible.[41] It should be visible if the limiting magnitude is approximately +5.1 or better and shows a great deal of detail at +6.1.[42] This makes the Milky Way difficult to see from brightly lit urban or suburban areas, but very prominent when viewed from rural areas when the Moon is below the horizon.[b] Maps of artificial night sky brightness show that more than one-third of Earth's population cannot see the Milky Way from their homes due to light pollution.[43]
+
+As viewed from Earth, the visible region of the Milky Way's galactic plane occupies an area of the sky that includes 30 constellations.[44] The Galactic Center lies in the direction of Sagittarius, where the Milky Way is brightest. From Sagittarius, the hazy band of white light appears to pass around to the galactic anticenter in Auriga. The band then continues the rest of the way around the sky, back to Sagittarius, dividing the sky into two roughly equal hemispheres.
+
+The galactic plane is inclined by about 60° to the ecliptic (the plane of Earth's orbit). Relative to the celestial equator, it passes as far north as the constellation of Cassiopeia and as far south as the constellation of Crux, indicating the high inclination of Earth's equatorial plane and the plane of the ecliptic, relative to the galactic plane. The north galactic pole is situated at right ascension 12h 49m, declination +27.4° (B1950) near β Comae Berenices, and the south galactic pole is near α Sculptoris. Because of this high inclination, depending on the time of night and year, the arch of the Milky Way may appear relatively low or relatively high in the sky. For observers from latitudes approximately 65° north to 65° south, the Milky Way passes directly overhead twice a day.
+
+The Milky Way is the second-largest galaxy in the Local Group (after the Andromeda Galaxy), with its stellar disk approximately 170,000–200,000 light-years (52–61 kpc) in diameter and, on average, approximately 1,000 ly (0.3 kpc) thick.[6][7] The Milky Way is approximately 890 billion times the mass of the Sun.[45] To compare the relative physical scale of the Milky Way, if the Solar System out to Neptune were the size of a US quarter (24.3 mm (0.955 in)), the Milky Way would be approximately the size of the contiguous United States.[46] There is a ring-like filament of stars rippling above and below the relatively flat galactic plane, wrapping around the Milky Way at a diameter of 150,000–180,000 light-years (46–55 kpc),[47] which may be part of the Milky Way itself.[26]
+
+Estimates of the mass of the Milky Way vary, depending upon the method and data used. The low end of the estimate range is 5.8×1011 solar masses (M☉), somewhat less than that of the Andromeda Galaxy.[48][49][50] Measurements using the Very Long Baseline Array in 2009 found velocities as large as 254 km/s (570,000 mph) for stars at the outer edge of the Milky Way.[51] Because the orbital velocity depends on the total mass inside the orbital radius, this suggests that the Milky Way is more massive, roughly equaling the mass of Andromeda Galaxy at 7×1011 M☉ within 160,000 ly (49 kpc) of its center.[52] In 2010, a measurement of the radial velocity of halo stars found that the mass enclosed within 80 kiloparsecs is 7×1011 M☉.[53] According to a study published in 2014, the mass of the entire Milky Way is estimated to be 8.5×1011 M☉,[54] but this is only half the mass of the Andromeda Galaxy.[54] A recent mass estimate for the Milky Way is 1.29×1012 M☉.[55]
+
+Much of the mass of the Milky Way seems to be dark matter, an unknown and invisible form of matter that interacts gravitationally with ordinary matter. A dark matter halo is conjectured to spread out relatively uniformly to a distance beyond one hundred kiloparsecs (kpc) from the Galactic Center. Mathematical models of the Milky Way suggest that the mass of dark matter is 1–1.5×1012 M☉.[9][10][56] Recent studies indicate a range in mass, as large as 4.5×1012 M☉[57] and as small as 8×1011 M☉.[58] 
+The total mass of all the stars in the Milky Way is estimated to be between 4.6×1010 M☉[59] and 6.43×1010 M☉.[9] In addition to the stars, there is also interstellar gas, comprising 90% hydrogen and 10% helium by mass,[60] with two thirds of the hydrogen found in the atomic form and the remaining one-third as molecular hydrogen.[61] The mass of the Milky Way's interstellar gas is equal to between 10%[61] and 15%[60] of the total mass of its stars. Interstellar dust accounts for an additional 1% of the total mass of the gas.[60]
+
+In March 2019, astronomers reported that the mass of the Milky Way galaxy is 1.5 trillion solar masses within a radius of about 129,000 light-years, over twice as much as was determined in earlier studies, and suggesting that about 90% of the mass of the galaxy is dark matter.[32][33]
+
+The Milky Way contains between 100 and 400 billion stars[62][63] and at least that many planets.[64] An exact figure would depend on counting the number of very-low-mass stars, which are difficult to detect, especially at distances of more than 300 ly (90 pc) from the Sun. As a comparison, the neighboring Andromeda Galaxy contains an estimated one trillion (1012) stars.[65] Perhaps, the Milky Way may contain ten billion white dwarfs, a billion neutron stars, and a hundred million stellar black holes.[c][66][67][68][69] Filling the space between the stars is a disk of gas and dust called the interstellar medium. This disk has at least a comparable extent in radius to the stars,[70] whereas the thickness of the gas layer ranges from hundreds of light-years for the colder gas to thousands of light-years for warmer gas.[71][72]
+
+The disk of stars in the Milky Way does not have a sharp edge beyond which there are no stars. Rather, the concentration of stars decreases with distance from the center of the Milky Way. For reasons that are not understood, beyond a radius of roughly 40,000 ly (13 kpc) from the center, the number of stars per cubic parsec drops much faster with radius.[73] Surrounding the galactic disk is a spherical Galactic Halo of stars and globular clusters that extends farther outward, but is limited in size by the orbits of two Milky Way satellites, the Large and Small Magellanic Clouds, whose closest approach to the Galactic Center is about 180,000 ly (55 kpc).[74] At this distance or beyond, the orbits of most halo objects would be disrupted by the Magellanic Clouds. Hence, such objects would probably be ejected from the vicinity of the Milky Way. The integrated absolute visual magnitude of the Milky Way is estimated to be around −20.9.[75][76][d]
+
+Both gravitational microlensing and planetary transit observations indicate that there may be at least as many planets bound to stars as there are stars in the Milky Way,[30][77] and microlensing measurements indicate that there are more rogue planets not bound to host stars than there are stars.[78][79] The Milky Way contains at least one planet per star, resulting in 100–400 billion planets, according to a January 2013 study of the five-planet star system Kepler-32 with the Kepler space observatory.[31] A different January 2013 analysis of Kepler data estimated that at least 17 billion Earth-sized exoplanets reside in the Milky Way.[80] On November 4, 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of Sun-like stars and red dwarfs within the Milky Way.[81][82][83] 11 billion of these estimated planets may be orbiting Sun-like stars.[84] The nearest exoplanet may be 4.2 light-years away, orbiting the red dwarf Proxima Centauri, according to a 2016 study.[85] Such Earth-sized planets may be more numerous than gas giants.[30] Besides exoplanets, "exocomets", comets beyond the Solar System, have also been detected and may be common in the Milky Way.[86]
+
+In June 2020, astronomers from the University of Nottingham reported the possible existence of over 30 "active communicating intelligent civilizations", or Communicating Extra-Terrestrial Intelligent (CETI) civilizations (none within our current ability to detect due to various reasons including distance or size) in our own Milky Way galaxy, based on the latest astrophysical information.[87][88][89]
+
+360-degree panorama view of the Milky Way (an assembled mosaic of photographs) by ESO, the galactic centre is in the middle of the view, with galactic north up
+
+The Milky Way consists of a bar-shaped core region surrounded by a warped disk of gas, dust and stars.[93][94] The mass distribution within the Milky Way closely resembles the type Sbc in the Hubble classification, which represents spiral galaxies with relatively loosely wound arms.[1] Astronomers first began to suspect that the Milky Way is a barred spiral galaxy, rather than an ordinary spiral galaxy, in the 1960s.[95][96][97] Their suspicions were confirmed by the Spitzer Space Telescope observations in 2005[98] that showed the Milky Way's central bar to be larger than previously thought.
+
+A galactic quadrant, or quadrant of the Milky Way, refers to one of four circular sectors in the division of the Milky Way. In astronomical practice, the delineation of the galactic quadrants is based upon the galactic coordinate system, which places the Sun as the origin of the mapping system.[99]
+
+Quadrants are described using ordinals – for example, "1st galactic quadrant",[100] "second galactic quadrant",[101] or "third quadrant of the Milky Way".[102] Viewing from the north galactic pole with 0 degrees (°) as the ray that runs starting from the Sun and through the Galactic Center, the quadrants are as follows:
+
+The Sun is 25,000–28,000 ly (7.7–8.6 kpc) from the Galactic Center. This value is estimated using geometric-based methods or by measuring selected astronomical objects that serve as standard candles, with different techniques yielding various values within this approximate range.[104][14][15][105][106][107] In the inner few kpc (around 10,000 light-years radius) is a dense concentration of mostly old stars in a roughly spheroidal shape called the bulge.[108] It has been proposed that the Milky Way lacks a bulge formed due to a collision and merger between previous galaxies, and that instead it only has a pseudobulge formed by its central bar.[109] However, confusion in the literature between the (peanut shell)-shaped structure created by instabilities in the bar, versus a possible bulge with an expected half-light radius of 0.5 kpc,[110] abounds.
+
+The Galactic Center is marked by an intense radio source named Sagittarius A* (pronounced Sagittarius A-star). The motion of material around the center indicates that Sagittarius A* harbors a massive, compact object.[111] This concentration of mass is best explained as a supermassive black hole[e][104][112] (SMBH) with an estimated mass of 4.1–4.5 million times the mass of the Sun.[112] The rate of accretion of the SMBH is consistent with an inactive galactic nucleus, being estimated at around 1×10−5 M☉ per year.[113] Observations indicate that there are SMBHs located near the center of most normal galaxies.[114][115]
+
+The nature of the Milky Way's bar is actively debated, with estimates for its half-length and orientation spanning from 1 to 5 kpc (3,000–16,000 ly) and 10–50 degrees relative to the line of sight from Earth to the Galactic Center.[106][107][116] Certain authors advocate that the Milky Way features two distinct bars, one nestled within the other.[117] However, RR Lyrae variables do not trace a prominent Galactic bar.[107][118][119] The bar may be surrounded by a ring called the "5-kpc ring" that contains a large fraction of the molecular hydrogen present in the Milky Way, as well as most of the Milky Way's star formation activity. Viewed from the Andromeda Galaxy, it would be the brightest feature of the Milky Way.[120] X-ray emission from the core is aligned with the massive stars surrounding the central bar[113] and the Galactic ridge.[121]
+
+In 2010, two gigantic spherical bubbles of high energy emission were detected to the north and the south of the Milky Way core, using data from the Fermi Gamma-ray Space Telescope. The diameter of each of the bubbles is about 25,000 light-years (7.7 kpc); they stretch up to Grus and to Virgo on the night-sky of the southern hemisphere.[122][123] Subsequently, observations with the Parkes Telescope at radio frequencies identified polarized emission that is associated with the Fermi bubbles. These observations are best interpreted as a magnetized outflow driven by star formation in the central 640 ly (200 pc) of the Milky Way.[124]
+
+Later, on January 5, 2015, NASA reported observing an X-ray flare 400 times brighter than usual, a record-breaker, from Sagittarius A*. The unusual event may have been caused by the breaking apart of an asteroid falling into the black hole or by the entanglement of magnetic field lines within gas flowing into Sagittarius A*.[92]
+
+Outside the gravitational influence of the Galactic bar, the structure of the interstellar medium and stars in the disk of the Milky Way is organized into four spiral arms.[125] Spiral arms typically contain a higher density of interstellar gas and dust than the Galactic average as well as a greater concentration of star formation, as traced by H II regions[126][127] and molecular clouds.[128]
+
+The Milky Way's spiral structure is uncertain, and there is currently no consensus on the nature of the Milky Way's spiral arms.[91] Perfect logarithmic spiral patterns only crudely describe features near the Sun,[127][129] because galaxies commonly have arms that branch, merge, twist unexpectedly, and feature a degree of irregularity.[107][129][130] The possible scenario of the Sun within a spur / Local arm[127] emphasizes that point and indicates that such features are probably not unique, and exist elsewhere in the Milky Way.[129] Estimates of the pitch angle of the arms range from about 7° to 25°.[70][131] There are thought to be four spiral arms that all start near the Milky Way's center.[132] These are named as follows, with the positions of the arms shown in the image at right:
+
+Two spiral arms, the Scutum–Centaurus arm and the Carina–Sagittarius arm, have tangent points inside the Sun's orbit about the center of the Milky Way. If these arms contain an overdensity of stars compared to the average density of stars in the Galactic disk, it would be detectable by counting the stars near the tangent point. Two surveys of near-infrared light, which is sensitive primarily to red giants and not affected by dust extinction, detected the predicted overabundance in the Scutum–Centaurus arm but not in the Carina–Sagittarius arm: the Scutum–Centaurus Arm contains approximately 30% more red giants than would be expected in the absence of a spiral arm.[131][134] This observation suggests that the Milky Way possesses only two major stellar arms: the Perseus arm and the Scutum–Centaurus arm. The rest of the arms contain excess gas but not excess old stars.[91] In December 2013, astronomers found that the distribution of young stars and star-forming regions matches the four-arm spiral description of the Milky Way.[135][136][137] Thus, the Milky Way appears to have two spiral arms as traced by old stars and four spiral arms as traced by gas and young stars. The explanation for this apparent discrepancy is unclear.[137]
+
+The Near 3 kpc Arm (also called Expanding 3 kpc Arm or simply 3 kpc Arm) was discovered in the 1950s by astronomer van Woerden and collaborators through 21-centimeter radio measurements of HI (atomic hydrogen).[138][139] It was found to be expanding away from the central bulge at more than 50 km/s. It is located in the fourth galactic quadrant at a distance of about 5.2 kpc from the Sun and 3.3 kpc from the Galactic Center. The Far 3 kpc Arm was discovered in 2008 by astronomer Tom Dame (Harvard–Smithsonian CfA). It is located in the first galactic quadrant at a distance of 3 kpc (about 10,000 ly) from the Galactic Center.[139][140]
+
+A simulation published in 2011 suggested that the Milky Way may have obtained its spiral arm structure as a result of repeated collisions with the Sagittarius Dwarf Elliptical Galaxy.[141]
+
+It has been suggested that the Milky Way contains two different spiral patterns: an inner one, formed by the Sagittarius arm, that rotates fast and an outer one, formed by the Carina and Perseus arms, whose rotation velocity is slower and whose arms are tightly wound. In this scenario, suggested by numerical simulations of the dynamics of the different spiral arms, the outer pattern would form an outer pseudoring,[142] and the two patterns would be connected by the Cygnus arm.[143]
+
+Outside of the major spiral arms is the Monoceros Ring (or Outer Ring), a ring of gas and stars torn from other galaxies billions of years ago. However, several members of the scientific community recently restated their position affirming the Monoceros structure is nothing more than an over-density produced by the flared and warped thick disk of the Milky Way.[144] The structure of the Milky Way's disk is warped along an "S" curve.[145]
+
+The Galactic disk is surrounded by a spheroidal halo of old stars and globular clusters, of which 90% lie within 100,000 light-years (30 kpc) of the Galactic Center.[146] However, a few globular clusters have been found farther, such as PAL 4 and AM1 at more than 200,000 light-years from the Galactic Center. About 40% of the Milky Way's clusters are on retrograde orbits, which means they move in the opposite direction from the Milky Way rotation.[147] The globular clusters can follow rosette orbits about the Milky Way, in contrast to the elliptical orbit of a planet around a star.[148]
+
+Although the disk contains dust that obscures the view in some wavelengths, the halo component does not. Active star formation takes place in the disk (especially in the spiral arms, which represent areas of high density), but does not take place in the halo, as there is little cool gas to collapse into stars.[16] Open clusters are also located primarily in the disk.[149]
+
+Discoveries in the early 21st century have added dimension to the knowledge of the Milky Way's structure. With the discovery that the disk of the Andromeda Galaxy (M31) extends much farther than previously thought,[150] the possibility of the disk of the Milky Way extending farther is apparent, and this is supported by evidence from the discovery of the Outer Arm extension of the Cygnus Arm[133][151] and of a similar extension of the Scutum–Centaurus Arm.[152] With the discovery of the Sagittarius Dwarf Elliptical Galaxy came the discovery of a ribbon of galactic debris as the polar orbit of the dwarf and its interaction with the Milky Way tears it apart. Similarly, with the discovery of the Canis Major Dwarf Galaxy, it was found that a ring of galactic debris from its interaction with the Milky Way encircles the Galactic disk.
+
+The Sloan Digital Sky Survey of the northern sky shows a huge and diffuse structure (spread out across an area around 5,000 times the size of a full moon) within the Milky Way that does not seem to fit within current models. The collection of stars rises close to perpendicular to the plane of the spiral arms of the Milky Way. The proposed likely interpretation is that a dwarf galaxy is merging with the Milky Way. This galaxy is tentatively named the Virgo Stellar Stream and is found in the direction of Virgo about 30,000 light-years (9 kpc) away.[153]
+
+In addition to the stellar halo, the Chandra X-ray Observatory, XMM-Newton, and Suzaku have provided evidence that there is a gaseous halo with a large amount of hot gas. The halo extends for hundreds of thousand of light-years, much farther than the stellar halo and close to the distance of the Large and Small Magellanic Clouds. The mass of this hot halo is nearly equivalent to the mass of the Milky Way itself.[154][155][156] The temperature of this halo gas is between 1 and 2.5 million K (1.8 and 4.5 million °F).[157]
+
+Observations of distant galaxies indicate that the Universe had about one-sixth as much baryonic (ordinary) matter as dark matter when it was just a few billion years old. However, only about half of those baryons are accounted for in the modern Universe based on observations of nearby galaxies like the Milky Way.[158] If the finding that the mass of the halo is comparable to the mass of the Milky Way is confirmed, it could be the identity of the missing baryons around the Milky Way.[158]
+
+The Sun is near the inner rim of the Orion Arm, within the Local Fluff of the Local Bubble, and in the Gould Belt. Based upon studies of stellar orbits around Sgr A* by Gillessen and associates (2016), the Sun lies at an estimated distance of 27.14 ± 0.46 kly (8.32 ± 0.14 kpc)[15] from the Galactic Center. Boehle and associates (2016) found a smaller value of 25.64 ± 0.46 kly (7.86 ± 0.14 kpc), also using a star orbit analysis.[14] The Sun is currently 5–30 parsecs (16–98 ly) above, or north of, the central plane of the Galactic disk.[159] The distance between the local arm and the next arm out, the Perseus Arm, is about 2,000 parsecs (6,500 ly).[160] The Sun, and thus the Solar System, is located in the Milky Way's galactic habitable zone.
+
+There are about 208 stars brighter than absolute magnitude 8.5 within a sphere with a radius of 15 parsecs (49 ly) from the Sun, giving a density of one star per 69 cubic parsecs, or one star per 2,360 cubic light-years (from List of nearest bright stars). On the other hand, there are 64 known stars (of any magnitude, not counting 4 brown dwarfs) within 5 parsecs (16 ly) of the Sun, giving a density of about one star per 8.2 cubic parsecs, or one per 284 cubic light-years (from List of nearest stars). This illustrates the fact that there are far more faint stars than bright stars: in the entire sky, there are about 500 stars brighter than apparent magnitude 4 but 15.5 million stars brighter than apparent magnitude 14.[161]
+
+The apex of the Sun's way, or the solar apex, is the direction that the Sun travels through space in the Milky Way. The general direction of the Sun's Galactic motion is towards the star Vega near the constellation of Hercules, at an angle of roughly 60 sky degrees to the direction of the Galactic Center. The Sun's orbit about the Milky Way is expected to be roughly elliptical with the addition of perturbations due to the Galactic spiral arms and non-uniform mass distributions. In addition, the Sun passes through the Galactic plane approximately 2.7 times per orbit.[162] This is very similar to how a simple harmonic oscillator works with no drag force (damping) term. These oscillations were until recently thought to coincide with mass lifeform extinction periods on Earth.[163] However, a reanalysis of the effects of the Sun's transit through the spiral structure based on CO data has failed to find a correlation.[164]
+
+It takes the Solar System about 240 million years to complete one orbit of the Milky Way (a galactic year),[16] so the Sun is thought to have completed 18–20 orbits during its lifetime and 1/1250 of a revolution since the origin of humans. The orbital speed of the Solar System about the center of the Milky Way is approximately 220 km/s (490,000 mph) or 0.073% of the speed of light. The Sun moves through the heliosphere at 84,000 km/h (52,000 mph). At this speed, it takes around 1,400 years for the Solar System to travel a distance of 1 light-year, or 8 days to travel 1 AU (astronomical unit).[165] The Solar System is headed in the direction of the zodiacal constellation Scorpius, which follows the ecliptic.[166]
+
+The stars and gas in the Milky Way rotate about its center differentially, meaning that the rotation period varies with location. As is typical for spiral galaxies, the orbital speed of most stars in the Milky Way does not depend strongly on their distance from the center. Away from the central bulge or outer rim, the typical stellar orbital speed is between 210 ± 10 km/s (470,000 ± 22,000 mph).[169] Hence the orbital period of the typical star is directly proportional only to the length of the path traveled. This is unlike the situation within the Solar System, where two-body gravitational dynamics dominate, and different orbits have significantly different velocities associated with them. The rotation curve (shown in the figure) describes this rotation. Toward the center of the Milky Way the orbit speeds are too low, whereas beyond 7 kpcs the speeds are too high to match what would be expected from the universal law of gravitation.
+
+If the Milky Way contained only the mass observed in stars, gas, and other baryonic (ordinary) matter, the rotation speed would decrease with distance from the center. However, the observed curve is relatively flat, indicating that there is additional mass that cannot be detected directly with electromagnetic radiation. This inconsistency is attributed to dark matter.[34] The rotation curve of the Milky Way agrees with the universal rotation curve of spiral galaxies, the best evidence for the existence of dark matter in galaxies. Alternatively, a minority of astronomers propose that a modification of the law of gravity may explain the observed rotation curve.[170]
+
+The Milky Way began as one or several small overdensities in the mass distribution in the Universe shortly after the Big Bang.[171] Some of these overdensities were the seeds of globular clusters in which the oldest remaining stars in what is now the Milky Way formed. Nearly half the matter in the Milky Way may have come from other distant galaxies.[171] Nonetheless, these stars and clusters now comprise the stellar halo of the Milky Way. Within a few billion years of the birth of the first stars, the mass of the Milky Way was large enough so that it was spinning relatively quickly. Due to conservation of angular momentum, this led the gaseous interstellar medium to collapse from a roughly spheroidal shape to a disk. Therefore, later generations of stars formed in this spiral disk. Most younger stars, including the Sun, are observed to be in the disk.[172][173]
+
+Since the first stars began to form, the Milky Way has grown through both galaxy mergers (particularly early in the Milky Way's growth) and accretion of gas directly from the Galactic halo.[173] The Milky Way is currently accreting material from several small galaxies, including two of its largest satellite galaxies, the Large and Small Magellanic Clouds, through the Magellanic Stream. Direct accretion of gas is observed in high-velocity clouds like the Smith Cloud.[174][175] However, properties of the Milky Way such as stellar mass, angular momentum, and metallicity in its outermost regions suggest it has undergone no mergers with large galaxies in the last 10 billion years. This lack of recent major mergers is unusual among similar spiral galaxies; its neighbour the Andromeda Galaxy appears to have a more typical history shaped by more recent mergers with relatively large galaxies.[176][177]
+
+According to recent studies, the Milky Way as well as the Andromeda Galaxy lie in what in the galaxy color–magnitude diagram is known as the "green valley", a region populated by galaxies in transition from the "blue cloud" (galaxies actively forming new stars) to the "red sequence" (galaxies that lack star formation). Star-formation activity in green valley galaxies is slowing as they run out of star-forming gas in the interstellar medium. In simulated galaxies with similar properties, star formation will typically have been extinguished within about five billion years from now, even accounting for the expected, short-term increase in the rate of star formation due to the collision between both the Milky Way and the Andromeda Galaxy.[178] In fact, measurements of other galaxies similar to the Milky Way suggest it is among the reddest and brightest spiral galaxies that are still forming new stars and it is just slightly bluer than the bluest red sequence galaxies.[179]
+
+Globular clusters are among the oldest objects in the Milky Way, which thus set a lower limit on the age of the Milky Way. The ages of individual stars in the Milky Way can be estimated by measuring the abundance of long-lived radioactive elements such as thorium-232 and uranium-238, then comparing the results to estimates of their original abundance, a technique called nucleocosmochronology. These yield values of about 12.5 ± 3 billion years for CS 31082-001[181] and 13.8 ± 4 billion years for BD +17° 3248.[182] Once a white dwarf is formed, it begins to undergo radiative cooling and the surface temperature steadily drops. By measuring the temperatures of the coolest of these white dwarfs and comparing them to their expected initial temperature, an age estimate can be made. With this technique, the age of the globular cluster M4 was estimated as 12.7 ± 0.7 billion years. Age estimates of the oldest of these clusters gives a best fit estimate of 12.6 billion years, and a 95% confidence upper limit of 16 billion years.[183]
+
+In November 2018, astronomers reported the discovery of one of the oldest stars in the universe. About 13.5 billion-years-old, 2MASS J18082002-5104378 B is a tiny ultra metal-poor (UMP) star made almost entirely of materials released from the Big Bang, and is possibly one of the very first stars. The discovery of the star in the Milky Way galaxy suggests that the galaxy may be at least 3 billion years older than previously thought.[184][185][186]
+
+Several individual stars have been found in the Milky Way's halo with measured ages very close to the 13.80-billion-year age of the Universe. In 2007, a star in the galactic halo, HE 1523-0901, was estimated to be about 13.2 billion years old. As the oldest known object in the Milky Way at that time, this measurement placed a lower limit on the age of the Milky Way.[187] This estimate was made using the UV-Visual Echelle Spectrograph of the Very Large Telescope to measure the relative strengths of spectral lines caused by the presence of thorium and other elements created by the R-process. The line strengths yield abundances of different elemental isotopes, from which an estimate of the age of the star can be derived using nucleocosmochronology.[187] Another star, HD 140283, is 14.5 ± 0.7 billion years old.[35][188]
+
+According to observations utilizing adaptive optics to correct for Earth's atmospheric distortion, stars in the galaxy's bulge date to about 12.8 billion years old.[189]
+
+The age of stars in the galactic thin disk has also been estimated using nucleocosmochronology. Measurements of thin disk stars yield an estimate that the thin disk formed 8.8 ± 1.7 billion years ago. These measurements suggest there was a hiatus of almost 5 billion years between the formation of the galactic halo and the thin disk.[190] Recent analysis of the chemical signatures of thousands of stars suggests that stellar formation might have dropped by an order of magnitude at the time of disk formation, 10 to 8 billion years ago, when interstellar gas was too hot to form new stars at the same rate as before.[191]
+
+The satellite galaxies surrounding the Milky way are not randomly distributed but seemed to be the result of a break-up of some larger system producing a ring structure 500,000 light-years in diameter and 50,000 light-years wide.[192] Close encounters between galaxies, like that expected in 4 billion years with the Andromeda Galaxy rips off huge tails of gas, which, over time can coalesce to form dwarf galaxies in a ring at an arbitrary angle to the main disc.[193]
+
+The Milky Way and the Andromeda Galaxy are a binary system of giant spiral galaxies belonging to a group of 50 closely bound galaxies known as the Local Group, surrounded by a Local Void, itself being part of the Virgo Supercluster. Surrounding the Virgo Supercluster are a number of voids, devoid of many galaxies, the Microscopium Void to the "north", the Sculptor Void to the "left", the Bootes Void to the "right" and the Canes-Major Void to the South. These voids change shape over time, creating filamentous structures of galaxies. The Virgo Supercluster, for instance, is being drawn towards the Great Attractor,[194] which in turn forms part of a greater structure, called Laniakea.[195]
+
+Two smaller galaxies and a number of dwarf galaxies in the Local Group orbit the Milky Way. The largest of these is the Large Magellanic Cloud with a diameter of 14,000 light-years. It has a close companion, the Small Magellanic Cloud. The Magellanic Stream is a stream of neutral hydrogen gas extending from these two small galaxies across 100° of the sky. The stream is thought to have been dragged from the Magellanic Clouds in tidal interactions with the Milky Way.[196] Some of the dwarf galaxies orbiting the Milky Way are Canis Major Dwarf (the closest), Sagittarius Dwarf Elliptical Galaxy, Ursa Minor Dwarf, Sculptor Dwarf, Sextans Dwarf, Fornax Dwarf, and Leo I Dwarf. The smallest dwarf galaxies of the Milky Way are only 500 light-years in diameter. These include Carina Dwarf, Draco Dwarf, and Leo II Dwarf. There may still be undetected dwarf galaxies that are dynamically bound to the Milky Way, which is supported by the detection of nine new satellites of the Milky Way in a relatively small patch of the night sky in 2015.[197] There are also some dwarf galaxies that have already been absorbed by the Milky Way, such as the progenitor of Omega Centauri.[198]
+
+In 2014 researchers reported that most satellite galaxies of the Milky Way lie in a very large disk and orbit in the same direction.[199] This came as a surprise: according to standard cosmology, the satellite galaxies should form in dark matter halos, and they should be widely distributed and moving in random directions. This discrepancy is still not fully explained.[200]
+
+In January 2006, researchers reported that the heretofore unexplained warp in the disk of the Milky Way has now been mapped and found to be a ripple or vibration set up by the Large and Small Magellanic Clouds as they orbit the Milky Way, causing vibrations when they pass through its edges. Previously, these two galaxies, at around 2% of the mass of the Milky Way, were considered too small to influence the Milky Way. However, in a computer model, the movement of these two galaxies creates a dark matter wake that amplifies their influence on the larger Milky Way.[201]
+
+Current measurements suggest the Andromeda Galaxy is approaching us at 100 to 140 km/s (220,000 to 310,000 mph). In 3 to 4 billion years, there may be an Andromeda–Milky Way collision, depending on the importance of unknown lateral components to the galaxies' relative motion. If they collide, the chance of individual stars colliding with each other is extremely low, but instead the two galaxies will merge to form a single elliptical galaxy or perhaps a large disk galaxy[202] over the course of about a billion years.[203]
+
+Although special relativity states that there is no "preferred" inertial frame of reference in space with which to compare the Milky Way, the Milky Way does have a velocity with respect to cosmological frames of reference.
+
+One such frame of reference is the Hubble flow, the apparent motions of galaxy clusters due to the expansion of space. Individual galaxies, including the Milky Way, have peculiar velocities relative to the average flow. Thus, to compare the Milky Way to the Hubble flow, one must consider a volume large enough so that the expansion of the Universe dominates over local, random motions. A large enough volume means that the mean motion of galaxies within this volume is equal to the Hubble flow. Astronomers believe the Milky Way is moving at approximately 630 km/s (1,400,000 mph) with respect to this local co-moving frame of reference.[204] The Milky Way is moving in the general direction of the Great Attractor and other galaxy clusters, including the Shapley supercluster, behind it.[205] The Local Group (a cluster of gravitationally bound galaxies containing, among others, the Milky Way and the Andromeda Galaxy) is part of a supercluster called the Local Supercluster, centered near the Virgo Cluster: although they are moving away from each other at 967 km/s (2,160,000 mph) as part of the Hubble flow, this velocity is less than would be expected given the 16.8 million pc distance due to the gravitational attraction between the Local Group and the Virgo Cluster.[206]
+
+Another reference frame is provided by the cosmic microwave background (CMB). The Milky Way is moving at 552 ± 6 km/s (1,235,000 ± 13,000 mph)[18] with respect to the photons of the CMB, toward 10.5 right ascension, −24° declination (J2000 epoch, near the center of Hydra). This motion is observed by satellites such as the Cosmic Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP) as a dipole contribution to the CMB, as photons in equilibrium in the CMB frame get blue-shifted in the direction of the motion and red-shifted in the opposite direction.[18]
+
+In the Babylonian epic poem Enûma Eliš, the Milky Way is created from the severed tail of the primeval salt water dragoness Tiamat, set in the sky by Marduk, the Babylonian national god, after slaying her.[207][208] This story was once thought to have been based on an older Sumerian version in which Tiamat is instead slain by Enlil of Nippur,[209][210] but is now thought to be purely an invention of Babylonian propagandists with the intention to show Marduk as superior to the Sumerian deities.[210]
+
+Llys Dôn (literally "The Court of Dôn") is the traditional Welsh name for the constellation Cassiopeia. At least three of Dôn's children also have astronomical associations: Caer Gwydion ("The fortress of Gwydion") is the traditional Welsh name for the Milky Way,[211][212] and Caer Arianrhod ("The Fortress of Arianrhod") being the constellation of Corona Borealis.[citation needed]
+
+In western culture, the name "Milky Way" is derived from its appearance as a dim un-resolved "milky" glowing band arching across the night sky. The term is a translation of the Classical Latin via lactea, in turn derived from the Hellenistic Greek γαλαξίας, short for γαλαξίας κύκλος (galaxías kýklos, "milky circle"). The Ancient Greek γαλαξίας (galaxias) – from root γαλακτ-, γάλα ("milk") + -ίας (forming adjectives) – is also the root of "galaxy", the name for our, and later all such, collections of stars.[19][213][214][215]
+
+In Greek mythology, the Milky Way was formed after the trickster god Hermes suckled the infant Heracles at the breast of Hera, the queen of the gods, while she was asleep.[216][217] When Hera awoke, she tore Heracles away from her breast and splattered her breast milk across the heavens.[216][217] In another version of the story, Athena, the patron goddess of heroes, tricked Hera into suckling Heracles voluntarily,[216][217] but he bit her nipple so hard that she flung him away, spraying milk everywhere.[216][217]
+
+The Milky Way, or "milk circle", was just one of 11 "circles" the Greeks identified in the sky, others being the zodiac, the meridian, the horizon, the equator, the tropics of Cancer and Capricorn, Arctic and Antarctic circles, and two colure circles passing through both poles.[218]
+
+In Meteorologica (DK 59 A80), Aristotle (384–322 BC) wrote that the Greek philosophers Anaxagoras (c. 500–428 BC) and Democritus (460–370 BC) proposed that the Milky Way might consist of distant stars.[219] However, Aristotle himself believed the Milky Way to be caused by "the ignition of the fiery exhalation of some stars which were large, numerous and close together"[220] and that the "ignition takes place in the upper part of the atmosphere, in the region of the world which is continuous with the heavenly motions."[221][222] The Neoplatonist philosopher Olympiodorus the Younger (c. 495–570 AD) criticized this view, arguing that if the Milky Way were sublunary, it should appear different at different times and places on Earth, and that it should have parallax, which it does not. In his view, the Milky Way is celestial. This idea would be influential later in the Islamic world.[223]
+
+The Persian astronomer Abū Rayhān al-Bīrūnī (973–1048) proposed that the Milky Way is "a collection of countless fragments of the nature of nebulous stars".[224] The Andalusian astronomer Avempace (d 1138) proposed the Milky Way to be made up of many stars but appears to be a continuous image due to the effect of refraction in Earth's atmosphere, citing his observation of a conjunction of Jupiter and Mars in 1106 or 1107 as evidence.[222] Ibn Qayyim Al-Jawziyya (1292–1350) proposed that the Milky Way is "a myriad of tiny stars packed together in the sphere of the fixed stars" and that these stars are larger than planets.[225]
+
+According to Jamil Ragep, the Persian astronomer Naṣīr al-Dīn al-Ṭūsī (1201–1274) in his Tadhkira writes:
+"The Milky Way, i.e. the Galaxy, is made up of a very large number of small, tightly clustered stars, which, on account of their concentration and smallness, seem to be cloudy patches. Because of this, it was likened to milk in color."[226]
+
+Proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei used a telescope to study the Milky Way and discovered that it is composed of a huge number of faint stars.[227][228] In a treatise in 1755, Immanuel Kant, drawing on earlier work by Thomas Wright,[229] speculated (correctly) that the Milky Way might be a rotating body of a huge number of stars, held together by gravitational forces akin to the Solar System but on much larger scales.[230] The resulting disk of stars would be seen as a band on the sky from our perspective inside the disk. Wright and Kant also conjectured that some of the nebulae visible in the night sky might be separate "galaxies" themselves, similar to our own. Kant referred to both the Milky Way and the "extragalactic nebulae" as "island universes", a term still current up to the 1930s.[231][232][233]
+
+The first attempt to describe the shape of the Milky Way and the position of the Sun within it was carried out by William Herschel in 1785 by carefully counting the number of stars in different regions of the visible sky. He produced a diagram of the shape of the Milky Way with the Solar System close to the center.[234]
+
+In 1845, Lord Rosse constructed a new telescope and was able to distinguish between elliptical and spiral-shaped nebulae. He also managed to make out individual point sources in some of these nebulae, lending credence to Kant's earlier conjecture.[235][236]
+
+In 1904, studying the proper motions of stars, Jacobus Kapteyn reported that these were not random, as it was believed in that time; stars could be divided into two streams, moving in nearly opposite directions.[237]  It was later realized that Kapteyn's data had been the first evidence of the rotation of our Galaxy,[238] which ultimately led to the finding of galactic rotation by Bertil Lindblad and Jan Oort.
+
+In 1917, Heber Curtis had observed the nova S Andromedae within the Great Andromeda Nebula (Messier object 31). Searching the photographic record, he found 11 more novae. Curtis noticed that these novae were, on average, 10 magnitudes fainter than those that occurred within the Milky Way. As a result, he was able to come up with a distance estimate of 150,000 parsecs. He became a proponent of the "island universes" hypothesis, which held that the spiral nebulae were independent galaxies.[239][240] In 1920 the Great Debate took place between Harlow Shapley and Heber Curtis, concerning the nature of the Milky Way, spiral nebulae, and the dimensions of the Universe. To support his claim that the Great Andromeda Nebula is an external galaxy, Curtis noted the appearance of dark lanes resembling the dust clouds in the Milky Way, as well as the significant Doppler shift.[241]
+
+The controversy was conclusively settled by Edwin Hubble in the early 1920s using the Mount Wilson observatory 2.5 m (100 in) Hooker telescope. With the light-gathering power of this new telescope, he was able to produce astronomical photographs that resolved the outer parts of some spiral nebulae as collections of individual stars. He was also able to identify some Cepheid variables that he could use as a benchmark to estimate the distance to the nebulae. He found that the Andromeda Nebula is 275,000 parsecs from the Sun, far too distant to be part of the Milky Way.[242][243]
+
+The ESA spacecraft Gaia provides distance estimates by determining the parallax of a billion stars and is mapping the Milky Way with four planned releases of maps in 2016, 2018, 2021 and 2024.[244][245] A study in 2020 concluded that Gaia detected a wobbling motion of the galaxy, which might be caused by "torques from a misalignment of the disc's rotation axis with respect to the principle axis of a non-spherical halo, or from accreted matter in the halo acquired during late infall, or from nearby, interacting satellite galaxies and their consequent tides".[246]

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+Rudolf Khametovich Nureyev (/ˈnjʊəriɛf, njʊˈreɪɛf/ NEWR-ee-ef, nyuurr-AY-ef; Tatar: Рудольф Хәмит улы Нуриев; Russian: Рудо́льф Хаме́тович Нуре́ев, IPA: [rʊˈdolʲf nʊˈrʲejɪf]; 17 March 1938 – 6 January 1993) was a Soviet ballet dancer and choreographer. Nureyev is regarded by some as the greatest male ballet dancer of his generation.[1][2][3][4]
+
+Nureyev was born on a Trans-Siberian train near Irkutsk, Siberia, Soviet Union to a Bashkir-Tatar family. He began his early career with the company that in the Soviet era was called the Kirov Ballet (now called by its original name, the Mariinsky Ballet) in Leningrad. He defected from the Soviet Union to the West in 1961, despite KGB efforts to stop him.[5] This was the first defection of a Soviet artist during the Cold War, and it created an international sensation. He went on to dance with The Royal Ballet in London and from 1983 to 1989 served as director of the Paris Opera Ballet. In addition to his technical prowess, Rudolf Nureyev was an accomplished choreographer serving as the chief choreographer of the Paris Opera Ballet. He produced his own interpretations of numerous classical works,[6] including Swan Lake, Giselle, and La Bayadère.[7]
+
+Rudolf Nureyev was born on a Trans-Siberian train near Irkutsk, Siberia, while his mother, Farida, was travelling to Vladivostok, where his father Khamet, a Red Army political commissar, was stationed.[8] He was raised as the only son with three older sisters in a Tatar Muslim family.[9][10][11]
+
+When his mother took Nureyev and his sisters into a performance of the ballet Song of the Cranes, he fell in love with dance.[8] As a child he was encouraged to dance in Bashkir folk performances and his precocity was soon noticed by teachers who encouraged him to train in Leningrad (now St. Petersburg). On a tour stop in Moscow with a local ballet company, Nureyev auditioned for the Bolshoi ballet company and was accepted. However, he felt that the Mariinsky Ballet school was the best, so he left the local touring company and bought a ticket to Leningrad.[12]
+
+Owing to the disruption of Soviet cultural life caused by World War II, Nureyev was unable to enroll in a major ballet school until 1955, aged 17, when he was accepted by the Vaganova Academy of Russian Ballet of Leningrad, the associate school of the Mariinsky Ballet. The ballet master Alexander Ivanovich Pushkin took an interest in him professionally and allowed Nureyev to live with him and his wife.[13]
+
+Upon his graduation in 1958, Nureyev joined the Kirov Ballet (now Mariinsky). He moved immediately beyond the corps level, and was given solo roles as a principal dancer from the outset.[2] Nureyev regularly partnered with Natalia Dudinskaya, the company's senior ballerina and wife of its director, Konstantin Sergeyev. Dudinskaya, who was 26 years his senior, first chose him as her partner[13] in the ballet Laurencia.
+
+Before long Rudolf Nureyev became one of the Soviet Union's best-known dancers. From 1958 to 1961, in his three years with the Kirov, he danced 15 roles, usually opposite his partner, Ninel Kurgapkina, with whom he was very well paired, although she was almost a decade older than he was.[14] Nureyev and Kurgapkina were invited to dance at a gathering at Khrushchev's dacha,[13] and in 1959 they were allowed to travel outside the Soviet Union, dancing in Vienna at the International Youth Festival. Not long after, he was told by the Ministry of Culture that he would not be allowed to go abroad again.[15] In one memorable incident, Nureyev interrupted a performance of Don Quixote for 40 minutes, insisting on dancing in tights and not in the customary trousers. He relented in the end, but his preferred dress code was adopted in later performances.[13]
+
+By the late 1950s, Rudolf Nureyev had become a sensation in the Soviet Union.
+
+Yet, as the Kirov Ballet was preparing to go on a tour to Paris and London, Nureyev's rebellious character and non-conformist attitude made him an unlikely candidate for the trip, which the Soviet government considered crucial to its ambitions to demonstrate its "cultural supremacy" over the West. Furthermore, tensions were growing between Nureyev and the Kirov's artistic director Konstantin Sergeyev, who was also the husband of Nureyev's former dance partner Natalia Dudinskaya.[16] After a representative of the French tour organizers saw Nureyev dance in Leningrad in 1960, the French organizers urged Soviet authorities to let him dance in Paris, and he was allowed to go.[13]
+
+In Paris, his performances electrified audiences and critics. Oliver Merlin in Le Monde wrote,
+
+I will never forget his arrival running across the back of the stage, and his catlike way of holding himself opposite the ramp. He wore a white sash over an ultramarine costume, had large wild eyes and hollow cheeks under a turban topped with a spray of feathers, bulging thighs, immaculate tights. This was already Nijinsky in Firebird.[17]
+
+Nureyev was seen to have broken the rules about mingling with foreigners and allegedly frequented gay bars in Paris, which alarmed the Kirov's management[18] and the KGB agents observing him. The KGB wanted to send him back to the Soviet Union. On 16 June 1961 when the Kirov company gathered at Le Bourget Airport in Paris to fly to London, Sergeyev took Nureyev aside and told him that he must return to Moscow for a special performance in the Kremlin, rather than go on to London with the rest of the company. Nureyev became suspicious and refused. Next he was told that his mother had fallen severely ill and he needed to go home immediately to see her.[19] Nureyev refused again, believing that on return to the USSR he was likely to be imprisoned. With the help of French police and a Parisian socialite friend, Clara Saint, who had been engaged to the son of the French Minister of Culture, Andre Malraux,[20] Nureyev escaped his KGB minders and asked for asylum. Sergeyev and the KGB tried to dissuade him, but he chose to stay in Paris.
+
+Within a week, he was signed by the Grand Ballet du Marquis de Cuevas and performing The Sleeping Beauty with Nina Vyroubova. On a tour of Denmark he met Erik Bruhn, soloist at the Royal Danish Ballet[21] who became his lover, his closest friend and his protector until Bruhn's death in 1986.[22]
+
+Soviet authorities made Nureyev's father, mother and dance teacher Pushkin write letters to him, urging him to return, without effect.[13] Although he petitioned the Soviet government for many years to be allowed to visit his mother, he was not allowed to do so until 1987, when his mother was dying and Mikhail Gorbachev consented to the visit. In 1989, he was invited to dance the role of James in La Sylphide with the Mariinsky Ballet at the Mariinsky Theatre in Leningrad.[23] The visit gave him the opportunity to see many of the teachers and colleagues he had not seen since his defection.[24]
+
+Dame Ninette de Valois offered him a contract to join The Royal Ballet as Principal Dancer. During his time at the company, however, many critics became enraged as Nureyev made substantial changes to the productions of Swan Lake and Giselle.[25] Nureyev stayed with the Royal Ballet until 1970, when he was promoted to Principal Guest Artist, enabling him to concentrate on his increasing schedule of international guest appearances and tours.  He continued to perform regularly with The Royal Ballet until committing his future to the Paris Opera Ballet in the 1980s.
+
+Nureyev's first appearance with Prima Ballerina Dame Margot Fonteyn was in a ballet matinée organized by The Royal Ballet: Giselle, 21 February 1962.[26]  The event was held in aid of the Royal Academy of Dance, a classical ballet teaching organisation of which she was president.  He danced Poème Tragique, a solo choreographed by Frederick Ashton, and the Black Swan pas de deux from Swan Lake. They were so well received that Fonteyn and Nureyev proceeded to form a partnership which endured for many years. They premiered Romeo and Juliet for the company in 1965.[27] Fans of the duo would tear up their programs to make confetti that'd be joyously thrown at the dancers. Nureyev and Fonteyn might do upwards of 20 curtain calls.[26][28] On 11 July 1967, Fonteyn and Nureyev, after performing in San Francisco, were arrested on nearby roofs having fled during a police raid on a home in the Haight-Ashbury district. They were bailed out and charges of disturbing the peace and visiting a place where marijuana was used were dropped later that day for lack of sufficient evidence.[29]
+
+Among many appearances in North America, Nureyev developed a long-lasting connection with the National Ballet of Canada, appearing as a guest artist on many occasions. In 1972, he staged a spectacular new production of Sleeping Beauty for the company, with his own additional choreography augmenting that of Petipa. The production toured widely in the US and Canada after its initial run in Toronto, one performance of which was televised live and subsequently issued in video. Among the National Ballet's ballerinas, Nureyev most frequently partnered Veronica Tennant and Karen Kain.
+
+In 1982, Nureyev became a naturalized citizen of Austria.[30] In 1983, he was appointed director of the Paris Opera Ballet, where, as well as directing, he continued to dance and to promote younger dancers. He remained there as a dancer and chief choreographer until 1989. Among the dancers he mentored were Sylvie Guillem, Isabelle Guérin, Manuel Legris, Elisabeth Maurin, Élisabeth Platel, Charles Jude, and Monique Loudières.
+
+His artistic directorship of the Paris Opera Ballet was a great success, lifting the company out of a dark period. His Sleeping Beauty remains in the repertoire and was revived and filmed with his protégé Manuel Legris in the lead.
+
+Despite advancing illness towards the end of his tenure, he worked tirelessly, staging new versions of old standbys and commissioning some of the most ground-breaking choreographic works of his time. His own Romeo and Juliet was a popular success. When he was sick towards the end of his life, he worked on a final production of La Bayadère which closely follows the Mariinsky Ballet version he danced as a young man.
+
+When AIDS appeared in France's news around 1982, Nureyev took little notice. The dancer tested positive for HIV in 1984, but for several years he simply denied that anything was wrong with his health. However, by the late 1980s his diminished capabilities disappointed his admirers who had fond memories of his outstanding prowess and skill.[31] Nureyev began a marked decline only in the summer of 1991 and entered the final phase of the disease in the spring of 1992.[32]
+
+In March 1992, living with advanced AIDS, he visited Kazan and appeared as a conductor in front of the audience at Musa Cälil Tatar Academic Opera and Ballet Theater, which now presents the Rudolf Nureyev Festival in Tatarstan.[33][34] Returning to Paris, with a high fever, he was admitted to the hospital Notre Dame du Perpétuel Secours in Levallois-Perret, a suburb northwest of Paris, and was operated on for pericarditis, an inflammation of the membranous sac around the heart. At that time, what inspired him to fight his illness was the hope that he could fulfill an invitation to conduct Prokofiev's Romeo and Juliet at an American Ballet Theatre benefit on 6 May 1992 at the Metropolitan Opera House in New York. He did so and was elated at the reception.[32]
+
+In July 1992, Nureyev showed renewed signs of pericarditis but determined to forswear further treatment. His last public appearance was on 8 October 1992, at the premiere at Palais Garnier of a new production of La Bayadère that he choreographed after Marius Petipa for the Paris Opera Ballet. Nureyev had managed to obtain a photocopy of the original score by Minkus when in Russia in 1989.[35]  The ballet was a personal triumph although the gravity of his condition was evident. The French Culture Minister, Jack Lang, presented him that evening on stage with France's highest cultural award, the Commandeur de l'Ordre des Arts et des Lettres.[32]
+
+Nureyev re-entered the hospital Notre Dame du Perpétuel Secours in Levallois-Perret on 20 November 1992 and remained there until his death from AIDS complications at age 54 on 6 January 1993. His funeral was held in the marble foyer of the Paris Garnier Opera House. Many paid tributes to his brilliance as a dancer. One such tribute came from Oleg Vinogradov of the Mariinsky Ballet, stating: "What Nureyev did in the west, he could never have done here."[36]
+
+Nureyev's grave, at a Russian cemetery in Sainte-Geneviève-des-Bois near Paris, features a tomb draped in a mosaic of an Oriental carpet. Nureyev was an avid collector of beautiful carpets and antique textiles.[32][33][37] As his coffin was lowered into the ground, music from the last act of Giselle was played and his ballet shoes were cast into the grave along with white lilies.[38]
+
+After so many years of having been denied a place in the Mariinsky Ballet's history, Nureyev's reputation was restored.[36] His name was re-entered in the history of the Mariinsky, and some of his personal effects were placed on display at the theatre museum in what was now St. Petersburg.[36] A rehearsal room was named in his honor at the famed Vaganova Academy.[36] As of October 2013, the Centre National du Costume de Scene has a permanent collection of Nureyev's costumes "that offers visitors a sense of his exuberant, vagabond personality and passion for all that was rare and beautiful."[39] In 2015, he was inducted into the Legacy Walk.[40]
+
+Since his death in 1993, the Paris Opera has instituted a tradition of presenting an evening of dance homage to Rudolf Nureyev every ten years. Because he was born in March, these performances have been given on 20 March 2003 and 6 March 2013.[41] Peers of Rudolf Nureyev who speak about and remember him, like Mikhail Baryshnikov, are often deeply touched.[42][43]
+
+A selected list of ballet performances, ballet productions and original ballets.[44]
+
+Yvette Chauviré of the Paris Opera Ballet often danced with Nureyev; he described her as a "legend".[45] (Chauviré attended his funeral with French dancer and actress Leslie Caron.)[46]
+
+At the Royal Ballet, Rudolf Nureyev and Margot Fonteyn  became long-standing dance partners. Nureyev once said of Fonteyn, who was 19 years older than he, that they danced with "one body, one soul". Together Nureyev and Fonteyn premiered Sir Frederick Ashton's ballet Marguerite and Armand, a ballet danced to Liszt's Piano Sonata in B minor, which became their signature piece. Kenneth MacMillan was forced to allow them to premiere his Romeo and Juliet, which was intended for two other dancers, Lynn Seymour and Christopher Gable.[47] Films exist of their partnership in Les Sylphides, Swan Lake, Romeo and Juliet, and other roles. They continued to dance together for many years after Nureyev's departure from the Royal Ballet. Their last performance together was in Baroque Pas de Trois on 16 September 1988 when Fonteyn was 69, Nureyev was aged 50, with Carla Fracci, aged 52, also starring.
+
+He celebrated another long-time partnership with Eva Evdokimova. They first appeared together in La Sylphide (1971) and in 1975 he selected her as his Sleeping Beauty in his staging for London Festival Ballet. Evdokimova remained his partner of choice for many guest appearances and tours across the globe with "Nureyev and Friends" for more than fifteen years.
+
+During his American stage debut in 1962,  Nureyev also partnered with Sonia Arova at New York City's Brooklyn Academy of Music. In collaboration with Ruth Page's Chicago Opera Ballet, they performed the grand pas de deux from Don Quixote.[48][49][50][51]
+
+Nureyev was above all a stickler for classical technique, and his mastery of it made him a model for an entire generation of dancers. If the standard of male dancing rose so visibly in the West after the 1960s, it was largely because of Nureyev's inspiration.[2]
+
+Nureyev's influence on the world of ballet changed the perception of male dancers; in his own productions of the classics the male roles received much more choreography.[52] Another important influence was his crossing the borders between classical ballet and modern dance by performing both.[53] Today it is normal for dancers to receive training in both styles, but Nureyev was the originator and excelled in modern and classical dance. He went out of his way to work with modern dance great, Martha Graham, and she created a work specially for him.[54] While Gene Kelly had done much to combine modern and classical styles in film, he came from a more Modern Dance influenced "popular dance" environment, while Nureyev made great strides in gaining acceptance of Modern Dance in the "Classical Ballet" sphere.[54]
+
+Rudolf Nureyev's charisma, commitment and generosity were such that he did not just pass on his knowledge.[55] He personified the school of life for a dancer. Several dancers, who were principals with the Paris Opera Ballet under his direction, went on to become ballet directors themselves inspired to continue Nureyev's work and ideas. Manuel Legris is director of the Vienna State Ballet, Laurent Hilaire is ballet director of the Stanislavski Theatre of Moscow and Charles Jude ballet director of the Grand Théâtre de Bordeaux.[55]
+
+Mikhail Baryshnikov, the other great dancer who like Nureyev defected to the West, holds Nureyev in high regard. Baryshnikov said in an interview that Rudolf Nureyev was an unusual man in all respects, instinctive, intelligence, constant curiosity, and extraordinary discipline, that was his goal of life and of course love in performing.[42][56]
+
+Nureyev had a late start to ballet and had to perfect his technique in order to be a success. John Tooley wrote that Nureyev grew up very poor and had to make up for three to five years in ballet education at a high-level ballet school, giving him a decisive impetus to acquire the maximum of technical skills[57] and to become the best dancer working on perfection during his whole career.[58] The challenge for all dancers whom Nureyev worked with was to follow suit and to share his total commitment for dance. Advocates to describe the Nureyev phenomenon precisely are John Tooley, former general director of the Royal Opera House, London, Pierre Bergé, former president of Opéra Bastille, venue of the Paris Opera Ballet (in addition to the Palais Garnier) and Manuel Legris, principal dancer with the Paris Opera Ballet nominated by Rudolf Nureyev in New York.
+
+Nureyev put it like this: "I approach dancing from a different angle than those who begin dancing at 8 or 9. Those who have studied from the beginning never question anything."[59] Nureyev entered the Vaganova Ballet Academy at the age of just 17 staying there for only 3 years compared to dancers who usually become principal dancers after entering the Vaganova school at 9 and go through the full 9 years of dance education. Vladimir Vasiliev, a peer of Nureyev at the Bolshoi and regarded along with Rudolf and Mikhail Baryshnikov as one of the top three ballet dancers, became a pupil of the Vaganova Ballet Academy in 1949, graduating in 1958 together with Nureyev. Like Nureyev, Baryshnikov spent only three years[60] at the Vaganova school of Leningrad.
+
+Paradoxically, both Rudolf Nureyev and Mikhail Baryshnikov became masters of perfection in dance.[57][1][61] Dance and life was one and the same, Pierre Bergé said about Rudolf Nureyev: "He was a dancer like any other dancer. It is extraordinary to have 19 points out of 20. It is extremely rare to have 20 out of 20. However, to have 21 out of 20 is even much rarer. And this was the situation with Nureyev."[62][63] Legris said: "Rudolf Nureyev was a high-speed train (he was a TGV)."[64][65] Working with Rudolf Nureyev involved having to surpass oneself and "stepping on it."[66]
+
+Rudolf Nureyev did not have much patience with rules, limitations and hierarchical order and had at times a volatile temper.[67] He was apt to throw tantrums in public when frustrated.[68] His impatience mainly showed itself when the failings of others interfered with his work.
+
+He socialized with Gore Vidal, Freddie Mercury, Jackie Kennedy Onassis, Mick Jagger, Liza Minnelli, Andy Warhol, Lee Radziwill and Talitha Pol, and occasionally visited the New York discotheque Studio 54 in the late 1970s, but developed an intolerance for celebrities.[69]
+He kept up old friendships in and out of the ballet world for decades, and was considered to be a loyal and generous friend.[70]
+
+Most ballerinas with whom Rudolf Nureyev danced, including Antoinette Sibley, Gelsey Kirkland and Annette Page, paid tribute to him as a considerate partner. He was known as extremely generous to many ballerinas, who credit him with helping them during difficult times. In particular, the Canadian ballerina Lynn Seymour – distressed when she was denied the opportunity to premiere MacMillan's Romeo and Juliet – says that Nureyev often found projects for her even when she was suffering from weight problems and depression and thus had trouble finding roles.[71]
+
+Depending on the source, Nureyev is described as either bisexual,[72][73] as he did have heterosexual relationships as a younger man, or homosexual.[74][75][76] He had a turbulent relationship life, with numerous bathhouse visits and anonymous pickups.[68] Nureyev met Erik Bruhn, the celebrated Danish dancer, after Nureyev defected to the West in 1961. Nureyev was a great admirer of Bruhn, having seen filmed performances of the Dane on tour in the Soviet Union with the American Ballet Theatre, although stylistically the two dancers were very different. Bruhn and Nureyev became a couple[74][77] and the two remained together off and on, with a very volatile relationship for 25 years, until Bruhn's death in 1986.[78]
+
+In 1973, Nureyev met the 23-year-old American dancer and classical arts student Robert Tracy[76] and a two-and-a-half-year love affair began. Tracy later became Nureyev's secretary and live-in companion for over 14 years in a long-term open relationship until death. According to Tracy, Nureyev said that he had a relationship with three women in his life, he had always wanted a son, and once had plans to father one with Nastassja Kinski.[52]
+
+Nureyev learned that he had contracted HIV in 1984. He lived with the disease in secret, occasionally performing but with a marked decline in appearances. He was admitted to the Hôpital Notre-Dame du Perpétuel Secours in Levallois, a suburb northwest of Paris, for pericarditis, an inflammation of the membranous sac around the heart. He eventually succumbed to the AIDS-related complication on 6 January 1993.[79]
+
+In 1962, Nureyev made his screen debut in a film version of Les Sylphides. He decided against an acting career in order to branch into modern dance with the Dutch National Ballet[80] in 1968. Nureyev also made his debut in 1962 on network television in America partnered with Maria Tallchief dancing the pas de deux from August Bournonville's Flower Festival in Genzano on the Bell Telephone Hour.[48][81][82]
+
+In 1972, Sir Robert Helpmann invited him to tour Australia with Nureyev's production of Don Quixote.[83] Also that year, Nureyev had a dance number in David Winters' Television special The Special London Bridge Special, starring Tom Jones, and Jennifer O'Neill. The star-studded also included sketches and cameos by The Carpenters, Kirk Douglas, Jonathan Winters, Hermione Gingold, Lorne Greene, Chief Dan George, Charlton Heston, George Kirby, Michael Landon, Terry-Thomas, Engelbert Humperdinck, Elliott Gould, and Merle Park.[84][85][86]
+
+In 1973, a film version of Don Quixote was directed by Nureyev and Helpmann and features Nureyev as Basilio, Lucette Aldous as Kitri, Helpmann as Don Quixote and artists of the Australian Ballet.
+
+In 1977, Nureyev played Rudolph Valentino in Ken Russell's film Valentino.
+
+In 1978 he appeared as a guest star on the television series The Muppet Show[87] where he danced in a parody called "Swine Lake", sang "Baby, It's Cold Outside" in a sauna duet with Miss Piggy, and sang and tap-danced in the show's finale, "Top Hat, White Tie and Tails". His appearance is credited with making Jim Henson's series become one of the sought after programs to appear in.[88]
+
+In 1983 he had a non-dancing role in the movie Exposed with Nastassja Kinski.
+
+In 1989, he toured the United States and Canada for 24 weeks with a revival of the Broadway musical The King and I.

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+
+Food is any substance[1] consumed to provide nutritional support for an organism. Food is usually of plant or animal origin, and contains essential nutrients, such as carbohydrates, fats, proteins, vitamins, or minerals. The substance is ingested by an organism and assimilated by the organism's cells to provide energy, maintain life, or stimulate growth.
+
+Historically, humans secured food through two methods: hunting and gathering and agriculture, which gave modern humans a mainly omnivorous diet. Worldwide, humanity has created numerous cuisines and culinary arts, including a wide array of ingredients, herbs, spices, techniques, and dishes.
+
+Today, the majority of the food energy required by the ever-increasing population of the world is supplied by the food industry. Food safety and food security are monitored by agencies like the International Association for Food Protection, World Resources Institute, World Food Programme, Food and Agriculture Organization, and International Food Information Council. They address issues such as sustainability, biological diversity, climate change, nutritional economics, population growth, water supply, and access to food.
+
+The right to food is a human right derived from the International Covenant on Economic, Social and Cultural Rights (ICESCR), recognizing the "right to an adequate standard of living, including adequate food", as well as the "fundamental right to be free from hunger".
+
+Most food has its origin in plants. Some food is obtained directly from plants; but even animals that are used as food sources are raised by feeding them food derived from plants. Cereal grain is a staple food that provides more food energy worldwide than any other type of crop.[2] Corn (maize), wheat, and rice – in all of their varieties – account for 87% of all grain production worldwide.[3][4][5] Most of the grain that is produced worldwide is fed to livestock.
+
+Some foods not from animal or plant sources include various edible fungi, especially mushrooms. Fungi and ambient bacteria are used in the preparation of fermented and pickled foods like leavened bread, alcoholic drinks, cheese, pickles, kombucha, and yogurt. Another example is blue-green algae such as Spirulina.[6] Inorganic substances such as salt, baking soda and cream of tartar are used to preserve or chemically alter an ingredient.
+
+Many plants and plant parts are eaten as food and around 2,000 plant species are cultivated for food. Many of these plant species have several distinct cultivars.[7]
+
+Seeds of plants are a good source of food for animals, including humans, because they contain the nutrients necessary for the plant's initial growth, including many healthful fats, such as omega fats. In fact, the majority of food consumed by human beings are seed-based foods. Edible seeds include cereals (corn, wheat, rice, et cetera), legumes (beans, peas, lentils, et cetera), and nuts. Oilseeds are often pressed to produce rich oils - sunflower, flaxseed, rapeseed (including canola oil), sesame, et cetera.[8]
+
+Seeds are typically high in unsaturated fats and, in moderation, are considered a health food. However, not all seeds are edible. Large seeds, such as those from a lemon, pose a choking hazard, while seeds from cherries and apples  contain cyanide which could be poisonous only if consumed in large volumes.[9]
+
+Fruits are the ripened ovaries of plants, including the seeds within. Many plants and animals have coevolved such that the fruits of the former are an attractive food source to the latter, because animals that eat the fruits may excrete the seeds some distance away. Fruits, therefore, make up a significant part of the diets of most cultures. Some botanical fruits, such as tomatoes, pumpkins, and eggplants, are eaten as vegetables.[10] (For more information, see list of fruits.)
+
+Vegetables are a second type of plant matter that is commonly eaten as food. These include root vegetables (potatoes and carrots), bulbs (onion family), leaf vegetables (spinach and lettuce), stem vegetables (bamboo shoots and asparagus), and inflorescence vegetables (globe artichokes and broccoli and other vegetables such as cabbage or cauliflower).[11]
+
+Animals are used as food either directly or indirectly by the products they produce. Meat is an example of a direct product taken from an animal, which comes from muscle systems or from organs (offal).
+
+Food products produced by animals include milk produced by mammary glands, which in many cultures is drunk or processed into dairy products (cheese, butter, etc.). In addition, birds and other animals lay eggs, which are often eaten, and bees produce honey, a reduced nectar from flowers, which is a popular sweetener in many cultures. Some cultures consume blood, sometimes in the form of blood sausage, as a thickener for sauces, or in a cured, salted form for times of food scarcity, and others use blood in stews such as jugged hare.[12]
+
+Some cultures and people do not consume meat or animal food products for cultural, dietary, health, ethical, or ideological reasons. Vegetarians choose to forgo food from animal sources to varying degrees. Vegans do not consume any foods that are or contain ingredients from an animal source.
+
+Adulteration is a legal term meaning that a food product fails to meet the legal standards. One form of adulteration is an addition of another substance to a food item in order to increase the quantity of the food item in raw form or prepared form, which may result in the loss of actual quality of food item. These substances may be either available food items or non-food items. Among meat and meat products some of the items used to adulterate are water or ice, carcasses, or carcasses of animals other than the animal meant to be consumed.[13]
+
+Camping food includes ingredients used to prepare food suitable for backcountry camping and backpacking. The foods differ substantially from the ingredients found in a typical home kitchen. The primary differences relate to campers' and backpackers' special needs for foods that have appropriate cooking time, perishability, weight, and nutritional content.
+
+To address these needs, camping food is often made up of either freeze-dried, precooked or dehydrated ingredients. Many campers use a combination of these foods.
+
+Freeze-drying requires the use of heavy machinery and is not something that most campers are able to do on their own. Freeze-dried ingredients are often considered superior to dehydrated ingredients however because they rehydrate at camp faster and retain more flavor than their dehydrated counterparts. Freeze-dried ingredients take so little time to rehydrate that they can often be eaten without cooking them first and have a texture similar to a crunchy chip.
+
+Dehydration can reduce the weight of the food by sixty to ninety percent by removing water through evaporation. Some foods dehydrate well, such as onions, peppers, and tomatoes.[14][15] Dehydration often produces a more compact, albeit slightly heavier, end result than freeze-drying.
+
+Surplus precooked military Meals, Meals, Ready-to-Eat (MREs) are sometimes used by campers. These meals contain pre-cooked foods in retort pouches. A retort pouch is a plastic and metal foil laminate pouch that is used as an alternative to traditional industrial canning methods.
+
+Diet food (or "dietetic food") refers to any food or beverage whose recipe is altered to reduce fat, carbohydrates, abhor/adhore sugar in order to make it part of a weight loss program or diet. Such foods are usually intended to assist in weight loss or a change in body type, although bodybuilding supplements are designed to aid in gaining weight or muscle.
+
+The process of making a diet version of a food usually requires finding an acceptable low-food-energy substitute for some high-food-energy ingredient.[16] This can be as simple as replacing some or all of the food's sugar with a sugar substitute as is common with diet soft drinks such as Coca-Cola (for example Diet Coke). In some snacks, the food may be baked instead of fried thus reducing the food energy. In other cases, low-fat ingredients may be used as replacements.
+
+In whole grain foods, the higher fiber content effectively displaces some of the starch components of the flour. Since certain fibers have no food energy, this results in a modest energy reduction. Another technique relies on the intentional addition of other reduced-food-energy ingredients, such as resistant starch or dietary fiber, to replace part of the flour and achieve a more significant energy reduction.
+
+Finger food is food meant to be eaten directly using the hands, in contrast to food eaten with a knife and fork, spoon, chopsticks, or other utensils.[17]  In some cultures, food is almost always eaten with the hands; for example, Ethiopian cuisine is eaten by rolling various dishes up in injera bread.[18]  Foods considered street foods are frequently, though not exclusively, finger foods.
+
+In the western world, finger foods are often either appetizers (hors d'œuvres) or entree/main course items. Examples of these are miniature meat pies, sausage rolls, sausages on sticks, cheese and olives on sticks, chicken drumsticks or wings, spring rolls, miniature quiches, samosas, sandwiches, Merenda or other such based foods, such as pitas or items in buns, bhajjis, potato wedges, vol au vents, several other such small items and risotto balls (arancini). Other well-known foods that are generally eaten with the hands include hamburgers, pizza, Chips, hot dogs, fruit and bread.
+
+In East Asia, foods like pancakes or flatbreads (bing 饼) and street foods such as chuan (串, also pronounced chuan) are often eaten with the hands.
+
+Fresh food is food which has not been preserved and has not spoiled yet. For vegetables and fruits, this means that they have been recently harvested and treated properly postharvest; for meat, it has recently been slaughtered and butchered; for fish, it has been recently caught or harvested and kept cold.
+
+Dairy products are fresh and will spoil quickly. Thus, fresh cheese is cheese which has not been dried or salted for aging. Soured cream may be considered "fresh" (crème fraîche).
+
+Fresh food has not been dried, smoked, salted, frozen, canned, pickled, or otherwise preserved.[19]
+
+Freezing food preserves it from the time it is prepared to the time it is eaten. Since early times, farmers, fishermen, and trappers have preserved grains and produce in unheated buildings during the winter season.[20] Freezing food slows down decomposition by turning residual moisture into ice, inhibiting the growth of most bacterial species. In the food commodity industry, there are two processes: mechanical and cryogenic (or flash freezing). The kinetics of the freezing is important to preserve food quality and texture. Quicker freezing generates smaller ice crystals and maintains cellular structure. Cryogenic freezing is the quickest freezing technology available utilizing the extremely low temperature of liquid nitrogen  −196 °C (−320 °F).[21]
+
+Preserving food in domestic kitchens during modern times is achieved using household freezers. Accepted advice to householders was to freeze food on the day of purchase. An initiative by a supermarket group in 2012 (backed by the UK's Waste & Resources Action Programme) promotes the freezing of food "as soon as possible up to the product's 'use by' date". The Food Standards Agency was reported as supporting the change, providing the food had been stored correctly up to that time.[22]
+
+A functional food is a food given an additional function (often one related to health-promotion or disease prevention) by adding new ingredients or more of existing ingredients.[23] The term may also apply to traits purposely bred into existing edible plants, such as purple or gold potatoes having enriched anthocyanin or carotenoid contents, respectively.[24] Functional foods may be "designed to have physiological benefits and/or reduce the risk of chronic disease beyond basic nutritional functions, and may be similar in appearance to conventional food and consumed as part of a regular diet".[25]
+
+The term was first used in Japan in the 1980s where there is a government approval process for functional foods called Foods for Specified Health Use (FOSHU).[26]
+
+Health food is food marketed to provide human health effects beyond a normal healthy diet required for human nutrition. Foods marketed as health foods may be part of one or more categories, such as natural foods, organic foods, whole foods,  vegetarian foods or dietary supplements. These products may be sold in health food stores or in the health food or organic sections of grocery stores.
+
+A healthy diet is a diet that helps to maintain or improve overall health. A healthy diet provides the body with essential nutrition: fluid, macronutrients, micronutrients, and adequate calories.[27][28]
+
+For people who are healthy, a healthy diet is not complicated and contains mostly fruits, vegetables, and whole grains, and includes little to no processed food and sweetened beverages.  The requirements for a healthy diet can be met from a variety of plant-based and animal-based foods, although a non-animal source of vitamin B12 is needed for those following a vegan diet.[29]  Various nutrition guides are published by medical and governmental institutions to educate individuals on what they should be eating to be healthy. Nutrition facts labels are also mandatory in some countries to allow consumers to choose between foods based on the components relevant to health.[30]
+
+A healthy lifestyle includes getting exercise every day along with eating a healthy diet. A healthy lifestyle may lower disease risks, such as obesity, heart disease, type 2 diabetes, hypertension and cancer.[27][31]
+
+There are specialized healthy diets, called medical nutrition therapy, for people with various diseases or conditions.  There are also prescientific ideas about such specialized diets, as in dietary therapy in traditional Chinese medicine.
+
+The World Health Organization (WHO) makes the following 5 recommendations with respect to both populations and individuals:[32]
+
+Live food is living food for carnivorous or omnivorous animals kept in captivity; in other words, small animals such as insects or mice fed to larger carnivorous or omnivorous species kept either in a zoo or as a pet.
+
+Live food is commonly used as feed for a variety of species of exotic pets and zoo animals, ranging from alligators to various snakes, frogs and lizards, but also including other, non-reptile, non-amphibian carnivores and omnivores (for instance, skunks, which are omnivorous mammals, can technically be fed a limited amount of live food, though this is not a common practice). Common live food ranges from crickets (used as an inexpensive form of feed for carnivorous and omnivorous reptiles such as bearded dragons and commonly available in pet stores for this reason), waxworms, mealworms and to a lesser extent cockroaches and locusts, to small birds and mammals such as mice or chickens.
+
+Medical foods are foods that are specially formulated and intended for the dietary management of a disease that has distinctive nutritional needs that cannot be met by normal diet alone. In the United States they were defined in the Food and Drug Administration's 1988 Orphan Drug Act Amendments[35] and are subject to the general food and safety labeling requirements of the Federal Food, Drug, and Cosmetic Act. In Europe the European Food Safety Authority established definitions for "foods for special medical purposes" (FSMPs) in 2015.[36]
+
+Medical foods, called "food for special medical purposes" in Europe,[37] are distinct from the broader category of foods for special dietary use, from traditional foods that bear a health claim, and from dietary supplements. In order to be considered a medical food the product must, at a minimum:[38][39]
+
+Medical foods can be classified into the following categories:
+
+Natural foods and "all-natural foods" are widely used terms in food labeling and marketing with a variety of definitions, most of which are vague. The term is often assumed to imply foods that are not processed and whose ingredients are all natural products (in the chemist's sense of that term), thus conveying an appeal to nature. But the lack of standards in most jurisdictions means that the term assures nothing. In some countries, the term "natural" is defined and enforced. In others, such as the United States, it is not enforced.
+
+“Natural foods” are often assumed to be foods that are not processed, or do not contain any food additives, or do not contain particular additives such as hormones, antibiotics, sweeteners, food colors, or flavorings that were not originally in the food.[40]  In fact, many people (63%) when surveyed showed a preference for products labeled "natural" compared to the unmarked counterparts, based on the common belief (86% of polled consumers) that the term "natural" indicated that the food does not contain any artificial ingredients.[41] The terms are variously used and misused on labels and in advertisements.[42]
+
+The international Food and Agriculture Organization’s Codex Alimentarius does not recognize the term “natural” but does have a standard for organic foods.[43]
+
+A negative-calorie food is food that supposedly requires more food energy to be digested than the food provides. Its thermic effect or specific dynamic action – the caloric "cost" of digesting the food – would be greater than its food energy content. Despite its recurring popularity in dieting guides, there is no scientific evidence supporting the idea that any food is calorically negative. While some chilled beverages are calorically negative, the effect is minimal[44] and drinking large amounts of water can be dangerous.
+
+Organic food is food produced by methods that comply with the standards of organic farming. Standards vary worldwide, but organic farming in general features practices that strive to cycle resources, promote ecological balance, and conserve biodiversity. Organizations regulating organic products may restrict the use of certain pesticides and fertilizers in farming. In general, organic foods are also usually not processed using irradiation, industrial solvents or synthetic food additives.[45]
+
+Currently, the European Union, the United States, Canada, Mexico, Japan, and many other countries require producers to obtain special certification in order to market food as organic within their borders. In the context of these regulations, organic food is produced in a way that complies with organic standards set by regional organizations, national governments, and international organizations. Although the produce of kitchen gardens may be organic, selling food with an organic label is regulated by governmental food safety authorities, such as the US Department of Agriculture (USDA) or European Commission (EC).[46]
+
+Fertilizing and the use of pesticides in conventional farming has caused, and is causing, enormous damage worldwide to local ecosystems, biodiversity, groundwater and drinking water supplies, and sometimes farmer health and fertility. These environmental, economic and health issues are intended to be minimized or avoided in organic farming. From a consumers perspective, there is not sufficient evidence in scientific and medical literature to support claims that organic food is safer or healthier to eat than conventionally grown food. While there may be some differences in the nutrient and antinutrient contents of organically- and conventionally-produced food, the variable nature of food production and handling makes it difficult to generalize results.[47][48][49][50][51] Claims that organic food tastes better are generally not supported by tests.[48][52]
+
+Peasant foods are dishes specific to a particular culture, made from accessible and inexpensive ingredients, and usually prepared and seasoned to make them more palatable. They often form a significant part of the diets of people who live in poverty, or have a lower income compared to the average for their society or country.
+
+Peasant foods have been described as being the diet of peasants, that is, tenant or poorer farmers and their farm workers,[53] and by extension, of other cash-poor people. They may use ingredients, such as offal and less-tender cuts of meat, which are not as marketable as a cash crop. Characteristic recipes often consist of hearty one-dish meals, in which chunks of meat and various vegetables are eaten in a savory broth, with bread or other staple food. Sausages are also amenable to varied readily available ingredients, and they themselves tend to contain offal and grains.
+
+Peasant foods often involve skilled preparation by knowledgeable cooks using inventiveness and skills passed down from earlier generations. Such dishes are often prized as ethnic foods by other cultures and by descendants of the native culture who still desire these traditional dishes.[citation needed]
+
+Prison food is the term for meals served to prisoners while incarcerated in correctional institutions. While some prisons prepare their own food, many use staff from on-site catering companies. Many prisons today support the requirements of specific religions, as well as vegetarianism.[54] It is said that prison food of many developed countries is adequate to maintain health and dieting.[55][unreliable source?]
+
+"Seasonal" here refers to the times of the year when the harvest or the flavor of a given type of food is at its peak. This is usually the time when the item is harvested, with some exceptions; an example being sweet potatoes which are best eaten quite a while after harvest. It also appeals to people who prefer a low carbon diet that reduces the greenhouse gas emissions resulting from food consumption (Food miles).
+
+Shelf-stable food (sometimes ambient food) is food of a type that can be safely stored at room temperature in a sealed container. This includes foods that would normally be stored refrigerated but which have been processed so that they can be safely stored at room or ambient temperature for a usefully long shelf life.
+
+Various food preservation and packaging techniques are used to extend a food's shelf life.  Decreasing the amount of available water in a product, increasing its acidity, or irradiating[56] or otherwise sterilizing the food and then sealing it in an air-tight container are all ways of depriving bacteria of suitable conditions in which to thrive. All of these approaches can all extend a food's shelf life without unacceptably changing its taste or texture.
+
+For some foods, alternative ingredients can be used. Common oils and fats become rancid relatively quickly if not refrigerated; replacing them with hydrogenated oils delays the onset of rancidity, increasing shelf life. This is a common approach in industrial food production, but recent concerns about health hazards associated with trans fats have led to their strict control in several jurisdictions.[57] Even where trans fats are not prohibited, in many places there are new labeling laws (or rules), which require information to be printed on packages, or to be published elsewhere, about the amount of trans fat contained in certain products.
+
+Space food is a type of food product created and processed for consumption by astronauts in outer space. The food has specific requirements of providing balanced nutrition for individuals working in space while being easy and safe to store, prepare and consume in the machinery-filled weightless environments of crewed spacecraft.
+
+In recent years, space food has been used by various nations engaging in space programs as a way to share and show off their cultural identity and facilitate intercultural communication. Although astronauts consume a wide variety of foods and beverages in space, the initial idea from The Man in Space Committee of the Space Science Board in 1963 was to supply astronauts with a formula diet that would supply all the needed vitamins and nutrients.[58]
+
+Traditional foods are foods and dishes that are passed through generations[59] or which have been consumed many generations.[60] Traditional foods and dishes are traditional in nature, and may have a historic precedent in a national dish, regional cuisine[59] or local cuisine. Traditional foods and beverages may be produced as homemade, by restaurants and small manufacturers, and by large food processing plant facilities.[61]
+
+Some traditional foods have geographical indications and traditional specialities in the European Union designations per European Union schemes of geographical indications and traditional specialties: Protected designation of origin (PDO), Protected geographical indication (PGI) and Traditional specialities guaranteed (TSG). These standards serve to promote and protect names of quality agricultural products and foodstuffs.[62]
+
+This article also includes information about traditional beverages.
+
+Whole foods are plant foods that are unprocessed and unrefined, or processed and refined as little as possible, before being consumed.[63] Examples of whole foods include whole grains, tubers, legumes, fruits, vegetables.[64]
+
+There is some confusion over the usage of the term surrounding the inclusion of certain foods, in particular animal foods. The modern usage of the term whole foods diet is now widely synonymous with "whole foods plant-based diet" with animal products, oil and salt no longer constituting whole foods.[65]
+
+The earliest use of the term in the post-industrial age appears to be in 1946 in The Farmer, a quarterly magazine published and edited from his farm by F. Newman Turner, a writer and pioneering organic farmer. The magazine sponsored the establishment of the Producer-Consumer Whole Food Society Ltd, with Newman Turner as president and Derek Randal as vice-president.[66] Whole food was defined as "mature produce of field, orchard, or garden without subtraction, addition, or alteration grown from seed without chemical dressing, in fertile soil manured solely with animal and vegetable wastes, and composts therefrom, and ground, raw rock and without chemical manures, sprays, or insecticides," having intent to connect suppliers and the growing public demand for such food.[66] Such diets are rich in whole and unrefined foods, like whole grains, dark green and yellow/orange-fleshed vegetables and fruits, legumes, nuts and seeds.[63]
+
+Most food has always been obtained through agriculture. With increasing concern over both the methods and products of modern industrial agriculture, there has been a growing trend toward sustainable agricultural practices. This approach, partly fueled by consumer demand, encourages biodiversity, local self-reliance and organic farming methods.[67] Major influences on food production include international organizations (e.g. the World Trade Organization and Common Agricultural Policy), national government policy (or law), and war.[68]
+
+Several organisations have begun calling for a new kind of agriculture in which agroecosystems provide food but also support vital ecosystem services so that soil fertility and biodiversity are maintained rather than compromised. According to the International Water Management Institute and UNEP, well-managed agroecosystems not only provide food, fiber and animal products, they also provide services such as flood mitigation, groundwater recharge, erosion control and habitats for plants, birds, fish and other animals.[69]
+
+Animals, specifically humans, have five different types of tastes: sweet, sour, salty, bitter, and umami. As animals have evolved, the tastes that provide the most energy (sugar and fats) are the most pleasant to eat while others, such as bitter, are not enjoyable.[70] Water, while important for survival, has no taste.[71] Fats, on the other hand, especially saturated fats, are thicker and rich and are thus considered more enjoyable to eat.
+
+Generally regarded as the most pleasant taste, sweetness is almost always caused by a type of simple sugar such as glucose or fructose, or disaccharides such as sucrose, a molecule combining glucose and fructose.[72] Complex carbohydrates are long chains and thus do not have the sweet taste. Artificial sweeteners such as sucralose are used to mimic the sugar molecule, creating the sensation of sweet, without the calories. Other types of sugar include raw sugar, which is known for its amber color, as it is unprocessed. As sugar is vital for energy and survival, the taste of sugar is pleasant.
+
+The stevia plant contains a compound known as steviol which, when extracted, has 300 times the sweetness of sugar while having minimal impact on blood sugar.[73]
+
+Sourness is caused by the taste of acids, such as vinegar in alcoholic beverages. Sour foods include citrus, specifically lemons, limes, and to a lesser degree oranges. Sour is evolutionarily significant as it is a sign for a food that may have gone rancid due to bacteria.[74] Many foods, however, are slightly acidic, and help stimulate the taste buds and enhance flavor.
+
+Saltiness is the taste of alkali metal ions such as sodium and potassium. It is found in almost every food in low to moderate proportions to enhance flavor, although to eat pure salt is regarded as highly unpleasant. There are many different types of salt, with each having a different degree of saltiness, including sea salt, fleur de sel, kosher salt, mined salt, and grey salt. Other than enhancing flavor, its significance is that the body needs and maintains a delicate electrolyte balance, which is the kidney's function. Salt may be iodized, meaning iodine has been added to it, a necessary nutrient that promotes thyroid function. Some canned foods, notably soups or packaged broths, tend to be high in salt as a means of preserving the food longer. Historically salt has long been used as a meat preservative as salt promotes water excretion. Similarly, dried foods also promote food safety.[75]
+
+Bitterness is a sensation often considered unpleasant characterized by having a sharp, pungent taste. Unsweetened dark chocolate, caffeine, lemon rind, and some types of fruit are known to be bitter.
+
+Umami, the Japanese word for delicious, is the least known in Western popular culture but has a long tradition in Asian cuisine. Umami is the taste of glutamates, especially monosodium glutamate (MSG).[72] It is characterized as savory, meaty, and rich in flavor.[76] Salmon and mushrooms are foods high in umami.[77]
+
+Many scholars claim that the rhetorical function of food is to represent the culture of a country, and that it can be used as a form of communication. According to Goode, Curtis and Theophano, food "is the last aspect of an ethnic culture to be lost".[78]
+
+Many cultures have a recognizable cuisine, a specific set of cooking traditions using various spices or a combination of flavors unique to that culture, which evolves over time. Other differences include preferences (hot or cold, spicy, etc.) and practices, the study of which is known as gastronomy. Many cultures have diversified their foods by means of preparation, cooking methods, and manufacturing. This also includes a complex food trade which helps the cultures to economically survive by way of food, not just by consumption.
+
+Some popular types of ethnic foods include Italian, French, Japanese, Chinese, American, Cajun, Thai, African, Indian and Nepalese. Various cultures throughout the world study the dietary analysis of food habits. While evolutionarily speaking, as opposed to culturally, humans are omnivores, religion and social constructs such as morality, activism, or environmentalism will often affect which foods they will consume. Food is eaten and typically enjoyed through the sense of taste, the perception of flavor from eating and drinking. Certain tastes are more enjoyable than others, for evolutionary purposes.
+
+Aesthetically pleasing and eye-appealing food presentations can encourage people to consume foods. A common saying is that people "eat with their eyes". Food presented in a clean and appetizing way will encourage a good flavor, even if unsatisfactory.[79][80]
+
+Texture plays a crucial role in the enjoyment of eating foods. Contrasts in textures, such as something crunchy in an otherwise smooth dish, may increase the appeal of eating it. Common examples include adding granola to yogurt, adding croutons to a salad or soup, and toasting bread to enhance its crunchiness for a smooth topping, such as jam or butter.[81]
+
+Another universal phenomenon regarding food is the appeal of contrast in taste and presentation. For example, such opposite flavors as sweetness and saltiness tend to go well together, as in kettle corn and nuts.
+
+While many foods can be eaten raw, many also undergo some form of preparation for reasons of safety, palatability, texture, or flavor. At the simplest level this may involve washing, cutting, trimming, or adding other foods or ingredients, such as spices. It may also involve mixing, heating or cooling, pressure cooking, fermentation, or combination with other food. In a home, most food preparation takes place in a kitchen. Some preparation is done to enhance the taste or aesthetic appeal; other preparation may help to preserve the food; others may be involved in cultural identity. A meal is made up of food which is prepared to be eaten at a specific time and place.[82]
+
+The preparation of animal-based food usually involves slaughter, evisceration, hanging, portioning, and rendering. In developed countries, this is usually done outside the home in slaughterhouses, which are used to process animals en masse for meat production. Many countries regulate their slaughterhouses by law. For example, the United States has established the Humane Slaughter Act of 1958, which requires that an animal be stunned before killing. This act, like those in many countries, exempts slaughter in accordance with religious law, such as kosher, shechita, and dhabīḥah halal. Strict interpretations of kashrut require the animal to be fully aware when its carotid artery is cut.[83]
+
+On the local level, a butcher may commonly break down larger animal meat into smaller manageable cuts, and pre-wrap them for commercial sale or wrap them to order in butcher paper. In addition, fish and seafood may be fabricated into smaller cuts by a fishmonger. However, fish butchery may be done onboard a fishing vessel and quick-frozen for the preservation of quality.[84]
+
+The term "cooking" encompasses a vast range of methods, tools, and combinations of ingredients to improve the flavor or digestibility of food. Cooking technique, known as culinary art, generally requires the selection, measurement, and combining of ingredients in an ordered procedure in an effort to achieve the desired result. Constraints on success include the variability of ingredients, ambient conditions, tools, and the skill of the individual cook.[85] The diversity of cooking worldwide is a reflection of the myriad nutritional, aesthetic, agricultural, economic, cultural, and religious considerations that affect it.[86]
+
+Cooking requires applying heat to a food which usually, though not always, chemically changes the molecules, thus changing its flavor, texture, appearance, and nutritional properties.[87] Cooking certain proteins, such as egg whites, meats, and fish, denatures the protein, causing it to firm. There is archaeological evidence of roasted foodstuffs at Homo erectus campsites dating from 420,000 years ago.[88] Boiling as a means of cooking requires a container, and has been practiced at least since the 10th millennium BC with the introduction of pottery.[89]
+
+There are many different types of equipment used for cooking.
+
+Ovens are mostly hollow devices that get very hot (up to 500 °F (260 °C)) and are used for baking or roasting and offer a dry-heat cooking method. Different cuisines will use different types of ovens. For example, Indian culture uses a tandoor oven, which is a cylindrical clay oven which operates at a single high temperature.[90] Western kitchens use variable temperature convection ovens, conventional ovens, toaster ovens, or non-radiant heat ovens like the microwave oven. Classic Italian cuisine includes the use of a brick oven containing burning wood. Ovens may be wood-fired, coal-fired, gas, electric, or oil-fired.[91]
+
+Various types of cook-tops are used as well. They carry the same variations of fuel types as the ovens mentioned above. Cook-tops are used to heat vessels placed on top of the heat source, such as a sauté pan, sauce pot, frying pan, or pressure cooker. These pieces of equipment can use either a moist or dry cooking method and include methods such as steaming, simmering, boiling, and poaching for moist methods, while the dry methods include sautéing, pan frying, and deep-frying.[92]
+
+In addition, many cultures use grills for cooking. A grill operates with a radiant heat source from below, usually covered with a metal grid and sometimes a cover. An open-pit barbecue in the American south is one example along with the American style outdoor grill fueled by wood, liquid propane, or charcoal along with soaked wood chips for smoking.[93] A Mexican style of barbecue is called barbacoa, which involves the cooking of meats such as whole sheep over an open fire. In Argentina, an asado (Spanish for "grilled") is prepared on a grill held over an open pit or fire made upon the ground, on which a whole animal or smaller cuts are grilled.[94]
+
+Certain cultures highlight animal and vegetable foods in a raw state. Salads consisting of raw vegetables or fruits are common in many cuisines. Sashimi in Japanese cuisine consists of raw sliced fish or other meat, and sushi often incorporates raw fish or seafood. Steak tartare and salmon tartare are dishes made from diced or ground raw beef or salmon, mixed with various ingredients and served with baguettes, brioche, or frites.[95] In Italy, carpaccio is a dish of very thinly sliced raw beef, drizzled with a vinaigrette made with olive oil.[96] The health food movement known as raw foodism promotes a mostly vegan diet of raw fruits, vegetables, and grains prepared in various ways, including juicing, food dehydration, sprouting, and other methods of preparation that do not heat the food above 118 °F (47.8 °C).[97] An example of a raw meat dish is ceviche, a Latin American dish made with raw meat that is "cooked" from the highly acidic citric juice from lemons and limes along with other aromatics such as garlic.
+
+Restaurants employ chefs to prepare the food, and waiters to serve customers at the table.[98] The term restaurant comes from an old term for a restorative meat broth; this broth (or bouillon) was served in elegant outlets in Paris from the mid 18th century.[99][100] These refined "restaurants" were a marked change from the usual basic eateries such as inns and taverns,[100] and some had developed from early Parisian cafés, such as Café Procope, by first serving bouillon, then adding other cooked food to their menus.[101]
+
+Commercial eateries existed during the Roman period, with evidence of 150 "thermopolia", a form of fast food restaurant, found in Pompeii,[102] and urban sales of prepared foods may have existed in China during the Song dynasty.[103]
+
+In 2005, the population of the United States spent $496 billion on out-of-home dining. Expenditures by type of out-of-home dining were as follows: 40% in full-service restaurants, 37.2% in limited service restaurants (fast food), 6.6% in schools or colleges, 5.4% in bars and vending machines, 4.7% in hotels and motels, 4.0% in recreational places, and 2.2% in others, which includes military bases.[104][better source needed][relevant?  – discuss]
+
+Packaged foods are manufactured outside the home for purchase. This can be as simple as a butcher preparing meat, or as complex as a modern international food industry. Early food processing techniques were limited by available food preservation, packaging, and transportation. This mainly involved salting, curing, curdling, drying, pickling, fermenting, and smoking.[105] Food manufacturing arose during the industrial revolution in the 19th century.[106] This development took advantage of new mass markets and emerging technology, such as milling, preservation, packaging and labeling, and transportation. It brought the advantages of pre-prepared time-saving food to the bulk of ordinary people who did not employ domestic servants.[107]
+
+At the start of the 21st century, a two-tier structure has arisen, with a few international food processing giants controlling a wide range of well-known food brands. There also exists a wide array of small local or national food processing companies.[108] Advanced technologies have also come to change food manufacture. Computer-based control systems, sophisticated processing and packaging methods, and logistics and distribution advances can enhance product quality, improve food safety, and reduce costs.[107]
+
+The World Bank reported that the European Union was the top food importer in 2005, followed at a distance by the US and Japan. Britain's need for food was especially well-illustrated in World War II.  Despite the implementation of food rationing, Britain remained dependent on food imports and the result was a long term engagement in the Battle of the Atlantic.
+
+Food is traded and marketed on a global basis. The variety and availability of food is no longer restricted by the diversity of locally grown food or the limitations of the local growing season.[109] Between 1961 and 1999, there was a 400% increase in worldwide food exports.[110] Some countries are now economically dependent on food exports, which in some cases account for over 80% of all exports.[111]
+
+In 1994, over 100 countries became signatories to the Uruguay Round of the General Agreement on Tariffs and Trade in a dramatic increase in trade liberalization. This included an agreement to reduce subsidies paid to farmers, underpinned by the WTO enforcement of agricultural subsidy, tariffs, import quotas, and settlement of trade disputes that cannot be bilaterally resolved.[112] Where trade barriers are raised on the disputed grounds of public health and safety, the WTO refer the dispute to the Codex Alimentarius Commission, which was founded in 1962 by the United Nations Food and Agriculture Organization and the World Health Organization. Trade liberalization has greatly affected world food trade.[113]
+
+Food marketing brings together the producer and the consumer. The marketing of even a single food product can be a complicated process involving many producers and companies. For example, fifty-six companies are involved in making one can of chicken noodle soup. These businesses include not only chicken and vegetable processors but also the companies that transport the ingredients and those who print labels and manufacture cans.[114] The food marketing system is the largest direct and indirect non-government employer in the United States.
+
+In the pre-modern era, the sale of surplus food took place once a week when farmers took their wares on market day into the local village marketplace. Here food was sold to grocers for sale in their local shops for purchase by local consumers.[86][107] With the onset of industrialization and the development of the food processing industry, a wider range of food could be sold and distributed in distant locations. Typically early grocery shops would be counter-based shops, in which purchasers told the shop-keeper what they wanted, so that the shop-keeper could get it for them.[86][115]
+
+In the 20th century, supermarkets were born. Supermarkets brought with them a self service approach to shopping using shopping carts, and were able to offer quality food at lower cost through economies of scale and reduced staffing costs. In the latter part of the 20th century, this has been further revolutionized by the development of vast warehouse-sized, out-of-town supermarkets, selling a wide range of food from around the world.[116]
+
+Unlike food processors, food retailing is a two-tier market in which a small number of very large companies control a large proportion of supermarkets. The supermarket giants wield great purchasing power over farmers and processors, and strong influence over consumers. Nevertheless, less than 10% of consumer spending on food goes to farmers, with larger percentages going to advertising, transportation, and intermediate corporations.[117]
+
+It is rare for price spikes to hit all major foods in most countries at once, but food prices suffered all-time peaks in 2008 and 2011, posting a 15% and 12% deflated increase year-over-year, representing prices higher than any data collected.[119] One reason for the increase in food prices may be the increase in oil prices at the same time.[120][121]
+
+In December 2007, 37 countries faced food crises, and 20 had imposed some sort of food-price controls. In China, the price of pork jumped 58% in 2007. In the 1980s and 1990s, farm subsidies and support programs allowed major grain exporting countries to hold large surpluses, which could be tapped during food shortages to keep prices down. However, new trade policies had made agricultural production much more responsive to market demands, putting global food reserves at their lowest since 1983.[122]
+
+Rising food prices in those years have been linked with social unrest around the world, including rioting in Bangladesh and Mexico,[123] and the Arab Spring.[124]
+Food prices worldwide increased in 2008.[125][126]
+One cause of rising food prices is wealthier Asian consumers are westernizing their diets, and farmers and nations of the third world are struggling to keep up the pace. The past five years have seen rapid growth in the contribution of Asian nations to the global fluid and powdered milk manufacturing industry, which in 2008 accounted for more than 30% of production, while China alone accounts for more than 10% of both production and consumption in the global fruit and vegetable processing and preserving industry.[127]
+
+In 2013 Overseas Development Institute researchers showed that rice has more than doubled in price since 2000, rising by 120% in real terms. This was as a result of shifts in trade policy and restocking by major producers. More fundamental drivers of increased prices are the higher costs of fertilizer, diesel, and labor. Parts of Asia see rural wages rise with potential large benefits for the 1.3 billion (2008 estimate) of Asia's poor in reducing the poverty they face. However, this negatively impacts more vulnerable groups who don't share in the economic boom, especially in Asian and African coastal cities. The researchers said the threat means social-protection policies are needed to guard against price shocks. The research proposed that in the longer run, the rises present opportunities to export for Western African farmers with high potential for rice production to replace imports with domestic production.[128]
+
+Most recently, global food prices have been more stable and relatively low, after a sizable increase in late 2017, they are back under 75% of the nominal value seen during the all-time high in the 2011 food crisis.
+
+Institutions such as hedge funds, pension funds and investment banks like Barclays Capital, Goldman Sachs and Morgan Stanley[123] have been instrumental in pushing up prices in the last five years, with investment in food commodities rising from $65bn to $126bn (£41bn to £79bn) between 2007 and 2012, contributing to 30-year highs. This has caused price fluctuations which are not strongly related to the actual supply of food, according to the United Nations.[123] Financial institutions now make up 61% of all investment in wheat futures. According to Olivier De Schutter, the UN special rapporteur on food, there was a rush by institutions to enter the food market following George W. Bush's Commodities Futures Modernization Act of 2000.[123] De Schutter told the Independent in March 2012: "What we are seeing now is that these financial markets have developed massively with the arrival of these new financial investors, who are purely interested in the short-term monetary gain and are not really interested in the physical thing – they never actually buy the ton of wheat or maize; they only buy a promise to buy or to sell. The result of this financialization of the commodities market is that the prices of the products respond increasingly to a purely speculative logic. This explains why in very short periods of time we see prices spiking or bubbles exploding because prices are less and less determined by the real match between supply and demand."[123] In 2011, 450 economists from around the world called on the G20 to regulate the commodities market more.[123]
+
+Some experts have said that speculation has merely aggravated other factors, such as climate change, competition with bio-fuels and overall rising demand.[123] However, some such as Jayati Ghosh, professor of economics at Jawaharlal Nehru University in New Delhi, have pointed out that prices have increased irrespective of supply and demand issues: Ghosh points to world wheat prices, which doubled in the period from June to December 2010, despite there being no fall in global supply.[123]
+
+Food deprivation leads to malnutrition and ultimately starvation. This is often connected with famine, which involves the absence of food in entire communities. This can have a devastating and widespread effect on human health and mortality. Rationing is sometimes used to distribute food in times of shortage, most notably during times of war.[68]
+
+Starvation is a significant international problem. Approximately 815 million people are undernourished, and over 16,000 children die per day from hunger-related causes.[129] Food deprivation is regarded as a deficit need in Maslow's hierarchy of needs and is measured using famine scales.[130]
+
+Food aid can benefit people suffering from a shortage of food. It can be used to improve peoples' lives in the short term, so that a society can increase its standard of living to the point that food aid is no longer required.[131] Conversely, badly managed food aid can create problems by disrupting local markets, depressing crop prices, and discouraging food production. Sometimes a cycle of food aid dependence can develop.[132] Its provision, or threatened withdrawal, is sometimes used as a political tool to influence the policies of the destination country, a strategy known as food politics. Sometimes, food aid provisions will require certain types of food be purchased from certain sellers, and food aid can be misused to enhance the markets of donor countries.[133] International efforts to distribute food to the neediest countries are often coordinated by the World Food Programme.[134]
+
+Foodborne illness, commonly called "food poisoning", is caused by bacteria, toxins, viruses, parasites, and prions. Roughly 7 million people die of food poisoning each year, with about 10 times as many suffering from a non-fatal version.[135] The two most common factors leading to cases of bacterial foodborne illness are cross-contamination of ready-to-eat food from other uncooked foods and improper temperature control. Less commonly, acute adverse reactions can also occur if chemical contamination of food occurs, for example from improper storage, or use of non-food grade soaps and disinfectants. Food can also be adulterated by a very wide range of articles (known as "foreign bodies") during farming, manufacture, cooking, packaging, distribution, or sale. These foreign bodies can include pests or their droppings, hairs, cigarette butts, wood chips, and all manner of other contaminants. It is possible for certain types of food to become contaminated if stored or presented in an unsafe container, such as a ceramic pot with lead-based glaze.[135]
+
+Food poisoning has been recognized as a disease since as early as Hippocrates.[136] The sale of rancid, contaminated, or adulterated food was commonplace until the introduction of hygiene, refrigeration, and vermin controls in the 19th century. Discovery of techniques for killing bacteria using heat, and other microbiological studies by scientists such as Louis Pasteur, contributed to the modern sanitation standards that are ubiquitous in developed nations today. This was further underpinned by the work of Justus von Liebig, which led to the development of modern food storage and food preservation methods.[137] In more recent years, a greater understanding of the causes of food-borne illnesses has led to the development of more systematic approaches such as the Hazard Analysis and Critical Control Points (HACCP), which can identify and eliminate many risks.[138]
+
+Recommended measures for ensuring food safety include maintaining a clean preparation area with foods of different types kept separate, ensuring an adequate cooking temperature, and refrigerating foods promptly after cooking.[139]
+
+Foods that spoil easily, such as meats, dairy, and seafood, must be prepared a certain way to avoid contaminating the people for whom they are prepared. As such, the rule of thumb is that cold foods (such as dairy products) should be kept cold and hot foods (such as soup) should be kept hot until storage. Cold meats, such as chicken, that are to be cooked should not be placed at room temperature for thawing, at the risk of dangerous bacterial growth, such as Salmonella or E. coli.[140]
+
+Some people have allergies or sensitivities to foods that are not problematic to most people. This occurs when a person's immune system mistakes a certain food protein for a harmful foreign agent and attacks it. About 2% of adults and 8% of children have a food allergy.[141] The amount of the food substance required to provoke a reaction in a particularly susceptible individual can be quite small. In some instances, traces of food in the air, too minute to be perceived through smell, have been known to provoke lethal reactions in extremely sensitive individuals. Common food allergens are gluten, corn, shellfish (mollusks), peanuts, and soy.[141] Allergens frequently produce symptoms such as diarrhea, rashes, bloating, vomiting, and regurgitation. The digestive complaints usually develop within half an hour of ingesting the allergen.[141]
+
+Rarely, food allergies can lead to a medical emergency, such as anaphylactic shock, hypotension (low blood pressure), and loss of consciousness. An allergen associated with this type of reaction is peanut, although latex products can induce similar reactions.[141] Initial treatment is with epinephrine (adrenaline), often carried by known patients in the form of an Epi-pen or Twinject.[142][143]
+
+Human diet was estimated to cause perhaps around 35% of cancers in a human epidemiological analysis by Richard Doll and Richard Peto in 1981.[144]  These cancer may be caused by carcinogens that are present in food naturally or as contaminants. Food contaminated with fungal growth may contain mycotoxins such as aflatoxins which may be found in contaminated corn and peanuts.  Other carcinogens identified in food include heterocyclic amines generated in meat when cooked at high temperature, polyaromatic hydrocarbons in charred meat and smoked fish, and nitrosamines generated from nitrites used as food preservatives in cured meat such as bacon.[145]
+
+Anticarcinogens that may help prevent cancer can also be found in many food especially fruit and vegetables. Antioxidants are important groups of compounds that may help remove potentially harmful chemicals. It is however often difficult to identify the specific components in diet that serve to increase or decrease cancer risk since many food, such as beef steak and broccoli, contain low concentrations of both carcinogens and anticarcinogens.[145]
+There are many international certifications in the cooking field, such as Monde Selection, A.A. Certification, iTQi. They use high-quality evaluation methods to make the food become safer.
+
+Many cultures hold some food preferences and some food taboos. Dietary choices can also define cultures and play a role in religion. For example, only kosher foods are permitted by Judaism, halal foods by Islam, and in Hinduism beef is restricted.[149] In addition, the dietary choices of different countries or regions have different characteristics. This is highly related to a culture's cuisine.
+
+Dietary habits play a significant role in the health and mortality of all humans. Imbalances between the consumed fuels and expended energy results in either starvation or excessive reserves of adipose tissue, known as body fat.[150] Poor intake of various vitamins and minerals can lead to diseases that can have far-reaching effects on health. For instance, 30% of the world's population either has, or is at risk for developing, iodine deficiency.[151] It is estimated that at least 3 million children are blind due to vitamin A deficiency.[152] Vitamin C deficiency results in scurvy.[153] Calcium, Vitamin D, and phosphorus are inter-related; the consumption of each may affect the absorption of the others. Kwashiorkor and marasmus are childhood disorders caused by lack of dietary protein.[154]
+
+Many individuals limit what foods they eat for reasons of morality or other habits. For instance, vegetarians choose to forgo food from animal sources to varying degrees. Others choose a healthier diet, avoiding sugars or animal fats and increasing consumption of dietary fiber and antioxidants.[155] Obesity, a serious problem in the western world, leads to higher chances of developing heart disease, diabetes, cancer and many other diseases.[156] More recently, dietary habits have been influenced by the concerns that some people have about possible impacts on health or the environment from genetically modified food.[157] Further concerns about the impact of industrial farming (grains) on animal welfare, human health, and the environment are also having an effect on contemporary human dietary habits. This has led to the emergence of a movement with a preference for organic and local food.[158]
+
+Between the extremes of optimal health and death from starvation or malnutrition, there is an array of disease states that can be caused or alleviated by changes in diet. Deficiencies, excesses, and imbalances in diet can produce negative impacts on health, which may lead to various health problems such as scurvy, obesity, or osteoporosis, diabetes, cardiovascular diseases as well as psychological and behavioral problems. The science of nutrition attempts to understand how and why specific dietary aspects influence health.
+
+Nutrients in food are grouped into several categories. Macronutrients are fat, protein, and carbohydrates. Micronutrients are the minerals and vitamins. Additionally, food contains water and dietary fiber.
+
+As previously discussed, the body is designed by natural selection to enjoy sweet and fattening foods for evolutionary diets, ideal for hunters and gatherers. Thus, sweet and fattening foods in nature are typically rare and are very pleasurable to eat. In modern times, with advanced technology, enjoyable foods are easily available to consumers. Unfortunately, this promotes obesity in adults and children alike.
+
+Some countries list a legal definition of food, often referring them with the word foodstuff. These countries list food as any item that is to be processed, partially processed, or unprocessed for consumption. The listing of items included as food includes any substance intended to be, or reasonably expected to be, ingested by humans. In addition to these foodstuffs, drink, chewing gum, water, or other items processed into said food items are part of the legal definition of food. Items not included in the legal definition of food include animal feed, live animals (unless being prepared for sale in a market), plants prior to harvesting, medicinal products, cosmetics, tobacco and tobacco products, narcotic or psychotropic substances, and residues and contaminants.[159]

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+Food is any substance[1] consumed to provide nutritional support for an organism. Food is usually of plant or animal origin, and contains essential nutrients, such as carbohydrates, fats, proteins, vitamins, or minerals. The substance is ingested by an organism and assimilated by the organism's cells to provide energy, maintain life, or stimulate growth.
+
+Historically, humans secured food through two methods: hunting and gathering and agriculture, which gave modern humans a mainly omnivorous diet. Worldwide, humanity has created numerous cuisines and culinary arts, including a wide array of ingredients, herbs, spices, techniques, and dishes.
+
+Today, the majority of the food energy required by the ever-increasing population of the world is supplied by the food industry. Food safety and food security are monitored by agencies like the International Association for Food Protection, World Resources Institute, World Food Programme, Food and Agriculture Organization, and International Food Information Council. They address issues such as sustainability, biological diversity, climate change, nutritional economics, population growth, water supply, and access to food.
+
+The right to food is a human right derived from the International Covenant on Economic, Social and Cultural Rights (ICESCR), recognizing the "right to an adequate standard of living, including adequate food", as well as the "fundamental right to be free from hunger".
+
+Most food has its origin in plants. Some food is obtained directly from plants; but even animals that are used as food sources are raised by feeding them food derived from plants. Cereal grain is a staple food that provides more food energy worldwide than any other type of crop.[2] Corn (maize), wheat, and rice – in all of their varieties – account for 87% of all grain production worldwide.[3][4][5] Most of the grain that is produced worldwide is fed to livestock.
+
+Some foods not from animal or plant sources include various edible fungi, especially mushrooms. Fungi and ambient bacteria are used in the preparation of fermented and pickled foods like leavened bread, alcoholic drinks, cheese, pickles, kombucha, and yogurt. Another example is blue-green algae such as Spirulina.[6] Inorganic substances such as salt, baking soda and cream of tartar are used to preserve or chemically alter an ingredient.
+
+Many plants and plant parts are eaten as food and around 2,000 plant species are cultivated for food. Many of these plant species have several distinct cultivars.[7]
+
+Seeds of plants are a good source of food for animals, including humans, because they contain the nutrients necessary for the plant's initial growth, including many healthful fats, such as omega fats. In fact, the majority of food consumed by human beings are seed-based foods. Edible seeds include cereals (corn, wheat, rice, et cetera), legumes (beans, peas, lentils, et cetera), and nuts. Oilseeds are often pressed to produce rich oils - sunflower, flaxseed, rapeseed (including canola oil), sesame, et cetera.[8]
+
+Seeds are typically high in unsaturated fats and, in moderation, are considered a health food. However, not all seeds are edible. Large seeds, such as those from a lemon, pose a choking hazard, while seeds from cherries and apples  contain cyanide which could be poisonous only if consumed in large volumes.[9]
+
+Fruits are the ripened ovaries of plants, including the seeds within. Many plants and animals have coevolved such that the fruits of the former are an attractive food source to the latter, because animals that eat the fruits may excrete the seeds some distance away. Fruits, therefore, make up a significant part of the diets of most cultures. Some botanical fruits, such as tomatoes, pumpkins, and eggplants, are eaten as vegetables.[10] (For more information, see list of fruits.)
+
+Vegetables are a second type of plant matter that is commonly eaten as food. These include root vegetables (potatoes and carrots), bulbs (onion family), leaf vegetables (spinach and lettuce), stem vegetables (bamboo shoots and asparagus), and inflorescence vegetables (globe artichokes and broccoli and other vegetables such as cabbage or cauliflower).[11]
+
+Animals are used as food either directly or indirectly by the products they produce. Meat is an example of a direct product taken from an animal, which comes from muscle systems or from organs (offal).
+
+Food products produced by animals include milk produced by mammary glands, which in many cultures is drunk or processed into dairy products (cheese, butter, etc.). In addition, birds and other animals lay eggs, which are often eaten, and bees produce honey, a reduced nectar from flowers, which is a popular sweetener in many cultures. Some cultures consume blood, sometimes in the form of blood sausage, as a thickener for sauces, or in a cured, salted form for times of food scarcity, and others use blood in stews such as jugged hare.[12]
+
+Some cultures and people do not consume meat or animal food products for cultural, dietary, health, ethical, or ideological reasons. Vegetarians choose to forgo food from animal sources to varying degrees. Vegans do not consume any foods that are or contain ingredients from an animal source.
+
+Adulteration is a legal term meaning that a food product fails to meet the legal standards. One form of adulteration is an addition of another substance to a food item in order to increase the quantity of the food item in raw form or prepared form, which may result in the loss of actual quality of food item. These substances may be either available food items or non-food items. Among meat and meat products some of the items used to adulterate are water or ice, carcasses, or carcasses of animals other than the animal meant to be consumed.[13]
+
+Camping food includes ingredients used to prepare food suitable for backcountry camping and backpacking. The foods differ substantially from the ingredients found in a typical home kitchen. The primary differences relate to campers' and backpackers' special needs for foods that have appropriate cooking time, perishability, weight, and nutritional content.
+
+To address these needs, camping food is often made up of either freeze-dried, precooked or dehydrated ingredients. Many campers use a combination of these foods.
+
+Freeze-drying requires the use of heavy machinery and is not something that most campers are able to do on their own. Freeze-dried ingredients are often considered superior to dehydrated ingredients however because they rehydrate at camp faster and retain more flavor than their dehydrated counterparts. Freeze-dried ingredients take so little time to rehydrate that they can often be eaten without cooking them first and have a texture similar to a crunchy chip.
+
+Dehydration can reduce the weight of the food by sixty to ninety percent by removing water through evaporation. Some foods dehydrate well, such as onions, peppers, and tomatoes.[14][15] Dehydration often produces a more compact, albeit slightly heavier, end result than freeze-drying.
+
+Surplus precooked military Meals, Meals, Ready-to-Eat (MREs) are sometimes used by campers. These meals contain pre-cooked foods in retort pouches. A retort pouch is a plastic and metal foil laminate pouch that is used as an alternative to traditional industrial canning methods.
+
+Diet food (or "dietetic food") refers to any food or beverage whose recipe is altered to reduce fat, carbohydrates, abhor/adhore sugar in order to make it part of a weight loss program or diet. Such foods are usually intended to assist in weight loss or a change in body type, although bodybuilding supplements are designed to aid in gaining weight or muscle.
+
+The process of making a diet version of a food usually requires finding an acceptable low-food-energy substitute for some high-food-energy ingredient.[16] This can be as simple as replacing some or all of the food's sugar with a sugar substitute as is common with diet soft drinks such as Coca-Cola (for example Diet Coke). In some snacks, the food may be baked instead of fried thus reducing the food energy. In other cases, low-fat ingredients may be used as replacements.
+
+In whole grain foods, the higher fiber content effectively displaces some of the starch components of the flour. Since certain fibers have no food energy, this results in a modest energy reduction. Another technique relies on the intentional addition of other reduced-food-energy ingredients, such as resistant starch or dietary fiber, to replace part of the flour and achieve a more significant energy reduction.
+
+Finger food is food meant to be eaten directly using the hands, in contrast to food eaten with a knife and fork, spoon, chopsticks, or other utensils.[17]  In some cultures, food is almost always eaten with the hands; for example, Ethiopian cuisine is eaten by rolling various dishes up in injera bread.[18]  Foods considered street foods are frequently, though not exclusively, finger foods.
+
+In the western world, finger foods are often either appetizers (hors d'œuvres) or entree/main course items. Examples of these are miniature meat pies, sausage rolls, sausages on sticks, cheese and olives on sticks, chicken drumsticks or wings, spring rolls, miniature quiches, samosas, sandwiches, Merenda or other such based foods, such as pitas or items in buns, bhajjis, potato wedges, vol au vents, several other such small items and risotto balls (arancini). Other well-known foods that are generally eaten with the hands include hamburgers, pizza, Chips, hot dogs, fruit and bread.
+
+In East Asia, foods like pancakes or flatbreads (bing 饼) and street foods such as chuan (串, also pronounced chuan) are often eaten with the hands.
+
+Fresh food is food which has not been preserved and has not spoiled yet. For vegetables and fruits, this means that they have been recently harvested and treated properly postharvest; for meat, it has recently been slaughtered and butchered; for fish, it has been recently caught or harvested and kept cold.
+
+Dairy products are fresh and will spoil quickly. Thus, fresh cheese is cheese which has not been dried or salted for aging. Soured cream may be considered "fresh" (crème fraîche).
+
+Fresh food has not been dried, smoked, salted, frozen, canned, pickled, or otherwise preserved.[19]
+
+Freezing food preserves it from the time it is prepared to the time it is eaten. Since early times, farmers, fishermen, and trappers have preserved grains and produce in unheated buildings during the winter season.[20] Freezing food slows down decomposition by turning residual moisture into ice, inhibiting the growth of most bacterial species. In the food commodity industry, there are two processes: mechanical and cryogenic (or flash freezing). The kinetics of the freezing is important to preserve food quality and texture. Quicker freezing generates smaller ice crystals and maintains cellular structure. Cryogenic freezing is the quickest freezing technology available utilizing the extremely low temperature of liquid nitrogen  −196 °C (−320 °F).[21]
+
+Preserving food in domestic kitchens during modern times is achieved using household freezers. Accepted advice to householders was to freeze food on the day of purchase. An initiative by a supermarket group in 2012 (backed by the UK's Waste & Resources Action Programme) promotes the freezing of food "as soon as possible up to the product's 'use by' date". The Food Standards Agency was reported as supporting the change, providing the food had been stored correctly up to that time.[22]
+
+A functional food is a food given an additional function (often one related to health-promotion or disease prevention) by adding new ingredients or more of existing ingredients.[23] The term may also apply to traits purposely bred into existing edible plants, such as purple or gold potatoes having enriched anthocyanin or carotenoid contents, respectively.[24] Functional foods may be "designed to have physiological benefits and/or reduce the risk of chronic disease beyond basic nutritional functions, and may be similar in appearance to conventional food and consumed as part of a regular diet".[25]
+
+The term was first used in Japan in the 1980s where there is a government approval process for functional foods called Foods for Specified Health Use (FOSHU).[26]
+
+Health food is food marketed to provide human health effects beyond a normal healthy diet required for human nutrition. Foods marketed as health foods may be part of one or more categories, such as natural foods, organic foods, whole foods,  vegetarian foods or dietary supplements. These products may be sold in health food stores or in the health food or organic sections of grocery stores.
+
+A healthy diet is a diet that helps to maintain or improve overall health. A healthy diet provides the body with essential nutrition: fluid, macronutrients, micronutrients, and adequate calories.[27][28]
+
+For people who are healthy, a healthy diet is not complicated and contains mostly fruits, vegetables, and whole grains, and includes little to no processed food and sweetened beverages.  The requirements for a healthy diet can be met from a variety of plant-based and animal-based foods, although a non-animal source of vitamin B12 is needed for those following a vegan diet.[29]  Various nutrition guides are published by medical and governmental institutions to educate individuals on what they should be eating to be healthy. Nutrition facts labels are also mandatory in some countries to allow consumers to choose between foods based on the components relevant to health.[30]
+
+A healthy lifestyle includes getting exercise every day along with eating a healthy diet. A healthy lifestyle may lower disease risks, such as obesity, heart disease, type 2 diabetes, hypertension and cancer.[27][31]
+
+There are specialized healthy diets, called medical nutrition therapy, for people with various diseases or conditions.  There are also prescientific ideas about such specialized diets, as in dietary therapy in traditional Chinese medicine.
+
+The World Health Organization (WHO) makes the following 5 recommendations with respect to both populations and individuals:[32]
+
+Live food is living food for carnivorous or omnivorous animals kept in captivity; in other words, small animals such as insects or mice fed to larger carnivorous or omnivorous species kept either in a zoo or as a pet.
+
+Live food is commonly used as feed for a variety of species of exotic pets and zoo animals, ranging from alligators to various snakes, frogs and lizards, but also including other, non-reptile, non-amphibian carnivores and omnivores (for instance, skunks, which are omnivorous mammals, can technically be fed a limited amount of live food, though this is not a common practice). Common live food ranges from crickets (used as an inexpensive form of feed for carnivorous and omnivorous reptiles such as bearded dragons and commonly available in pet stores for this reason), waxworms, mealworms and to a lesser extent cockroaches and locusts, to small birds and mammals such as mice or chickens.
+
+Medical foods are foods that are specially formulated and intended for the dietary management of a disease that has distinctive nutritional needs that cannot be met by normal diet alone. In the United States they were defined in the Food and Drug Administration's 1988 Orphan Drug Act Amendments[35] and are subject to the general food and safety labeling requirements of the Federal Food, Drug, and Cosmetic Act. In Europe the European Food Safety Authority established definitions for "foods for special medical purposes" (FSMPs) in 2015.[36]
+
+Medical foods, called "food for special medical purposes" in Europe,[37] are distinct from the broader category of foods for special dietary use, from traditional foods that bear a health claim, and from dietary supplements. In order to be considered a medical food the product must, at a minimum:[38][39]
+
+Medical foods can be classified into the following categories:
+
+Natural foods and "all-natural foods" are widely used terms in food labeling and marketing with a variety of definitions, most of which are vague. The term is often assumed to imply foods that are not processed and whose ingredients are all natural products (in the chemist's sense of that term), thus conveying an appeal to nature. But the lack of standards in most jurisdictions means that the term assures nothing. In some countries, the term "natural" is defined and enforced. In others, such as the United States, it is not enforced.
+
+“Natural foods” are often assumed to be foods that are not processed, or do not contain any food additives, or do not contain particular additives such as hormones, antibiotics, sweeteners, food colors, or flavorings that were not originally in the food.[40]  In fact, many people (63%) when surveyed showed a preference for products labeled "natural" compared to the unmarked counterparts, based on the common belief (86% of polled consumers) that the term "natural" indicated that the food does not contain any artificial ingredients.[41] The terms are variously used and misused on labels and in advertisements.[42]
+
+The international Food and Agriculture Organization’s Codex Alimentarius does not recognize the term “natural” but does have a standard for organic foods.[43]
+
+A negative-calorie food is food that supposedly requires more food energy to be digested than the food provides. Its thermic effect or specific dynamic action – the caloric "cost" of digesting the food – would be greater than its food energy content. Despite its recurring popularity in dieting guides, there is no scientific evidence supporting the idea that any food is calorically negative. While some chilled beverages are calorically negative, the effect is minimal[44] and drinking large amounts of water can be dangerous.
+
+Organic food is food produced by methods that comply with the standards of organic farming. Standards vary worldwide, but organic farming in general features practices that strive to cycle resources, promote ecological balance, and conserve biodiversity. Organizations regulating organic products may restrict the use of certain pesticides and fertilizers in farming. In general, organic foods are also usually not processed using irradiation, industrial solvents or synthetic food additives.[45]
+
+Currently, the European Union, the United States, Canada, Mexico, Japan, and many other countries require producers to obtain special certification in order to market food as organic within their borders. In the context of these regulations, organic food is produced in a way that complies with organic standards set by regional organizations, national governments, and international organizations. Although the produce of kitchen gardens may be organic, selling food with an organic label is regulated by governmental food safety authorities, such as the US Department of Agriculture (USDA) or European Commission (EC).[46]
+
+Fertilizing and the use of pesticides in conventional farming has caused, and is causing, enormous damage worldwide to local ecosystems, biodiversity, groundwater and drinking water supplies, and sometimes farmer health and fertility. These environmental, economic and health issues are intended to be minimized or avoided in organic farming. From a consumers perspective, there is not sufficient evidence in scientific and medical literature to support claims that organic food is safer or healthier to eat than conventionally grown food. While there may be some differences in the nutrient and antinutrient contents of organically- and conventionally-produced food, the variable nature of food production and handling makes it difficult to generalize results.[47][48][49][50][51] Claims that organic food tastes better are generally not supported by tests.[48][52]
+
+Peasant foods are dishes specific to a particular culture, made from accessible and inexpensive ingredients, and usually prepared and seasoned to make them more palatable. They often form a significant part of the diets of people who live in poverty, or have a lower income compared to the average for their society or country.
+
+Peasant foods have been described as being the diet of peasants, that is, tenant or poorer farmers and their farm workers,[53] and by extension, of other cash-poor people. They may use ingredients, such as offal and less-tender cuts of meat, which are not as marketable as a cash crop. Characteristic recipes often consist of hearty one-dish meals, in which chunks of meat and various vegetables are eaten in a savory broth, with bread or other staple food. Sausages are also amenable to varied readily available ingredients, and they themselves tend to contain offal and grains.
+
+Peasant foods often involve skilled preparation by knowledgeable cooks using inventiveness and skills passed down from earlier generations. Such dishes are often prized as ethnic foods by other cultures and by descendants of the native culture who still desire these traditional dishes.[citation needed]
+
+Prison food is the term for meals served to prisoners while incarcerated in correctional institutions. While some prisons prepare their own food, many use staff from on-site catering companies. Many prisons today support the requirements of specific religions, as well as vegetarianism.[54] It is said that prison food of many developed countries is adequate to maintain health and dieting.[55][unreliable source?]
+
+"Seasonal" here refers to the times of the year when the harvest or the flavor of a given type of food is at its peak. This is usually the time when the item is harvested, with some exceptions; an example being sweet potatoes which are best eaten quite a while after harvest. It also appeals to people who prefer a low carbon diet that reduces the greenhouse gas emissions resulting from food consumption (Food miles).
+
+Shelf-stable food (sometimes ambient food) is food of a type that can be safely stored at room temperature in a sealed container. This includes foods that would normally be stored refrigerated but which have been processed so that they can be safely stored at room or ambient temperature for a usefully long shelf life.
+
+Various food preservation and packaging techniques are used to extend a food's shelf life.  Decreasing the amount of available water in a product, increasing its acidity, or irradiating[56] or otherwise sterilizing the food and then sealing it in an air-tight container are all ways of depriving bacteria of suitable conditions in which to thrive. All of these approaches can all extend a food's shelf life without unacceptably changing its taste or texture.
+
+For some foods, alternative ingredients can be used. Common oils and fats become rancid relatively quickly if not refrigerated; replacing them with hydrogenated oils delays the onset of rancidity, increasing shelf life. This is a common approach in industrial food production, but recent concerns about health hazards associated with trans fats have led to their strict control in several jurisdictions.[57] Even where trans fats are not prohibited, in many places there are new labeling laws (or rules), which require information to be printed on packages, or to be published elsewhere, about the amount of trans fat contained in certain products.
+
+Space food is a type of food product created and processed for consumption by astronauts in outer space. The food has specific requirements of providing balanced nutrition for individuals working in space while being easy and safe to store, prepare and consume in the machinery-filled weightless environments of crewed spacecraft.
+
+In recent years, space food has been used by various nations engaging in space programs as a way to share and show off their cultural identity and facilitate intercultural communication. Although astronauts consume a wide variety of foods and beverages in space, the initial idea from The Man in Space Committee of the Space Science Board in 1963 was to supply astronauts with a formula diet that would supply all the needed vitamins and nutrients.[58]
+
+Traditional foods are foods and dishes that are passed through generations[59] or which have been consumed many generations.[60] Traditional foods and dishes are traditional in nature, and may have a historic precedent in a national dish, regional cuisine[59] or local cuisine. Traditional foods and beverages may be produced as homemade, by restaurants and small manufacturers, and by large food processing plant facilities.[61]
+
+Some traditional foods have geographical indications and traditional specialities in the European Union designations per European Union schemes of geographical indications and traditional specialties: Protected designation of origin (PDO), Protected geographical indication (PGI) and Traditional specialities guaranteed (TSG). These standards serve to promote and protect names of quality agricultural products and foodstuffs.[62]
+
+This article also includes information about traditional beverages.
+
+Whole foods are plant foods that are unprocessed and unrefined, or processed and refined as little as possible, before being consumed.[63] Examples of whole foods include whole grains, tubers, legumes, fruits, vegetables.[64]
+
+There is some confusion over the usage of the term surrounding the inclusion of certain foods, in particular animal foods. The modern usage of the term whole foods diet is now widely synonymous with "whole foods plant-based diet" with animal products, oil and salt no longer constituting whole foods.[65]
+
+The earliest use of the term in the post-industrial age appears to be in 1946 in The Farmer, a quarterly magazine published and edited from his farm by F. Newman Turner, a writer and pioneering organic farmer. The magazine sponsored the establishment of the Producer-Consumer Whole Food Society Ltd, with Newman Turner as president and Derek Randal as vice-president.[66] Whole food was defined as "mature produce of field, orchard, or garden without subtraction, addition, or alteration grown from seed without chemical dressing, in fertile soil manured solely with animal and vegetable wastes, and composts therefrom, and ground, raw rock and without chemical manures, sprays, or insecticides," having intent to connect suppliers and the growing public demand for such food.[66] Such diets are rich in whole and unrefined foods, like whole grains, dark green and yellow/orange-fleshed vegetables and fruits, legumes, nuts and seeds.[63]
+
+Most food has always been obtained through agriculture. With increasing concern over both the methods and products of modern industrial agriculture, there has been a growing trend toward sustainable agricultural practices. This approach, partly fueled by consumer demand, encourages biodiversity, local self-reliance and organic farming methods.[67] Major influences on food production include international organizations (e.g. the World Trade Organization and Common Agricultural Policy), national government policy (or law), and war.[68]
+
+Several organisations have begun calling for a new kind of agriculture in which agroecosystems provide food but also support vital ecosystem services so that soil fertility and biodiversity are maintained rather than compromised. According to the International Water Management Institute and UNEP, well-managed agroecosystems not only provide food, fiber and animal products, they also provide services such as flood mitigation, groundwater recharge, erosion control and habitats for plants, birds, fish and other animals.[69]
+
+Animals, specifically humans, have five different types of tastes: sweet, sour, salty, bitter, and umami. As animals have evolved, the tastes that provide the most energy (sugar and fats) are the most pleasant to eat while others, such as bitter, are not enjoyable.[70] Water, while important for survival, has no taste.[71] Fats, on the other hand, especially saturated fats, are thicker and rich and are thus considered more enjoyable to eat.
+
+Generally regarded as the most pleasant taste, sweetness is almost always caused by a type of simple sugar such as glucose or fructose, or disaccharides such as sucrose, a molecule combining glucose and fructose.[72] Complex carbohydrates are long chains and thus do not have the sweet taste. Artificial sweeteners such as sucralose are used to mimic the sugar molecule, creating the sensation of sweet, without the calories. Other types of sugar include raw sugar, which is known for its amber color, as it is unprocessed. As sugar is vital for energy and survival, the taste of sugar is pleasant.
+
+The stevia plant contains a compound known as steviol which, when extracted, has 300 times the sweetness of sugar while having minimal impact on blood sugar.[73]
+
+Sourness is caused by the taste of acids, such as vinegar in alcoholic beverages. Sour foods include citrus, specifically lemons, limes, and to a lesser degree oranges. Sour is evolutionarily significant as it is a sign for a food that may have gone rancid due to bacteria.[74] Many foods, however, are slightly acidic, and help stimulate the taste buds and enhance flavor.
+
+Saltiness is the taste of alkali metal ions such as sodium and potassium. It is found in almost every food in low to moderate proportions to enhance flavor, although to eat pure salt is regarded as highly unpleasant. There are many different types of salt, with each having a different degree of saltiness, including sea salt, fleur de sel, kosher salt, mined salt, and grey salt. Other than enhancing flavor, its significance is that the body needs and maintains a delicate electrolyte balance, which is the kidney's function. Salt may be iodized, meaning iodine has been added to it, a necessary nutrient that promotes thyroid function. Some canned foods, notably soups or packaged broths, tend to be high in salt as a means of preserving the food longer. Historically salt has long been used as a meat preservative as salt promotes water excretion. Similarly, dried foods also promote food safety.[75]
+
+Bitterness is a sensation often considered unpleasant characterized by having a sharp, pungent taste. Unsweetened dark chocolate, caffeine, lemon rind, and some types of fruit are known to be bitter.
+
+Umami, the Japanese word for delicious, is the least known in Western popular culture but has a long tradition in Asian cuisine. Umami is the taste of glutamates, especially monosodium glutamate (MSG).[72] It is characterized as savory, meaty, and rich in flavor.[76] Salmon and mushrooms are foods high in umami.[77]
+
+Many scholars claim that the rhetorical function of food is to represent the culture of a country, and that it can be used as a form of communication. According to Goode, Curtis and Theophano, food "is the last aspect of an ethnic culture to be lost".[78]
+
+Many cultures have a recognizable cuisine, a specific set of cooking traditions using various spices or a combination of flavors unique to that culture, which evolves over time. Other differences include preferences (hot or cold, spicy, etc.) and practices, the study of which is known as gastronomy. Many cultures have diversified their foods by means of preparation, cooking methods, and manufacturing. This also includes a complex food trade which helps the cultures to economically survive by way of food, not just by consumption.
+
+Some popular types of ethnic foods include Italian, French, Japanese, Chinese, American, Cajun, Thai, African, Indian and Nepalese. Various cultures throughout the world study the dietary analysis of food habits. While evolutionarily speaking, as opposed to culturally, humans are omnivores, religion and social constructs such as morality, activism, or environmentalism will often affect which foods they will consume. Food is eaten and typically enjoyed through the sense of taste, the perception of flavor from eating and drinking. Certain tastes are more enjoyable than others, for evolutionary purposes.
+
+Aesthetically pleasing and eye-appealing food presentations can encourage people to consume foods. A common saying is that people "eat with their eyes". Food presented in a clean and appetizing way will encourage a good flavor, even if unsatisfactory.[79][80]
+
+Texture plays a crucial role in the enjoyment of eating foods. Contrasts in textures, such as something crunchy in an otherwise smooth dish, may increase the appeal of eating it. Common examples include adding granola to yogurt, adding croutons to a salad or soup, and toasting bread to enhance its crunchiness for a smooth topping, such as jam or butter.[81]
+
+Another universal phenomenon regarding food is the appeal of contrast in taste and presentation. For example, such opposite flavors as sweetness and saltiness tend to go well together, as in kettle corn and nuts.
+
+While many foods can be eaten raw, many also undergo some form of preparation for reasons of safety, palatability, texture, or flavor. At the simplest level this may involve washing, cutting, trimming, or adding other foods or ingredients, such as spices. It may also involve mixing, heating or cooling, pressure cooking, fermentation, or combination with other food. In a home, most food preparation takes place in a kitchen. Some preparation is done to enhance the taste or aesthetic appeal; other preparation may help to preserve the food; others may be involved in cultural identity. A meal is made up of food which is prepared to be eaten at a specific time and place.[82]
+
+The preparation of animal-based food usually involves slaughter, evisceration, hanging, portioning, and rendering. In developed countries, this is usually done outside the home in slaughterhouses, which are used to process animals en masse for meat production. Many countries regulate their slaughterhouses by law. For example, the United States has established the Humane Slaughter Act of 1958, which requires that an animal be stunned before killing. This act, like those in many countries, exempts slaughter in accordance with religious law, such as kosher, shechita, and dhabīḥah halal. Strict interpretations of kashrut require the animal to be fully aware when its carotid artery is cut.[83]
+
+On the local level, a butcher may commonly break down larger animal meat into smaller manageable cuts, and pre-wrap them for commercial sale or wrap them to order in butcher paper. In addition, fish and seafood may be fabricated into smaller cuts by a fishmonger. However, fish butchery may be done onboard a fishing vessel and quick-frozen for the preservation of quality.[84]
+
+The term "cooking" encompasses a vast range of methods, tools, and combinations of ingredients to improve the flavor or digestibility of food. Cooking technique, known as culinary art, generally requires the selection, measurement, and combining of ingredients in an ordered procedure in an effort to achieve the desired result. Constraints on success include the variability of ingredients, ambient conditions, tools, and the skill of the individual cook.[85] The diversity of cooking worldwide is a reflection of the myriad nutritional, aesthetic, agricultural, economic, cultural, and religious considerations that affect it.[86]
+
+Cooking requires applying heat to a food which usually, though not always, chemically changes the molecules, thus changing its flavor, texture, appearance, and nutritional properties.[87] Cooking certain proteins, such as egg whites, meats, and fish, denatures the protein, causing it to firm. There is archaeological evidence of roasted foodstuffs at Homo erectus campsites dating from 420,000 years ago.[88] Boiling as a means of cooking requires a container, and has been practiced at least since the 10th millennium BC with the introduction of pottery.[89]
+
+There are many different types of equipment used for cooking.
+
+Ovens are mostly hollow devices that get very hot (up to 500 °F (260 °C)) and are used for baking or roasting and offer a dry-heat cooking method. Different cuisines will use different types of ovens. For example, Indian culture uses a tandoor oven, which is a cylindrical clay oven which operates at a single high temperature.[90] Western kitchens use variable temperature convection ovens, conventional ovens, toaster ovens, or non-radiant heat ovens like the microwave oven. Classic Italian cuisine includes the use of a brick oven containing burning wood. Ovens may be wood-fired, coal-fired, gas, electric, or oil-fired.[91]
+
+Various types of cook-tops are used as well. They carry the same variations of fuel types as the ovens mentioned above. Cook-tops are used to heat vessels placed on top of the heat source, such as a sauté pan, sauce pot, frying pan, or pressure cooker. These pieces of equipment can use either a moist or dry cooking method and include methods such as steaming, simmering, boiling, and poaching for moist methods, while the dry methods include sautéing, pan frying, and deep-frying.[92]
+
+In addition, many cultures use grills for cooking. A grill operates with a radiant heat source from below, usually covered with a metal grid and sometimes a cover. An open-pit barbecue in the American south is one example along with the American style outdoor grill fueled by wood, liquid propane, or charcoal along with soaked wood chips for smoking.[93] A Mexican style of barbecue is called barbacoa, which involves the cooking of meats such as whole sheep over an open fire. In Argentina, an asado (Spanish for "grilled") is prepared on a grill held over an open pit or fire made upon the ground, on which a whole animal or smaller cuts are grilled.[94]
+
+Certain cultures highlight animal and vegetable foods in a raw state. Salads consisting of raw vegetables or fruits are common in many cuisines. Sashimi in Japanese cuisine consists of raw sliced fish or other meat, and sushi often incorporates raw fish or seafood. Steak tartare and salmon tartare are dishes made from diced or ground raw beef or salmon, mixed with various ingredients and served with baguettes, brioche, or frites.[95] In Italy, carpaccio is a dish of very thinly sliced raw beef, drizzled with a vinaigrette made with olive oil.[96] The health food movement known as raw foodism promotes a mostly vegan diet of raw fruits, vegetables, and grains prepared in various ways, including juicing, food dehydration, sprouting, and other methods of preparation that do not heat the food above 118 °F (47.8 °C).[97] An example of a raw meat dish is ceviche, a Latin American dish made with raw meat that is "cooked" from the highly acidic citric juice from lemons and limes along with other aromatics such as garlic.
+
+Restaurants employ chefs to prepare the food, and waiters to serve customers at the table.[98] The term restaurant comes from an old term for a restorative meat broth; this broth (or bouillon) was served in elegant outlets in Paris from the mid 18th century.[99][100] These refined "restaurants" were a marked change from the usual basic eateries such as inns and taverns,[100] and some had developed from early Parisian cafés, such as Café Procope, by first serving bouillon, then adding other cooked food to their menus.[101]
+
+Commercial eateries existed during the Roman period, with evidence of 150 "thermopolia", a form of fast food restaurant, found in Pompeii,[102] and urban sales of prepared foods may have existed in China during the Song dynasty.[103]
+
+In 2005, the population of the United States spent $496 billion on out-of-home dining. Expenditures by type of out-of-home dining were as follows: 40% in full-service restaurants, 37.2% in limited service restaurants (fast food), 6.6% in schools or colleges, 5.4% in bars and vending machines, 4.7% in hotels and motels, 4.0% in recreational places, and 2.2% in others, which includes military bases.[104][better source needed][relevant?  – discuss]
+
+Packaged foods are manufactured outside the home for purchase. This can be as simple as a butcher preparing meat, or as complex as a modern international food industry. Early food processing techniques were limited by available food preservation, packaging, and transportation. This mainly involved salting, curing, curdling, drying, pickling, fermenting, and smoking.[105] Food manufacturing arose during the industrial revolution in the 19th century.[106] This development took advantage of new mass markets and emerging technology, such as milling, preservation, packaging and labeling, and transportation. It brought the advantages of pre-prepared time-saving food to the bulk of ordinary people who did not employ domestic servants.[107]
+
+At the start of the 21st century, a two-tier structure has arisen, with a few international food processing giants controlling a wide range of well-known food brands. There also exists a wide array of small local or national food processing companies.[108] Advanced technologies have also come to change food manufacture. Computer-based control systems, sophisticated processing and packaging methods, and logistics and distribution advances can enhance product quality, improve food safety, and reduce costs.[107]
+
+The World Bank reported that the European Union was the top food importer in 2005, followed at a distance by the US and Japan. Britain's need for food was especially well-illustrated in World War II.  Despite the implementation of food rationing, Britain remained dependent on food imports and the result was a long term engagement in the Battle of the Atlantic.
+
+Food is traded and marketed on a global basis. The variety and availability of food is no longer restricted by the diversity of locally grown food or the limitations of the local growing season.[109] Between 1961 and 1999, there was a 400% increase in worldwide food exports.[110] Some countries are now economically dependent on food exports, which in some cases account for over 80% of all exports.[111]
+
+In 1994, over 100 countries became signatories to the Uruguay Round of the General Agreement on Tariffs and Trade in a dramatic increase in trade liberalization. This included an agreement to reduce subsidies paid to farmers, underpinned by the WTO enforcement of agricultural subsidy, tariffs, import quotas, and settlement of trade disputes that cannot be bilaterally resolved.[112] Where trade barriers are raised on the disputed grounds of public health and safety, the WTO refer the dispute to the Codex Alimentarius Commission, which was founded in 1962 by the United Nations Food and Agriculture Organization and the World Health Organization. Trade liberalization has greatly affected world food trade.[113]
+
+Food marketing brings together the producer and the consumer. The marketing of even a single food product can be a complicated process involving many producers and companies. For example, fifty-six companies are involved in making one can of chicken noodle soup. These businesses include not only chicken and vegetable processors but also the companies that transport the ingredients and those who print labels and manufacture cans.[114] The food marketing system is the largest direct and indirect non-government employer in the United States.
+
+In the pre-modern era, the sale of surplus food took place once a week when farmers took their wares on market day into the local village marketplace. Here food was sold to grocers for sale in their local shops for purchase by local consumers.[86][107] With the onset of industrialization and the development of the food processing industry, a wider range of food could be sold and distributed in distant locations. Typically early grocery shops would be counter-based shops, in which purchasers told the shop-keeper what they wanted, so that the shop-keeper could get it for them.[86][115]
+
+In the 20th century, supermarkets were born. Supermarkets brought with them a self service approach to shopping using shopping carts, and were able to offer quality food at lower cost through economies of scale and reduced staffing costs. In the latter part of the 20th century, this has been further revolutionized by the development of vast warehouse-sized, out-of-town supermarkets, selling a wide range of food from around the world.[116]
+
+Unlike food processors, food retailing is a two-tier market in which a small number of very large companies control a large proportion of supermarkets. The supermarket giants wield great purchasing power over farmers and processors, and strong influence over consumers. Nevertheless, less than 10% of consumer spending on food goes to farmers, with larger percentages going to advertising, transportation, and intermediate corporations.[117]
+
+It is rare for price spikes to hit all major foods in most countries at once, but food prices suffered all-time peaks in 2008 and 2011, posting a 15% and 12% deflated increase year-over-year, representing prices higher than any data collected.[119] One reason for the increase in food prices may be the increase in oil prices at the same time.[120][121]
+
+In December 2007, 37 countries faced food crises, and 20 had imposed some sort of food-price controls. In China, the price of pork jumped 58% in 2007. In the 1980s and 1990s, farm subsidies and support programs allowed major grain exporting countries to hold large surpluses, which could be tapped during food shortages to keep prices down. However, new trade policies had made agricultural production much more responsive to market demands, putting global food reserves at their lowest since 1983.[122]
+
+Rising food prices in those years have been linked with social unrest around the world, including rioting in Bangladesh and Mexico,[123] and the Arab Spring.[124]
+Food prices worldwide increased in 2008.[125][126]
+One cause of rising food prices is wealthier Asian consumers are westernizing their diets, and farmers and nations of the third world are struggling to keep up the pace. The past five years have seen rapid growth in the contribution of Asian nations to the global fluid and powdered milk manufacturing industry, which in 2008 accounted for more than 30% of production, while China alone accounts for more than 10% of both production and consumption in the global fruit and vegetable processing and preserving industry.[127]
+
+In 2013 Overseas Development Institute researchers showed that rice has more than doubled in price since 2000, rising by 120% in real terms. This was as a result of shifts in trade policy and restocking by major producers. More fundamental drivers of increased prices are the higher costs of fertilizer, diesel, and labor. Parts of Asia see rural wages rise with potential large benefits for the 1.3 billion (2008 estimate) of Asia's poor in reducing the poverty they face. However, this negatively impacts more vulnerable groups who don't share in the economic boom, especially in Asian and African coastal cities. The researchers said the threat means social-protection policies are needed to guard against price shocks. The research proposed that in the longer run, the rises present opportunities to export for Western African farmers with high potential for rice production to replace imports with domestic production.[128]
+
+Most recently, global food prices have been more stable and relatively low, after a sizable increase in late 2017, they are back under 75% of the nominal value seen during the all-time high in the 2011 food crisis.
+
+Institutions such as hedge funds, pension funds and investment banks like Barclays Capital, Goldman Sachs and Morgan Stanley[123] have been instrumental in pushing up prices in the last five years, with investment in food commodities rising from $65bn to $126bn (£41bn to £79bn) between 2007 and 2012, contributing to 30-year highs. This has caused price fluctuations which are not strongly related to the actual supply of food, according to the United Nations.[123] Financial institutions now make up 61% of all investment in wheat futures. According to Olivier De Schutter, the UN special rapporteur on food, there was a rush by institutions to enter the food market following George W. Bush's Commodities Futures Modernization Act of 2000.[123] De Schutter told the Independent in March 2012: "What we are seeing now is that these financial markets have developed massively with the arrival of these new financial investors, who are purely interested in the short-term monetary gain and are not really interested in the physical thing – they never actually buy the ton of wheat or maize; they only buy a promise to buy or to sell. The result of this financialization of the commodities market is that the prices of the products respond increasingly to a purely speculative logic. This explains why in very short periods of time we see prices spiking or bubbles exploding because prices are less and less determined by the real match between supply and demand."[123] In 2011, 450 economists from around the world called on the G20 to regulate the commodities market more.[123]
+
+Some experts have said that speculation has merely aggravated other factors, such as climate change, competition with bio-fuels and overall rising demand.[123] However, some such as Jayati Ghosh, professor of economics at Jawaharlal Nehru University in New Delhi, have pointed out that prices have increased irrespective of supply and demand issues: Ghosh points to world wheat prices, which doubled in the period from June to December 2010, despite there being no fall in global supply.[123]
+
+Food deprivation leads to malnutrition and ultimately starvation. This is often connected with famine, which involves the absence of food in entire communities. This can have a devastating and widespread effect on human health and mortality. Rationing is sometimes used to distribute food in times of shortage, most notably during times of war.[68]
+
+Starvation is a significant international problem. Approximately 815 million people are undernourished, and over 16,000 children die per day from hunger-related causes.[129] Food deprivation is regarded as a deficit need in Maslow's hierarchy of needs and is measured using famine scales.[130]
+
+Food aid can benefit people suffering from a shortage of food. It can be used to improve peoples' lives in the short term, so that a society can increase its standard of living to the point that food aid is no longer required.[131] Conversely, badly managed food aid can create problems by disrupting local markets, depressing crop prices, and discouraging food production. Sometimes a cycle of food aid dependence can develop.[132] Its provision, or threatened withdrawal, is sometimes used as a political tool to influence the policies of the destination country, a strategy known as food politics. Sometimes, food aid provisions will require certain types of food be purchased from certain sellers, and food aid can be misused to enhance the markets of donor countries.[133] International efforts to distribute food to the neediest countries are often coordinated by the World Food Programme.[134]
+
+Foodborne illness, commonly called "food poisoning", is caused by bacteria, toxins, viruses, parasites, and prions. Roughly 7 million people die of food poisoning each year, with about 10 times as many suffering from a non-fatal version.[135] The two most common factors leading to cases of bacterial foodborne illness are cross-contamination of ready-to-eat food from other uncooked foods and improper temperature control. Less commonly, acute adverse reactions can also occur if chemical contamination of food occurs, for example from improper storage, or use of non-food grade soaps and disinfectants. Food can also be adulterated by a very wide range of articles (known as "foreign bodies") during farming, manufacture, cooking, packaging, distribution, or sale. These foreign bodies can include pests or their droppings, hairs, cigarette butts, wood chips, and all manner of other contaminants. It is possible for certain types of food to become contaminated if stored or presented in an unsafe container, such as a ceramic pot with lead-based glaze.[135]
+
+Food poisoning has been recognized as a disease since as early as Hippocrates.[136] The sale of rancid, contaminated, or adulterated food was commonplace until the introduction of hygiene, refrigeration, and vermin controls in the 19th century. Discovery of techniques for killing bacteria using heat, and other microbiological studies by scientists such as Louis Pasteur, contributed to the modern sanitation standards that are ubiquitous in developed nations today. This was further underpinned by the work of Justus von Liebig, which led to the development of modern food storage and food preservation methods.[137] In more recent years, a greater understanding of the causes of food-borne illnesses has led to the development of more systematic approaches such as the Hazard Analysis and Critical Control Points (HACCP), which can identify and eliminate many risks.[138]
+
+Recommended measures for ensuring food safety include maintaining a clean preparation area with foods of different types kept separate, ensuring an adequate cooking temperature, and refrigerating foods promptly after cooking.[139]
+
+Foods that spoil easily, such as meats, dairy, and seafood, must be prepared a certain way to avoid contaminating the people for whom they are prepared. As such, the rule of thumb is that cold foods (such as dairy products) should be kept cold and hot foods (such as soup) should be kept hot until storage. Cold meats, such as chicken, that are to be cooked should not be placed at room temperature for thawing, at the risk of dangerous bacterial growth, such as Salmonella or E. coli.[140]
+
+Some people have allergies or sensitivities to foods that are not problematic to most people. This occurs when a person's immune system mistakes a certain food protein for a harmful foreign agent and attacks it. About 2% of adults and 8% of children have a food allergy.[141] The amount of the food substance required to provoke a reaction in a particularly susceptible individual can be quite small. In some instances, traces of food in the air, too minute to be perceived through smell, have been known to provoke lethal reactions in extremely sensitive individuals. Common food allergens are gluten, corn, shellfish (mollusks), peanuts, and soy.[141] Allergens frequently produce symptoms such as diarrhea, rashes, bloating, vomiting, and regurgitation. The digestive complaints usually develop within half an hour of ingesting the allergen.[141]
+
+Rarely, food allergies can lead to a medical emergency, such as anaphylactic shock, hypotension (low blood pressure), and loss of consciousness. An allergen associated with this type of reaction is peanut, although latex products can induce similar reactions.[141] Initial treatment is with epinephrine (adrenaline), often carried by known patients in the form of an Epi-pen or Twinject.[142][143]
+
+Human diet was estimated to cause perhaps around 35% of cancers in a human epidemiological analysis by Richard Doll and Richard Peto in 1981.[144]  These cancer may be caused by carcinogens that are present in food naturally or as contaminants. Food contaminated with fungal growth may contain mycotoxins such as aflatoxins which may be found in contaminated corn and peanuts.  Other carcinogens identified in food include heterocyclic amines generated in meat when cooked at high temperature, polyaromatic hydrocarbons in charred meat and smoked fish, and nitrosamines generated from nitrites used as food preservatives in cured meat such as bacon.[145]
+
+Anticarcinogens that may help prevent cancer can also be found in many food especially fruit and vegetables. Antioxidants are important groups of compounds that may help remove potentially harmful chemicals. It is however often difficult to identify the specific components in diet that serve to increase or decrease cancer risk since many food, such as beef steak and broccoli, contain low concentrations of both carcinogens and anticarcinogens.[145]
+There are many international certifications in the cooking field, such as Monde Selection, A.A. Certification, iTQi. They use high-quality evaluation methods to make the food become safer.
+
+Many cultures hold some food preferences and some food taboos. Dietary choices can also define cultures and play a role in religion. For example, only kosher foods are permitted by Judaism, halal foods by Islam, and in Hinduism beef is restricted.[149] In addition, the dietary choices of different countries or regions have different characteristics. This is highly related to a culture's cuisine.
+
+Dietary habits play a significant role in the health and mortality of all humans. Imbalances between the consumed fuels and expended energy results in either starvation or excessive reserves of adipose tissue, known as body fat.[150] Poor intake of various vitamins and minerals can lead to diseases that can have far-reaching effects on health. For instance, 30% of the world's population either has, or is at risk for developing, iodine deficiency.[151] It is estimated that at least 3 million children are blind due to vitamin A deficiency.[152] Vitamin C deficiency results in scurvy.[153] Calcium, Vitamin D, and phosphorus are inter-related; the consumption of each may affect the absorption of the others. Kwashiorkor and marasmus are childhood disorders caused by lack of dietary protein.[154]
+
+Many individuals limit what foods they eat for reasons of morality or other habits. For instance, vegetarians choose to forgo food from animal sources to varying degrees. Others choose a healthier diet, avoiding sugars or animal fats and increasing consumption of dietary fiber and antioxidants.[155] Obesity, a serious problem in the western world, leads to higher chances of developing heart disease, diabetes, cancer and many other diseases.[156] More recently, dietary habits have been influenced by the concerns that some people have about possible impacts on health or the environment from genetically modified food.[157] Further concerns about the impact of industrial farming (grains) on animal welfare, human health, and the environment are also having an effect on contemporary human dietary habits. This has led to the emergence of a movement with a preference for organic and local food.[158]
+
+Between the extremes of optimal health and death from starvation or malnutrition, there is an array of disease states that can be caused or alleviated by changes in diet. Deficiencies, excesses, and imbalances in diet can produce negative impacts on health, which may lead to various health problems such as scurvy, obesity, or osteoporosis, diabetes, cardiovascular diseases as well as psychological and behavioral problems. The science of nutrition attempts to understand how and why specific dietary aspects influence health.
+
+Nutrients in food are grouped into several categories. Macronutrients are fat, protein, and carbohydrates. Micronutrients are the minerals and vitamins. Additionally, food contains water and dietary fiber.
+
+As previously discussed, the body is designed by natural selection to enjoy sweet and fattening foods for evolutionary diets, ideal for hunters and gatherers. Thus, sweet and fattening foods in nature are typically rare and are very pleasurable to eat. In modern times, with advanced technology, enjoyable foods are easily available to consumers. Unfortunately, this promotes obesity in adults and children alike.
+
+Some countries list a legal definition of food, often referring them with the word foodstuff. These countries list food as any item that is to be processed, partially processed, or unprocessed for consumption. The listing of items included as food includes any substance intended to be, or reasonably expected to be, ingested by humans. In addition to these foodstuffs, drink, chewing gum, water, or other items processed into said food items are part of the legal definition of food. Items not included in the legal definition of food include animal feed, live animals (unless being prepared for sale in a market), plants prior to harvesting, medicinal products, cosmetics, tobacco and tobacco products, narcotic or psychotropic substances, and residues and contaminants.[159]

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+Coordinates: 34°N 106°W / 34°N 106°W / 34; -106
+
+New Mexico (Spanish: Nuevo México; Spanish pronunciation: [ˈnweβo ˈmexiko] (listen), Navajo: Yootó Hahoodzo; Navajo pronunciation: [jòːtxó xɑ̀xòːtsò]) is a state in the Southwestern region of the United States of America; its capital is Santa Fe, which was founded in 1610 as capital of Nuevo México (itself established as a province of New Spain in 1598), while its largest city is Albuquerque with its accompanying metropolitan area. It is one of the Mountain States and shares the Four Corners region with Utah, Colorado, and Arizona. New Mexico is also bordered by the state of Texas to the east-southeast, Oklahoma to the northeast, and the Mexican states of Chihuahua to the south and Sonora to the southwest. With an estimated population of 2,096,829 as of the July 1, 2019, U.S. Census Bureau estimate, New Mexico is the 36th largest state by population. With a total area of 121,590 sq mi (314,900 km2), it is the fifth-largest and sixth-least densely populated of the 50 states. Due to their geographic locations, northern and eastern New Mexico exhibit a colder, alpine climate, while western and southern New Mexico exhibit a warmer, arid climate.
+
+The economy of New Mexico is dependent on oil drilling, mineral extraction, dryland farming, cattle ranching, lumber milling, and retail trade. As of 2018, its total gross domestic product (GDP) was $101 billion[8] with a GDP per capita of $45,465. New Mexico's status as a tax haven yields low to moderate personal income taxes on residents and military personnel, and gives tax credits and exemptions to favorable industries. Because of this, its film industry has grown and contributed $1.23 billion to its overall economy. Due to its large area and economic climate, New Mexico has a large U.S. military presence marked notably with the White Sands Missile Range. Various U.S. national security agencies base their research and testing arms in New Mexico such as the Sandia and Los Alamos National Laboratories. During the 1940s, Project Y of the Manhattan Project developed and built the country's first atomic bomb and nuclear test, Trinity.
+
+Inhabited by Native Americans for many thousands of years before European exploration, it was colonized by the Spanish in 1598 as part of the Imperial Spanish viceroyalty of New Spain. In 1563, it was named Nuevo México after the Aztec Valley of Mexico by Spanish settlers, more than 250 years before the establishment and naming of the present-day country of Mexico; thus, the present-day state of New Mexico was not named after the country today known as Mexico.[9][10] After Mexican independence in 1821, New Mexico became a Mexican territory with considerable autonomy. This autonomy was threatened, however, by the centralizing tendencies of the Mexican government from the 1830s onward, with rising tensions eventually leading to the Revolt of 1837. At the same time, the region became more economically dependent on the United States. At the conclusion of the Mexican–American War in 1848, the United States annexed New Mexico as the U.S. New Mexico Territory. It was admitted to the Union as the 47th state on January 6, 1912.
+
+Its history has given New Mexico the highest percentage of Hispanic and Latino Americans, and the second-highest percentage of Native Americans as a population proportion (after Alaska).[11] New Mexico is home to part of the Navajo Nation, 19 federally recognized Pueblo communities of Puebloan peoples, and three different federally recognized Apache tribes. In prehistoric times, the area was home to Ancestral Puebloans, Mogollon, and the modern extant Comanche and Utes[12] inhabited the state. The largest Hispanic and Latino groups represented include the Hispanos of New Mexico, Chicanos, and Mexicans. The New Mexican flag features the state's Spanish origins with the same scarlet and gold coloration as Spain's Cross of Burgundy, along with the ancient sun symbol of the Zia, a Puebloan tribe.[13] These indigenous, Hispanic, Mexican, Latin, and American frontier roots are reflected in the eponymous New Mexican cuisine and the New Mexico music genre.
+
+New Mexico received its name long before the present-day nation of Mexico won independence from Spain and adopted that name in 1821. Though the name "Mexico" itself derives from Nahuatl, and in that language it originally referred to the heartland of the Empire of the Mexicas (Aztec Empire) in the Valley of Mexico far from the area of New Mexico, Spanish explorers also used the term "Mexico" to name the region of New Mexico (Nuevo México in Spanish) in 1563. In 1581, the Chamuscado and Rodríguez Expedition named the region north of the Rio Grande "San Felipe del Nuevo México".[14] The Spaniards had hoped to find wealthy indigenous Mexica (Aztec) cultures there similar to those of the Aztec (Mexica) Empire of the Valley of Mexico. The indigenous cultures of New Mexico, however, proved to be unrelated to the Mexicas, and they were not wealthy,[15][16] but the name persisted. Before statehood, the name "New Mexico" applied to various configurations of a former U.S. New Mexico Territory and, even prior to its former Mexican territorial status, a former provincial kingdom of New Spain called Nuevo México, all in the same general area, but of varying extensions.[17]
+
+With a total area of 121,590 square miles (314,900 km2),[1] New Mexico is the fifth-largest state. New Mexico's eastern border lies along 103°W longitude with the state of Oklahoma, and (due to a 19th-century surveying error)[18] 2.2 miles (3.5 kilometres) west of 103°W longitude with Texas.[19] On the southern border, Texas makes up the eastern two-thirds, while the Mexican states of Chihuahua and Sonora make up the western third, with Chihuahua making up about 90% of that. The western border with Arizona runs along the 109° 03'W longitude.[20] The southwestern corner of the state is known as the Bootheel. The 37°N parallel forms the northern boundary with Colorado. The states of New Mexico, Colorado, Arizona, and Utah come together at the Four Corners in New Mexico's northwestern corner. New Mexico has almost no natural water sources. Its surface water area is about 292 square miles (760 km2).[1]
+
+The New Mexican landscape ranges from wide, rose-colored deserts to broken mesas to high, snow-capped peaks. Despite New Mexico's arid image, heavily forested mountain wildernesses cover a significant portion of the state, especially towards the north. The Sangre de Cristo Mountains, the southernmost part of the Rocky Mountains, run roughly north–south along the east side of the Rio Grande in the rugged, pastoral north. The most important of New Mexico's rivers are the Rio Grande, Pecos, Canadian, San Juan, and Gila. The Rio Grande is tied for the fourth-longest river in the United States.[21]
+
+The U.S. government protects millions of acres of New Mexico as national forests, including:[22]
+
+Areas managed by the National Park Service include:[23]
+
+Areas managed by the New Mexico State Parks Division:[24]
+
+Visitors also frequent the surviving native pueblos of New Mexico. Tourists visiting these sites bring significant money to the state. Other areas of geographical and scenic interest include Kasha-Katuwe Tent Rocks National Monument and the Gila Wilderness in the southwest of the state.[25]
+
+New Mexico's climate is generally semiarid to arid, though areas of continental and alpine climates exist, and its territory is mostly covered by mountains, high plains, and desert. The Great Plains (High Plains) are in eastern New Mexico, similar to the Colorado high plains in eastern Colorado. The two states share similar terrain, with both having plains, mountains, basins, mesas, and desert lands. New Mexico's statewide average precipitation is 13.9 inches (350 mm) a year, with average monthly amounts peaking in the summer, as at Albuquerque, and Las Cruces in the south. The average annual temperatures can range from 64 °F (18 °C) in the southeast to below 40 °F (4 °C) in the northern mountains.[20] During the summer, daytime temperatures can often exceed 100 °F (38 °C) at elevations below 5,000 feet (1,500 m), the average high temperature in July ranges from 97 °F (36 °C) at the lower elevations down to 78 °F (26 °C) at the higher elevations. In the colder months of November to March, many cities in New Mexico can have nighttime temperature lows in the teens above zero, or lower. The highest temperature recorded in New Mexico was 122 °F (50 °C) at the Waste Isolation Pilot Plant (WIPP) near Loving on June 27, 1994, and the lowest recorded temperature is −50 °F (−46 °C) at Gavilan on February 1, 1951.[26]
+
+Astronomical observatories in New Mexico take advantage of unusually clear skies, including the Apache Point Observatory, the Very Large Array, the Magdalena Ridge Observatory, and others.[27][28]
+
+New Mexico has five unique floristic zones, providing diverse sets of habitats for many plants and animals. The Llano Estacado (or Shortgrass Prairie) in the eastern part of the state is characterized by sod-forming short grasses such as blue grama, and it used to sustain bison. The Chihuahuan Desert extends through the south of the state and is characterized by shrubby creosote. The Colorado Plateau in the northwest corner of New Mexico is high desert with cold winters, and is characterized by sagebrush, shadescale, greasewood, and other plants adapted to the saline and seleniferous soil. The mountainous Mogollon Plateau in the west-central of the state and southern Rocky Mountains in the north-central, have a wide range in elevation (4,000 to 13,000 ft or 1,200 to 4,000 m), with vegetation types corresponding to elevation gradients, such as piñon-juniper woodlands near the base, through evergreen conifers, spruce-fir and aspen forests, Krummholz, and alpine tundra. The Apachian zone tucked into the southwestern bootheel of the state has high-calcium soil, oak woodlands, and Arizona cypress, and other plants that are not found in other parts of the state.[29][30]
+
+Some of the native wildlife includes black bears, bighorn sheep, bobcats, cougars, coyotes, deer, elk, jackrabbits, kangaroo rats, javelina, porcupines, pronghorn antelope, roadrunners, western diamondbacks, wild turkeys,[31][32][33] and the endangered Mexican gray wolf and Rio Grande silvery minnow.[34]
+
+In January 2016, New Mexico sued the United States Environmental Protection Agency over negligence after the 2015 Gold King Mine waste water spill. The spill had caused heavy metals such as cadmium and lead and toxins such as arsenic to flow into the Animas River, polluting water basins of several states[35]
+
+The first known inhabitants of New Mexico were members of the Clovis culture of Paleo-Indians.[36]:19 Later inhabitants include American Indians of the Mogollon and Ancestral Pueblo peoples cultures.[37]:52
+
+By the time of European contact in the 16th century, the region was settled by the villages of the Pueblo peoples and groups of Navajo, Apache, and Ute.[36]:6,48
+
+Francisco Vásquez de Coronado assembled an enormous expedition at Compostela in 1540–1542 to explore and find the mythical Seven Golden Cities of Cibola as described by Fray Marcos de Niza.[37]:19–24 The name New Mexico was first used by a seeker of gold mines named Francisco de Ibarra, who explored far to the north of New Spain in 1563 and reported his findings as being in "a New Mexico".[38] Juan de Oñate officially established the name when he was appointed the first governor of the new Province of New Mexico in 1598.[37]:36–37 The same year, he founded the San Juan de los Caballeros colony, the first permanent European settlement in the future state of New Mexico,[39] on the Rio Grande near Ohkay Owingeh Pueblo.[37]:37 Oñate extended El Camino Real de Tierra Adentro, Royal Road of the Interior, by 700 miles (1,100 km) from Santa Bárbara, Chihuahua, to his remote colony.[40]:49
+
+The settlement of Santa Fe was established at the foot of the Sangre de Cristo Mountains, the southernmost subrange of the Rocky Mountains, around 1608.[40]:182 The city, along with most of the settled areas of the state, was abandoned by the Spanish for 12 years (1680–92)[41] as a result of the successful Pueblo Revolt, the only successful revolt against European expansion by Native Americans.[42] After the death of the Pueblo leader Popé, Diego de Vargas restored the area to Spanish rule.[37]:68–75 While developing Santa Fe as a trade center, the returning settlers founded Albuquerque in 1706 from existing surrounding communities,[37]:84 naming it for the viceroy of New Spain, Francisco Fernández de la Cueva, 10th Duke of Alburquerque.[43]
+
+As a part of New Spain, the claims for the province of New Mexico passed to independent Mexico in 1821 following the Mexican War of Independence.[37]:109 The Republic of Texas claimed the portion east of the Rio Grande when it seceded from Mexico in 1836, when it incorrectly assumed the older Hispanic settlements of the upper Rio Grande were the same as the newly established Mexican settlements of Texas. Texas's only attempt to establish a presence or control in the claimed territory was the failed Texan Santa Fe Expedition. Their entire army was captured and jailed by Hispanic New Mexico militia.
+
+At the turn of the 19th century, the extreme northeastern part of New Mexico, north of the Canadian River and east of the Sangre de Cristo Mountains, was still claimed by France, which sold it in 1803 as part of the Louisiana Purchase. When the Louisiana Territory was admitted as a state in 1812, the U.S. reclassified it as part of the Missouri Territory. The region (along with territory that makes up present-day southeastern Colorado, the Texas and Oklahoma Panhandles, and southwestern Kansas) was ceded to Spain under the Adams-Onis Treaty in 1819.
+
+By 1800, the population of New Mexico had reached 25,000.[44]
+
+Following the victory of the United States in the Mexican–American War (1846–48), under the Treaty of Guadalupe Hidalgo in 1848, Mexico ceded its northern holdings including the territories of California, Texas, and New Mexico, to the United States of America.[37]:132 The United States vowed to accept the residents' claims to their lands and to accept them as full citizens with rights of suffrage.
+
+After Texas was admitted as a state to the Union, it continued to claim a northeastern portion of New Mexico. It was forced by the US government to drop these claims, in the Compromise of 1850, Texas ceded these claims to the United States of the area in New Mexico lying east of the Rio Grande, in exchange for $10 million from the federal government.[37]:135
+
+Congress established the separate New Mexico Territory in September 1850.[45] It included most of the present-day states of Arizona and New Mexico, and part of Colorado. When the boundary was fixed, a surveyor's error awarded the Permian Basin to the State of Texas.[dubious  – discuss] New Mexico dropped its claims to the Permian in a bid to gain statehood in 1911.
+
+In 1853, the United States acquired the mostly desert southwestern bootheel of the state and southern Arizona south of the Gila River in the Gadsden Purchase. It wanted to control lands needed for the right-of-way to encourage construction of a transcontinental railroad.[37]:136
+
+New Mexico played a role in the Trans-Mississippi Theater of the American Civil War. Both Confederate and Union governments claimed ownership and territorial rights over New Mexico Territory. In 1861, the Confederacy claimed the southern tract as its own Arizona Territory and waged the ambitious New Mexico Campaign in an attempt to control the American Southwest and open up access to Union California. Confederate power in the New Mexico Territory was effectively broken after the Battle of Glorieta Pass in 1862. However, the Confederate territorial government continued to operate out of Texas, and Confederate troops marched under the Arizona flag until the end of the war. Additionally, more than 8,000 men from New Mexico Territory served in the Union Army.[46]
+
+In the late 19th century, the majority of officially European-descended residents in New Mexico were ethnic Mexicans, many of whom had deep roots in the area from early Spanish colonial times. Politically, they still controlled most of the town and county offices through area elections, and wealthy sheepherder families commanded considerable influence. The Anglo-Americans tended to have more ties to the territorial governor and judges, who were appointed by officials out of the region. The two groups struggled for power and the future of the territory. The Anglo minority was "outnumbered, but well-organized and growing".[47] Anglo-Americans made distinctions between the wealthy Mexicans and poor, ill-educated laborers.
+
+The United States Congress admitted New Mexico as the 47th state on January 6, 1912.[37]:166
+
+European-American settlers in the state had an uneasy relationship with the large Native American tribes, most of whose members lived on reservations at the beginning of the 20th century. Although Congress passed a law in 1924 that granted all Native Americans U.S. citizenship, as well as the right to vote in federal and state elections, New Mexico was among several states with Jim Crow laws, e.g. those who do not pay taxes cannot vote.[48]
+
+A major oil discovery in 1928 brought wealth to the state, especially Lea County and the town of Hobbs. The town was named after James Hobbs, a homesteader there in 1907.[49] The Midwest State No. 1 well, begun in late 1927 with a standard cable-tool drilling rig, revealed the first signs of oil from the Hobbs field on June 13, 1928. Drilled to 4,330 feet and completed a few months later, the well produced 700 barrels of oil per day on state land. The Midwest Refining Company's Hobbs well produced oil until 2002. The New Mexico Bureau of Mines and Mineral Resources called it "the most important single discovery of oil in New Mexico's history".[50]
+
+During World War II, the first atomic bombs were designed and manufactured at Los Alamos, a site developed by the federal government specifically to support a high-intensity scientific effort to rapidly complete research and testing of this weapon. The first bomb was tested at Trinity site in the desert between Socorro and Alamogordo on what is now White Sands Missile Range.[37]:179–180
+
+Native Americans from New Mexico fought for the United States in both the First and Second World Wars. Veterans were disappointed to return and find their civil rights limited by state discrimination. In Arizona and New Mexico, veterans challenged state laws or practices prohibiting them from voting. In 1948, after veteran Miguel Trujillo, Sr. of Isleta Pueblo was told by the county registrar that he could not register to vote, he filed suit against the county in federal district court. A three-judge panel overturned as unconstitutional New Mexico's provisions that Indians who did not pay taxes (and could not document if they had paid taxes) could not vote.[48] Judge Phillips wrote:
+
+Any other citizen, regardless of race, in the State of New Mexico who has not paid one cent of tax of any kind or character, if he possesses the other qualifications, may vote. An Indian, and only an Indian, in order to meet the qualifications to vote must have paid a tax. How you can escape the conclusion that makes a requirement with respect to an Indian as a qualification to exercise the elective franchise and does not make that requirement with respect to the member of any race is beyond me.[48]
+
+New Mexico has received large amounts of federal government spending on major military and research institutions in the state. It is home to three Air Force bases, White Sands Missile Range, and the federal research laboratories Los Alamos National Laboratory and Sandia National Laboratories. The state's population grew rapidly after World War II, growing from 531,818 in 1940 to 1,819,046 in 2000.[53] Both residents and businesses moved to the state; some northerners came at first for the mild winters; others for retirement.
+
+On May 22, 1957, a B-36 accidentally dropped a nuclear bomb 4.5 miles from the control tower while landing at Kirtland Air Force Base. (Only its conventional "trigger" detonated.)[54][55]
+
+In the late 20th century, Native Americans were authorized by federal law to establish gaming casinos on their reservations under certain conditions, in states which had authorized such gaming. Such facilities have helped tribes close to population centers to generate revenues for reinvestment in economic development and welfare of their peoples.
+
+In the 21st century, employment growth areas in New Mexico include electronic circuitry, scientific research, call centers, and Indian casinos.[56]
+
+The United States Census Bureau estimates that the population of New Mexico was 2,096,829 on July 1, 2019, a 1.83% increase since the 2010 census.[52] The 2000 census recorded the population of New Mexico to be 1,819,046; ten years later it was 2,059,179—an 11.7% increase.[57]
+
+Of the people residing in New Mexico 51.4% were born there; 37.9% were born in another state; 1.1% were born in Puerto Rico, U.S. Island areas, or abroad to American parent(s); and 9.7% were foreign born.[58]
+
+As of May 1, 2010, 7.5% of New Mexico's population was reported as under 5 years of age, 25% under 18, and 13% were 65 or older.[59]
+
+As of 2000, 8% of the residents of the state were foreign-born.[59]
+
+Among U.S. states, New Mexico has the highest percentage of Hispanic ancestry, at 47% (as of July 1, 2012). This classification covers people of very different cultures and histories, including descendants of Spanish colonists with deep roots in the region, and recent immigrants from a variety of nations in Latin America, each with their own cultures.
+
+According to the United States Census Bureau Model-based Small Area Income and Poverty Estimates, the number of persons in poverty has increased to 400,779 (19.8% of the population) persons in 2010 from 2000. At that time, the estimated number of persons in poverty was recorded at 309,193 (17.3% of the population). The latest available data for 2014 estimate the number of persons in poverty at 420,388 (20.6% of the population).[57]
+
+Note: Births in table do not add up, because Hispanics are counted both by their ethnicity and by their race, giving a higher overall number.
+
+New Mexico is a majority-minority state.[67]
+
+The U.S. Census Bureau estimated that 48% of the total 2015 population was Hispanic or Latino of any race, the highest of any state. The majority of Hispanics in New Mexico claim to be descendants of Spanish colonists who settled here during the 16th, 17th, and 18th centuries. They speak New Mexican Spanish or English at home.[59]
+
+The state also has a large Native American population, second in percentage behind that of Alaska.[59][68] The 2018 racial composition of the population was estimated to be:[69]
+
+According to the United States Census Bureau, 1.5% of the population identifies as multiracial/mixed-race, a population larger than both the Asian and NHPI population groups.[59] In 2008, New Mexico had the highest percentage (47%) of Hispanics (of any race) of any state,[59] with 83% native-born and 17% foreign-born.[73]
+
+According to the 2000 United States Census,[74]:6
+the most commonly claimed ancestry groups in New Mexico were:
+
+According to the 2010 U.S. Census, 28.45% of the population age 5 and older speak Spanish at home, while 3.50% speak Navajo.[75] Some speakers of New Mexican Spanish are descendants of Spanish settlers who arrived in New Mexico in the 16th, 17th, and 18th centuries.[76] While it is a common folk belief that New Mexican Spanish is an archaic form of 17th-century Castilian Spanish, and archaisms do exist, research reveals that traditional New Mexican Spanish "is neither more Iberian nor more archaic than other New World Spanishes".[77][78]
+
+Besides Navajo, which is also spoken in Arizona, a few other Native American languages are spoken by smaller groups in New Mexico, most of which are only spoken in the state. Native New Mexican languages include Mescalero Apache, Jicarilla Apache, Tewa, Southern Tiwa, Northern Tiwa, Towa, Keres (Eastern and Western), and Zuni. Mescalero and Jicarilla Apache are closely related Southern Athabaskan languages, and both are also related to Navajo. Tewa, the Tiwa languages, and Towa belong to the Kiowa-Tanoan language family, and thus all descend from a common ancestor. Keres and Zuni are language isolates, and have no relatives outside of New Mexico.
+
+The original state constitution of 1912 provided for a bilingual government with laws being published in both English and Spanish;[79] this requirement was renewed twice, in 1931 and 1943.[80] Nonetheless, the constitution does not declare any language as "official".[81] While Spanish was permitted in the legislature until 1935, all state officials are required to have a good knowledge of English. Cobarrubias and Fishman therefore argue that New Mexico cannot be considered a bilingual state as not all laws are published in both languages.[80] Others, such as Juan Perea, claim that the state was officially bilingual until 1953.[82]
+
+With regard to the judiciary, witnesses have the right to testify in either of the two languages, and monolingual speakers of Spanish have the same right to be considered for jury duty as do speakers of English.[81][83] In public education, the state has the constitutional obligation to provide bilingual education and Spanish-speaking instructors in school districts where the majority of students are hispanophone.[81]
+
+In 1995, the state adopted an official bilingual song, "New Mexico – Mi Lindo Nuevo México".[84]:75,81 In 1989, New Mexico became the first state to officially adopt the English Plus resolution,[85] and in 2008, the first to officially adopt a Navajo textbook for use in public schools.[86]
+
+According to Association of Religion Data Archives (ARDA), the largest denominations in 2010 were the Catholic Church with 684,941; the Southern Baptist Convention with 113,452; The Church of Jesus Christ of Latter-day Saints with 67,637, and the United Methodist Church with 36,424 adherents.[88] According to a 2008 survey by the Pew Research Center, the most common self-reported religious affiliation of New Mexico residents are mentioned in reference.[citation needed]
+
+Within the hierarchy of the Catholic Church, New Mexico belongs to the Ecclesiastical Province of Santa Fe. New Mexico has three dioceses, one of which is an archdiocese:[89]
+Archdiocese of Santa Fe,
+Diocese of Gallup,
+Diocese of Las Cruces.
+
+Oil and gas production, tourism, and federal government spending are important drivers of the state economy. State government has an elaborate system of tax credits and technical assistance to promote job growth and business investment, especially in new technologies.
+
+In 2010, New Mexico's Gross Domestic Product was $80 billion, and an estimated $85 billion for 2013.[90] In 2007, the per capita personal income was $31,474 (rank 43rd in the nation).[91] In 2005, the percentage of persons below the poverty level was 18.4%.[92]
+The New Mexico Tourism Department estimates that in Fiscal Year 2006, the travel industry in New Mexico generated expenditures of $6.5 billion.[93] As of April 2012[update], the state's unemployment rate was 7.2%.[94] During the late-2000s recession, New Mexico's unemployment rate peaked at 8.0% for the period June–October 2010.[95]
+
+New Mexico is the third-largest crude oil and ninth-largest natural gas producer in the United States.[96] The Permian and San Juan Basins, which are located partly in New Mexico, account for some of these natural resources. In 2000 the value of oil and gas produced was $8.2 billion,[97] and in 2006, New Mexico accounted for 3.4% of the crude oil, 8.5% of the dry natural gas, and 10.2% of the natural gas liquids produced in the United States.[98] However, the boom in hydraulic fracturing and horizontal drilling beginning in the mid-2010s led to a large increase in the production of crude oil from the Permian Basin and other U.S. sources; these developments allowed the United States to again become the world's largest producer of crude oil, in 2018.[99][100][101][102] New Mexico's oil and gas operations contribute to the state's above-average release of the greenhouse gas methane, including from a national methane hot spot in the Four Corners area.[103][104][105][106]
+
+Federal government spending is a major driver of the New Mexico economy. In 2005, the federal government spent $2.03 on New Mexico for every dollar of tax revenue collected from the state. This rate of return is higher than any other state in the Union.[107]
+
+Many of the federal jobs relate to the military; the state hosts three air force bases (Kirtland Air Force Base, Holloman Air Force Base, and Cannon Air Force Base); a testing range (White Sands Missile Range); and an army proving ground (Fort Bliss's McGregor Range). A May 2005 estimate by New Mexico State University is that 11.65% of the state's total employment arises directly or indirectly from military spending.[108]
+Other federal installations include the technology labs of Los Alamos National Laboratory and Sandia National Laboratories.
+
+New Mexico provides a number of economic incentives to businesses operating in the state, including various types of tax credits and tax exemptions. Most of the incentives are based on job creation.[109]
+
+New Mexico law allows governments to provide land, buildings, and infrastructure to businesses to promote job creation. Several municipalities have imposed an Economic Development Gross Receipts Tax (a form of Municipal Infrastructure GRT) that is used to pay for these infrastructure improvements and for marketing their areas.[110]
+
+The state provides financial incentives for film production.[111][112] The New Mexico Film Office estimated at the end of 2007 that the incentive program had brought more than 85 film projects to the state since 2003 and had added $1.2 billion to the economy.[113]
+
+Since 2008, personal income tax rates for New Mexico have ranged from 1.7% to 4.9%, within four income brackets.[114] As of 2007, active-duty military salaries are exempt from state income tax.[115] New Mexico is one of the largest tax havens in the U.S., offering numerous economic incentives and tax breaks on personal and corporate income.[116][117] It does not have inheritance tax, estate tax, or sales taxes.[114][118]
+
+New Mexico imposes a Gross Receipts Tax (GRT) on many transactions, which may even include some governmental receipts. This resembles a sales tax but, unlike the sales taxes in many states, it applies to services as well as tangible goods. Normally, the provider or seller passes the tax on to the purchaser, however legal incidence and burden apply to the business, as an excise tax. GRT is imposed by the state and there may an additional locality component to produce a total tax rate.[119] As of July 1, 2013 the combined tax rate ranged from 5.125% to 8.6875%.[120]
+
+Property tax is imposed on real property by the state, by counties, and by school districts. In general, personal-use personal property is not subject to property taxation. On the other hand, property tax is levied on most business-use personal property. The taxable value of property is 1/3 of the assessed value. A tax rate of about 30 mills is applied to the taxable value, resulting in an effective tax rate of about 1%. In the 2005 tax year, the average millage was about 26.47 for residential property, and 29.80 for non-residential property. Assessed values of residences cannot be increased by more than 3% per year unless the residence is remodeled or sold. Property tax deductions are available for military veterans and heads of household.[121]
+
+New Mexico has long been an important corridor for trade and migration. The builders of the ruins at Chaco Canyon also created a radiating network of roads from the mysterious settlement.[122] Chaco Canyon's trade function shifted to Casas Grandes in the present-day Mexican state of Chihuahua, however, north–south trade continued. The pre-Columbian trade with Mesoamerican cultures included northbound exotic birds, seashells and copper. Turquoise, pottery, and salt were some of the goods transported south along the Rio Grande. Present-day New Mexico's pre-Columbian trade is especially remarkable for being undertaken on foot. The north–south trade route later became a path for colonists with horses arriving from New Spain as well as trade and communication. The route was called El Camino Real de Tierra Adentro.[123]
+
+The Santa Fe Trail was the 19th-century territory's vital commercial and military highway link to the Eastern United States.[124] All with termini in Northern New Mexico, the Camino Real, the Santa Fe Trail and the Old Spanish Trail are all recognized as National Historic Trails. New Mexico's latitude and low passes made it an attractive east–west transportation corridor.[125] As a territory, the Gadsden Purchase increased New Mexico's land area for the purpose of the construction of a southern transcontinental railroad, that of the Southern Pacific Railroad. Another transcontinental railroad was completed by the Atchison, Topeka and Santa Fe Railway. The railroads essentially replaced the earlier trails but brought on a population boom. Early transcontinental auto trails later crossed the state bringing more migrants. Railroads were later supplemented or replaced by a system of highways and airports. Today, New Mexico's Interstate Highways approximate the earlier land routes of the Camino Real, the Santa Fe Trail and the transcontinental railroads.
+
+New Mexico has only three Interstate Highways. In Albuquerque, I-25 and I-40 meet at a stack interchange called The Big I.
+
+Interstate 10 travels in the southwest portion of New Mexico starting from the Arizona stateline near Lordsburg to the Texas stateline south past Las Cruces, near El Paso, Texas.
+
+Interstate 25 is a major north–south interstate highway starting from Las Cruces, New Mexico to the Colorado stateline near Raton.
+
+Interstate 40 is a major east–west interstate highway starting from the Arizona stateline west of Gallup to the Texas stateline east from Tucumcari.
+
+New Mexico currently has 15 United States Highways. This includes US 54, US 56, US 60, US 62, US 64, US 70, US 82, US 84, US 87, US 160, US 180, US 285, US 380, US 491, and US 550.
+
+US 66, The Mother Road, was replaced by I-40 in 1985. US 85 is currently unsigned by the NMDOT, but the AASHTO still recognize it. It runs in the same trace with I-10 and I-25. US 666, The Devils Highway, was replaced by US 491 in 2003 because the number "666" is the "Number of the Beast".
+
+New Mexico has had a problem with drunk driving, but that has lessened. According to the Los Angeles Times, for years the state had the highest alcohol-related crash rates in the U.S., but ranked 25th in alcohol-related fatal crash rates, as of July 2009[update].[126]
+
+The automobile changed the character of New Mexico, marking the start of large-scale immigration to the state from elsewhere in the United States. Settlers moving West during the Great Depression and post-World War II American culture immortalized the National Old Trails Highway, later U.S. Route 66. Today, New Mexico relies heavily upon the automobile for transportation.
+
+New Mexico had 59,927 route miles of highway as of 2000[update], of which 7,037 receive federal aid.[127] In that same year there were 1,003 miles (1,614 km) of freeways, of which 1000 were the route miles of Interstate Highways 10, 25 and 40.[128] The former number has increased with the upgrading of roads near Pojoaque, Santa Fe and Las Cruces to freeways. The highway traffic fatality rate was 1.9 fatalities per million miles traveled in 2000, the 13th highest rate among U.S. states.[129] Notable bridges include the Rio Grande Gorge Bridge near Taos. As of 2001[update], 703 highway bridges, or one percent, were declared "structurally deficient" or "structurally obsolete".[130]
+
+Rural and intercity public transportation by road is provided by Americanos USA, LLC, Greyhound Lines and several government operators.
+
+The New Mexico Rail Runner Express is a commuter rail system serving the metropolitan area of Albuquerque, New Mexico. It began operation on July 14, 2006.[131] The system runs from Belen to downtown Santa Fe. Larger cities in New Mexico typically have some form of public transportation by road; ABQ RIDE is the largest such system in the state.[132]
+
+There were 2,354 route miles of railroads in the year 2000; this number increased with the opening of the Rail Runner's extension to Santa Fe.[133] In addition to local railroads and other tourist lines, the state jointly owns and operates a heritage narrow-gauge steam railroad, the Cumbres and Toltec Scenic Railway, with the state of Colorado. Narrow gauge railroads once connected many communities in the northern part of the state, from Farmington to Santa Fe.[134]:110 No fewer than 100 railroads of various names and lineage have operated in the jurisdiction at some point.[134]:8 New Mexico's rail transportation system reached its height in terms of length following admission as a state; in 1914 eleven railroads operated 3124 route miles.[134]:10
+
+Railroad surveyors arrived in New Mexico in the 1850s.[135] The first railroads incorporated in 1869.[134]:9 The first operational railroad, the Atchison, Topeka & Santa Fe Railway (ATSF), entered the territory by way of the lucrative and contested Raton Pass in 1878. It eventually reached El Paso, Texas in 1881 and with the Southern Pacific Railroad created the nation's second transcontinental railroad with a junction at Deming. The Southern Pacific Railroad entered the territory from the Territory of Arizona in 1880.[134]:9, 18, 58–59[135] The Denver & Rio Grande Railway, who would generally use narrow gauge equipment in New Mexico, entered the territory from Colorado and began service to Española on December 31, 1880.[134]:95–96[135] These first railroads were built as long-distance corridors, later railroad construction also targeted resource extraction.[134]:8–11
+
+New Mexico is served by two class I railroads, the BNSF Railway and the Union Pacific Railroad. Combined, they operate 2,200 route miles of railway in the state.[133]
+
+A commuter rail operation, the New Mexico Rail Runner Express, connects the state's capital, its largest city, and other communities.[136] The privately operated state owned railroad began operations in July 2006.[131] The BNSF Railway's entire line from Belen to Raton, New Mexico was sold to the state, partially for the construction of phase II of this operation, which opened in December 2008.[137] Phase II of Rail Runner extended the line northward to Santa Fe from the Sandoval County station, the northernmost station under Phase I service. The service now connects Santa Fe, Sandoval, Bernalillo, and Valencia counties. The trains connect Albuquerque's population base and central business district to downtown Santa Fe with up to eight roundtrips in a day. The section of the line running south to Belen is served less frequently.[138] Rail Runner operates scheduled service seven days per week.[139]
+
+With the rise of rail transportation many settlements grew or were founded and the territory became a tourist destination. As early as 1878, the ATSF promoted tourism in the region with emphasis on Native American imagery.[140]:64 Named trains often reflected the territory they traveled: Super Chief, the streamlined successor to the Chief;[140] Navajo, an early transcontinental tourist train; and Cavern, a through car operation connecting Clovis and Carlsbad (by the early 1950s as train 23–24),[134]:49–50[141]:51 were some of the named passenger trains of the ATSF that connoted New Mexico.
+
+Passenger train service once connected nine of New Mexico's present ten most populous cities (the exception is Rio Rancho), while today passenger train service connects two: Albuquerque and Santa Fe.[136] With the decline of most intercity rail service in the United States in the late 1960s, New Mexico was left with minimal services. No less than six daily long-distance roundtrip trains supplemented by many branch line and local trains served New Mexico in the early 1960s. Declines in passenger revenue, but not necessarily ridership, prompted many railroads to turn over their passenger services in truncated form to Amtrak, a state owned enterprise. Amtrak, also known as the National Passenger Railroad Corporation, began operating the two extant long-distance routes in May 1971.[134][140][141] Resurrection of passenger rail service from Denver to El Paso, a route once plied in part by the ATSF's El Pasoan,[141]:37 has been proposed over the years. As early as the 1980s, former Governor Toney Anaya proposed building a high-speed rail line connecting the two cities with New Mexico's major cities.[142] Front Range Commuter Rail is a project to connect Wyoming and New Mexico with high-speed rail.[143]
+
+Amtrak's Southwest Chief passes through daily at stations in Gallup, Albuquerque, Lamy, Las Vegas, and Raton, offering connections to Los Angeles, Chicago and intermediate points.[144] The Southwest Chief is a fast Amtrak long-distance train, being permitted a maximum speed of 90 mph (140 km/h) in various places on the tracks of the BNSF Railway.[145] It also operates on New Mexico Rail Runner Express trackage. The Southwest Chief is the successor to the Super Chief and El Capitan.[141]:115 The streamliner Super Chief, a favorite of early Hollywood stars, was one of the most famous named trains in the United States and one of the most esteemed for its luxury and exoticness—train cars were named for regional Native American tribes and outfitted with the artwork of many local artists—but also for its speed: as few as 39 hours 45 minutes westbound.[140]
+
+The Sunset Limited makes stops three times a week in both directions at Lordsburg, and Deming, serving Los Angeles, New Orleans and intermediate points.[146] The Sunset Limited is the successor to the Southern Pacific Railroad's train of the same name and operates exclusively on Union Pacific trackage in New Mexico.
+
+The Albuquerque International Sunport is the state's primary port of entry for air transportation.
+
+Upham, near Truth or Consequences, is the location of the world's first operational and purpose-built commercial spaceport, Spaceport America.[147][148][149] Rocket launches began in April 2007.[149] It is undeveloped and has one tenant, UP Aerospace, launching small payloads.[150] Virgin Galactic, a space tourism company, plans to make this their primary operating base.[148][151]
+
+The Constitution of New Mexico established New Mexico's governmental structure. The executive branch of government is fragmented as outlined in the state constitution. The executive is composed of the Governor and other statewide elected officials including the Lieutenant Governor (elected on the same ticket as the Governor), Attorney General, Secretary of State, State Auditor, State Treasurer, and Commissioner of Public Lands. The governor appoints a cabinet who lead agencies statutorily designated under their jurisdiction. The New Mexico Legislature consists of the House of Representatives and Senate. The judiciary is composed of the New Mexico Supreme Court and lower courts. There is also local government, consisting of counties, municipalities and special districts.[152]
+
+Current Governor Michelle Lujan Grisham (D) and Lieutenant Governor Howie Morales (D) were first elected in 2018. Terms for both the Governor and Lieutenant Governor expire in January 2023. Governors serve a term of four years, and may seek re-election for one additional term (limit of two terms). Other constitutional officers, all of whose terms also expire in January 2023, include Secretary of State Maggie Toulouse Oliver (D),[153] Attorney General Hector Balderas (D),[154] State Auditor Brian Colón (D),[155] State Land Commissioner Stephanie Garcia Richard (D),[156] and State Treasurer Tim Eichenberg (D).[157]
+
+Currently, both chambers of the New Mexico State Legislature have Democratic majorities. There are 26 Democrats and 16 Republicans in the Senate, and 47 Democrats and 23 Republicans in the House of Representatives.
+
+New Mexico's members of the United States Senate are Democrats Martin Heinrich and Tom Udall. Democrats represent the state's three United States House of Representatives congressional districts with Deb Haaland, Xochitl Torres Small, and Ben Ray Luján representing the first, second, and third districts respectively.[159][160] See New Mexico congressional map.
+
+New Mexico has traditionally been considered a swing state, whose population has favored both Democratic and Republican presidential candidates, but it has become more of a Democratic stronghold beginning with the presidential election of 2008. The governor is Michelle Lujan Grisham (D), who succeeded Susana Martinez (R) on January 1, 2019 after she served two terms as governor from 2011 to 2019. Gary Johnson served as governor from 1995 to 2003. Johnson served as a Republican, but in 2012 and 2016, he ran for president from the Libertarian Party. In previous presidential elections, Al Gore carried the state (by 366 votes) in 2000; George W. Bush won New Mexico's five electoral votes in 2004, and the state's electoral votes were won by Barack Obama and Hillary Clinton in 2008, 2012, and 2016. Since achieving statehood in 1912, New Mexico has been carried by the national popular vote victor in every presidential election of the past 104 years, except 1976, when Gerald Ford won the state by 2%, but lost the national popular vote by 2%.[161] It has also awarded its electoral votes to the candidate who would ultimately win, with the exception of 1976, 2000, and 2016.
+
+Democrats in the state are usually strongest in the Santa Fe Area, various areas of the Albuquerque Metro Area (such as the southeast and central areas, including the affluent Nob Hill neighborhood and the vicinity of the University of New Mexico), Northern and West Central New Mexico, and most of the Native American reservations, particularly the Navajo Nation. Republicans have traditionally had their strongholds in the eastern and southern parts of the state, the Farmington area, Rio Rancho, and the newly developed areas in the Northwest mesa. Albuquerque's Northeast Heights have historically leaned Republican, but have become a key swing area for Democrats in recent election cycles. While registered Democrats outnumber registered Republicans by nearly 200,000, New Mexico voters have favored moderate to conservative candidates of both parties at the state and federal levels.
+
+New Mexico abolished its death penalty statute, though not retroactively, effective July 1, 2009. This means individuals on New Mexico's Death Row can still be executed. On March 18, 2009, then Governor Bill Richardson signed the law abolishing the death penalty in New Mexico following the assembly and senate vote the week before, thus becoming the 15th U.S. state to abolish the penalty.[162]
+
+On gun control, New Mexico arguably has some of the least restrictive firearms laws in the country. State law pre-empts all local gun control ordinances. New Mexico residents may purchase any firearm deemed legal under federal law. There are no waiting periods under state law for picking up a firearm after it has been purchased, and there are no restrictions on magazine capacity. Additionally, New Mexico is a "shall-issue" state for concealed carry permits.
+
+Before December 2013, New Mexico law neither explicitly allowed nor prohibited same-sex marriage. Policy concerning the issuance of marriage licenses to same-sex couples was determined at the county level; that is, some county clerks issued marriage licenses to same-sex couples while others did not. In December 2013, the New Mexico Supreme Court issued a unanimous ruling directing all county clerks to issue marriage licenses to same-sex couples, thereby making New Mexico the 17th state to recognize same-sex marriage at the statewide level.
+
+Due to its relatively low population, in combination with numerous federally funded research facilities, New Mexico had the highest concentration of PhD holders of any state in 2000.[163] Despite this, the state routinely ranks near the bottom in surveys of the quality of primary and secondary school education.[164] In a landmark decision, a state judge ruled in 2018 that "New Mexico is violating the constitutional rights of at-risk students by failing to provide them with sufficient education,"[165] and ordered that the governor and Legislature provide an adequate system by April 2019.[165][166]
+
+New Mexico has a higher concentration of persons who do not finish high school or have some college without a degree than the nation as a whole. For the state, 23.9% of people over 25 have gone to college but not earned a degree.[57] This is compared with 21.0% of the nation as a whole according to United States Census Bureau 2014 American Community Survey estimates.[167] Los Alamos County has the highest number percent of post secondary degree holders of any county in New Mexico with 38.7% of the population (4,899 persons) estimated by the 2010-2014 American Community Survey.[168]
+
+The New Mexico Public Education Department oversees the operation of primary and secondary schools; individual school districts directly operate and staff said schools.
+
+New Mexico is one of eight states that funds college scholarships through the state lottery.[169][170][171] The state of New Mexico requires that the lottery put 30% of its gross sales into the scholarship fund.[172]
+The scholarship is available to residents who graduated from a state high school, and attend a state university full-time while maintaining a 2.5 GPA or higher.[173]
+It covered 100% of tuition when it was first instated in 1996,[174] decreased to 90%, then dropped to 60% in 2017.[170] The value slightly increased in 2018, and new legislation was passed to outline what funds are available per type of institution.[174]
+
+Zimmerman Library at The University of New Mexico
+
+Zuhl Library at New Mexico State University
+
+Walkway outside Golden Library at Eastern New Mexico University
+
+Donnelly Library at New Mexico Highlands University
+
+With a Native American population of 134,000 in 1990,[175] New Mexico still ranks as an important center of Native American culture. Both the Navajo and Apache share Athabaskan origin. The Apache and some Ute live on federal reservations within the state. With 16 million acres (6,500,000 ha), mostly in neighboring Arizona, the reservation of the Navajo Nation ranks as the largest in the United States. The prehistorically agricultural Pueblo Indians live in pueblos scattered throughout the state. Almost half of New Mexicans claim Hispanic origin; many are descendants of colonial settlers. They settled in the state's northern portion. Most of the Mexican immigrants reside in the southern part of the state. Also 10-15% of the population, mainly in the north, may contain Hispanic Jewish ancestry.[citation needed]
+
+Many New Mexicans speak a unique dialect of Spanish. Because of the historical isolation of New Mexico from other speakers of the Spanish language, some of the vocabulary of New Mexican Spanish is unknown to other Spanish speakers. It uses numerous Native American words for local features and includes anglicized words that express American concepts and modern inventions.
+
+Albuquerque has the New Mexico Museum of Natural History and Science, the National Hispanic Cultural Center, and the National Museum of Nuclear Science & History, as well as hosts the famed annual Albuquerque International Balloon Fiesta every fall.
+
+The earliest New Mexico artists whose work survives today are the Mimbres Indians, whose black and white pottery could be mistaken for modern art, except for the fact that it was produced before 1130 CE. See Mimbres culture. Many examples of this work can be seen at the Deming Luna Mimbres Museum[176] and at the Western New Mexico University Museum.[177]
+
+A large artistic community thrives in Santa Fe, and has included such people as Bruce Nauman, Richard Tuttle, John Connell and Steina Vasulka. The capital city has several art museums, including the New Mexico Museum of Art, Museum of Spanish Colonial Art, Museum of International Folk Art, Museum of Indian Arts and Culture, Museum of Contemporary Native Arts, SITE Santa Fe and others. Colonies for artists and writers thrive, and the small city teems with art galleries. In August, the city hosts the annual Santa Fe Indian Market, which is the oldest and largest juried Native American art showcase in the world. Performing arts include the renowned Santa Fe Opera which presents five operas in repertory each July to August, the Santa Fe Chamber Music Festival held each summer, and the restored Lensic Theater a principal venue for many kinds of performances. Santa Fe is also home to Frogville Records, an indie record label. The weekend after Labor Day boasts the burning of Zozobra, a 50 ft (15 m) marionette, during Fiestas de Santa Fe.
+
+Art is also a frequent theme in Albuquerque, New Mexico's largest city. The National Hispanic Cultural Center has held hundreds of performing arts events, art showcases, and other events related to Spanish culture in New Mexico and worldwide in the centerpiece Roy E Disney Center for the Performing Arts or in other venues at the 53 acre facility. New Mexico residents and visitors alike can enjoy performing art from around the world at Popejoy Hall on the campus of the University of New Mexico. Popejoy Hall hosts singers, dancers, Broadway shows, other types of acts, and Shakespeare.[178] Albuquerque also has the unique and memorable KiMo Theater built in 1927 in the Pueblo Revival Style architecture. The KiMo presents live theater and concerts as well as movies and simulcast operas.[179] In addition to other general interest theaters, Albuquerque also has the African American Performing Arts Center and Exhibit Hall which showcases achievements by people of African descent[180] and the Indian Pueblo Cultural Center which highlights the cultural heritage of the First Nations people of New Mexico.[181]
+
+New Mexico holds strong to its Spanish heritage. Old Spanish traditions such zarzuelas and flamenco are popular in New Mexico.[182][183] Flamenco dancer and native New Mexican María Benítez founded the Maria Benítez Institute for Spanish Arts "to present programs of the highest quality of the rich artistic heritage of Spain, as expressed through music, dance, visual arts, and other art forms". There is also the Festival Flamenco Internacional de Alburquerque held each year in which native Spanish and New Mexican flamenco dancers perform at the University of New Mexico.
+
+In the mid-20th century there was a thriving Hispano school of literature and scholarship being produced in both English and Spanish. Among the more notable authors were: Angélico Chávez, Nina Otero-Warren, Fabiola Cabeza de Baca, Aurelio Espinosa, Cleofas Jaramillo, Juan Bautista Rael, and Aurora Lucero-White Lea. As well, writer D. H. Lawrence lived near Taos in the 1920s, at the D. H. Lawrence Ranch, where there is a shrine said to contain his ashes.
+
+New Mexico's strong Spanish, Native American, and Wild West frontier motifs have provided material for many authors in the state, including internationally recognized Rudolfo Anaya and Tony Hillerman.[184]
+
+Silver City, in the southwestern mountains of the state, was originally a mining town, and at least one nearby mine still operates. It is perhaps better known now as the home of or exhibition center for large numbers of artists, visual and otherwise.[185] Another former mining town turned art haven is Madrid, New Mexico.[186] It was brought to national fame as the filming location for the movie Wild Hogs in 2007. The City of Las Cruces, in southern New Mexico, has a museum system that is affiliated with the Smithsonian Institution Affiliations Program.[187] Las Cruces also has a variety of cultural and artistic opportunities for residents and visitors.[188]
+
+Aside from the aforementioned Wild Hogs, other movies filmed in New Mexico include Sunshine Cleaning and Vampires.
+
+The various seasons of the A&E/Netflix series Longmire have been filmed in several New Mexico locations, including Las Vegas, Santa Fe, Eagle Nest, and Red River.[189]
+
+The widely acclaimed TV show Breaking Bad and its spin-off Better Call Saul were both set and filmed in and around Albuquerque.[190]
+
+No major league professional sports teams are based in New Mexico, but the Albuquerque Isotopes are a Pacific Coast League Triple-A baseball affiliate of the MLB Colorado Rockies. New Mexico is home to several baseball teams of the Pecos League: the Roswell Invaders, Ruidoso Osos, Santa Fe Fuego and the White Sands Pupfish. The Duke City Gladiators of the Indoor Football League (IFL) plays their home games at Tingley Coliseum in Albuquerque. New Mexico United, also based in Albuquerque, began play in the second tier of the American soccer pyramid, the USL Championship, in 2019. Another soccer team from that city, Albuquerque Sol FC, plays in the fourth-tier USL League Two.
+
+Collegiate athletics in New Mexico involve various New Mexico Lobos and New Mexico State Aggies teams in many sports. For many years the two universities have had a rivalry often referred to as the "Rio Grande Rivalry" or the "Battle of I-25" in recognition of the campuses' both being located along that highway. NMSU also has a rivalry with the University of Texas at El Paso that is called "The Battle of I-10". The winner of the NMSU-UTEP football game receives the Silver Spade trophy.
+
+Olympic gold medalist Tom Jager, who is an advocate of controversial high-altitude training for swimming, has conducted training camps in Albuquerque (elevation 5,312 ft (1,619.1 m)) and Los Alamos (7,320 ft (2,231 m)).[191]
+
+NRA Whittington Center in Raton is the United States' largest and most comprehensive competitive shooting range and training facility.[192]
+

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+Coordinates: 34°N 106°W / 34°N 106°W / 34; -106
+
+New Mexico (Spanish: Nuevo México; Spanish pronunciation: [ˈnweβo ˈmexiko] (listen), Navajo: Yootó Hahoodzo; Navajo pronunciation: [jòːtxó xɑ̀xòːtsò]) is a state in the Southwestern region of the United States of America; its capital is Santa Fe, which was founded in 1610 as capital of Nuevo México (itself established as a province of New Spain in 1598), while its largest city is Albuquerque with its accompanying metropolitan area. It is one of the Mountain States and shares the Four Corners region with Utah, Colorado, and Arizona. New Mexico is also bordered by the state of Texas to the east-southeast, Oklahoma to the northeast, and the Mexican states of Chihuahua to the south and Sonora to the southwest. With an estimated population of 2,096,829 as of the July 1, 2019, U.S. Census Bureau estimate, New Mexico is the 36th largest state by population. With a total area of 121,590 sq mi (314,900 km2), it is the fifth-largest and sixth-least densely populated of the 50 states. Due to their geographic locations, northern and eastern New Mexico exhibit a colder, alpine climate, while western and southern New Mexico exhibit a warmer, arid climate.
+
+The economy of New Mexico is dependent on oil drilling, mineral extraction, dryland farming, cattle ranching, lumber milling, and retail trade. As of 2018, its total gross domestic product (GDP) was $101 billion[8] with a GDP per capita of $45,465. New Mexico's status as a tax haven yields low to moderate personal income taxes on residents and military personnel, and gives tax credits and exemptions to favorable industries. Because of this, its film industry has grown and contributed $1.23 billion to its overall economy. Due to its large area and economic climate, New Mexico has a large U.S. military presence marked notably with the White Sands Missile Range. Various U.S. national security agencies base their research and testing arms in New Mexico such as the Sandia and Los Alamos National Laboratories. During the 1940s, Project Y of the Manhattan Project developed and built the country's first atomic bomb and nuclear test, Trinity.
+
+Inhabited by Native Americans for many thousands of years before European exploration, it was colonized by the Spanish in 1598 as part of the Imperial Spanish viceroyalty of New Spain. In 1563, it was named Nuevo México after the Aztec Valley of Mexico by Spanish settlers, more than 250 years before the establishment and naming of the present-day country of Mexico; thus, the present-day state of New Mexico was not named after the country today known as Mexico.[9][10] After Mexican independence in 1821, New Mexico became a Mexican territory with considerable autonomy. This autonomy was threatened, however, by the centralizing tendencies of the Mexican government from the 1830s onward, with rising tensions eventually leading to the Revolt of 1837. At the same time, the region became more economically dependent on the United States. At the conclusion of the Mexican–American War in 1848, the United States annexed New Mexico as the U.S. New Mexico Territory. It was admitted to the Union as the 47th state on January 6, 1912.
+
+Its history has given New Mexico the highest percentage of Hispanic and Latino Americans, and the second-highest percentage of Native Americans as a population proportion (after Alaska).[11] New Mexico is home to part of the Navajo Nation, 19 federally recognized Pueblo communities of Puebloan peoples, and three different federally recognized Apache tribes. In prehistoric times, the area was home to Ancestral Puebloans, Mogollon, and the modern extant Comanche and Utes[12] inhabited the state. The largest Hispanic and Latino groups represented include the Hispanos of New Mexico, Chicanos, and Mexicans. The New Mexican flag features the state's Spanish origins with the same scarlet and gold coloration as Spain's Cross of Burgundy, along with the ancient sun symbol of the Zia, a Puebloan tribe.[13] These indigenous, Hispanic, Mexican, Latin, and American frontier roots are reflected in the eponymous New Mexican cuisine and the New Mexico music genre.
+
+New Mexico received its name long before the present-day nation of Mexico won independence from Spain and adopted that name in 1821. Though the name "Mexico" itself derives from Nahuatl, and in that language it originally referred to the heartland of the Empire of the Mexicas (Aztec Empire) in the Valley of Mexico far from the area of New Mexico, Spanish explorers also used the term "Mexico" to name the region of New Mexico (Nuevo México in Spanish) in 1563. In 1581, the Chamuscado and Rodríguez Expedition named the region north of the Rio Grande "San Felipe del Nuevo México".[14] The Spaniards had hoped to find wealthy indigenous Mexica (Aztec) cultures there similar to those of the Aztec (Mexica) Empire of the Valley of Mexico. The indigenous cultures of New Mexico, however, proved to be unrelated to the Mexicas, and they were not wealthy,[15][16] but the name persisted. Before statehood, the name "New Mexico" applied to various configurations of a former U.S. New Mexico Territory and, even prior to its former Mexican territorial status, a former provincial kingdom of New Spain called Nuevo México, all in the same general area, but of varying extensions.[17]
+
+With a total area of 121,590 square miles (314,900 km2),[1] New Mexico is the fifth-largest state. New Mexico's eastern border lies along 103°W longitude with the state of Oklahoma, and (due to a 19th-century surveying error)[18] 2.2 miles (3.5 kilometres) west of 103°W longitude with Texas.[19] On the southern border, Texas makes up the eastern two-thirds, while the Mexican states of Chihuahua and Sonora make up the western third, with Chihuahua making up about 90% of that. The western border with Arizona runs along the 109° 03'W longitude.[20] The southwestern corner of the state is known as the Bootheel. The 37°N parallel forms the northern boundary with Colorado. The states of New Mexico, Colorado, Arizona, and Utah come together at the Four Corners in New Mexico's northwestern corner. New Mexico has almost no natural water sources. Its surface water area is about 292 square miles (760 km2).[1]
+
+The New Mexican landscape ranges from wide, rose-colored deserts to broken mesas to high, snow-capped peaks. Despite New Mexico's arid image, heavily forested mountain wildernesses cover a significant portion of the state, especially towards the north. The Sangre de Cristo Mountains, the southernmost part of the Rocky Mountains, run roughly north–south along the east side of the Rio Grande in the rugged, pastoral north. The most important of New Mexico's rivers are the Rio Grande, Pecos, Canadian, San Juan, and Gila. The Rio Grande is tied for the fourth-longest river in the United States.[21]
+
+The U.S. government protects millions of acres of New Mexico as national forests, including:[22]
+
+Areas managed by the National Park Service include:[23]
+
+Areas managed by the New Mexico State Parks Division:[24]
+
+Visitors also frequent the surviving native pueblos of New Mexico. Tourists visiting these sites bring significant money to the state. Other areas of geographical and scenic interest include Kasha-Katuwe Tent Rocks National Monument and the Gila Wilderness in the southwest of the state.[25]
+
+New Mexico's climate is generally semiarid to arid, though areas of continental and alpine climates exist, and its territory is mostly covered by mountains, high plains, and desert. The Great Plains (High Plains) are in eastern New Mexico, similar to the Colorado high plains in eastern Colorado. The two states share similar terrain, with both having plains, mountains, basins, mesas, and desert lands. New Mexico's statewide average precipitation is 13.9 inches (350 mm) a year, with average monthly amounts peaking in the summer, as at Albuquerque, and Las Cruces in the south. The average annual temperatures can range from 64 °F (18 °C) in the southeast to below 40 °F (4 °C) in the northern mountains.[20] During the summer, daytime temperatures can often exceed 100 °F (38 °C) at elevations below 5,000 feet (1,500 m), the average high temperature in July ranges from 97 °F (36 °C) at the lower elevations down to 78 °F (26 °C) at the higher elevations. In the colder months of November to March, many cities in New Mexico can have nighttime temperature lows in the teens above zero, or lower. The highest temperature recorded in New Mexico was 122 °F (50 °C) at the Waste Isolation Pilot Plant (WIPP) near Loving on June 27, 1994, and the lowest recorded temperature is −50 °F (−46 °C) at Gavilan on February 1, 1951.[26]
+
+Astronomical observatories in New Mexico take advantage of unusually clear skies, including the Apache Point Observatory, the Very Large Array, the Magdalena Ridge Observatory, and others.[27][28]
+
+New Mexico has five unique floristic zones, providing diverse sets of habitats for many plants and animals. The Llano Estacado (or Shortgrass Prairie) in the eastern part of the state is characterized by sod-forming short grasses such as blue grama, and it used to sustain bison. The Chihuahuan Desert extends through the south of the state and is characterized by shrubby creosote. The Colorado Plateau in the northwest corner of New Mexico is high desert with cold winters, and is characterized by sagebrush, shadescale, greasewood, and other plants adapted to the saline and seleniferous soil. The mountainous Mogollon Plateau in the west-central of the state and southern Rocky Mountains in the north-central, have a wide range in elevation (4,000 to 13,000 ft or 1,200 to 4,000 m), with vegetation types corresponding to elevation gradients, such as piñon-juniper woodlands near the base, through evergreen conifers, spruce-fir and aspen forests, Krummholz, and alpine tundra. The Apachian zone tucked into the southwestern bootheel of the state has high-calcium soil, oak woodlands, and Arizona cypress, and other plants that are not found in other parts of the state.[29][30]
+
+Some of the native wildlife includes black bears, bighorn sheep, bobcats, cougars, coyotes, deer, elk, jackrabbits, kangaroo rats, javelina, porcupines, pronghorn antelope, roadrunners, western diamondbacks, wild turkeys,[31][32][33] and the endangered Mexican gray wolf and Rio Grande silvery minnow.[34]
+
+In January 2016, New Mexico sued the United States Environmental Protection Agency over negligence after the 2015 Gold King Mine waste water spill. The spill had caused heavy metals such as cadmium and lead and toxins such as arsenic to flow into the Animas River, polluting water basins of several states[35]
+
+The first known inhabitants of New Mexico were members of the Clovis culture of Paleo-Indians.[36]:19 Later inhabitants include American Indians of the Mogollon and Ancestral Pueblo peoples cultures.[37]:52
+
+By the time of European contact in the 16th century, the region was settled by the villages of the Pueblo peoples and groups of Navajo, Apache, and Ute.[36]:6,48
+
+Francisco Vásquez de Coronado assembled an enormous expedition at Compostela in 1540–1542 to explore and find the mythical Seven Golden Cities of Cibola as described by Fray Marcos de Niza.[37]:19–24 The name New Mexico was first used by a seeker of gold mines named Francisco de Ibarra, who explored far to the north of New Spain in 1563 and reported his findings as being in "a New Mexico".[38] Juan de Oñate officially established the name when he was appointed the first governor of the new Province of New Mexico in 1598.[37]:36–37 The same year, he founded the San Juan de los Caballeros colony, the first permanent European settlement in the future state of New Mexico,[39] on the Rio Grande near Ohkay Owingeh Pueblo.[37]:37 Oñate extended El Camino Real de Tierra Adentro, Royal Road of the Interior, by 700 miles (1,100 km) from Santa Bárbara, Chihuahua, to his remote colony.[40]:49
+
+The settlement of Santa Fe was established at the foot of the Sangre de Cristo Mountains, the southernmost subrange of the Rocky Mountains, around 1608.[40]:182 The city, along with most of the settled areas of the state, was abandoned by the Spanish for 12 years (1680–92)[41] as a result of the successful Pueblo Revolt, the only successful revolt against European expansion by Native Americans.[42] After the death of the Pueblo leader Popé, Diego de Vargas restored the area to Spanish rule.[37]:68–75 While developing Santa Fe as a trade center, the returning settlers founded Albuquerque in 1706 from existing surrounding communities,[37]:84 naming it for the viceroy of New Spain, Francisco Fernández de la Cueva, 10th Duke of Alburquerque.[43]
+
+As a part of New Spain, the claims for the province of New Mexico passed to independent Mexico in 1821 following the Mexican War of Independence.[37]:109 The Republic of Texas claimed the portion east of the Rio Grande when it seceded from Mexico in 1836, when it incorrectly assumed the older Hispanic settlements of the upper Rio Grande were the same as the newly established Mexican settlements of Texas. Texas's only attempt to establish a presence or control in the claimed territory was the failed Texan Santa Fe Expedition. Their entire army was captured and jailed by Hispanic New Mexico militia.
+
+At the turn of the 19th century, the extreme northeastern part of New Mexico, north of the Canadian River and east of the Sangre de Cristo Mountains, was still claimed by France, which sold it in 1803 as part of the Louisiana Purchase. When the Louisiana Territory was admitted as a state in 1812, the U.S. reclassified it as part of the Missouri Territory. The region (along with territory that makes up present-day southeastern Colorado, the Texas and Oklahoma Panhandles, and southwestern Kansas) was ceded to Spain under the Adams-Onis Treaty in 1819.
+
+By 1800, the population of New Mexico had reached 25,000.[44]
+
+Following the victory of the United States in the Mexican–American War (1846–48), under the Treaty of Guadalupe Hidalgo in 1848, Mexico ceded its northern holdings including the territories of California, Texas, and New Mexico, to the United States of America.[37]:132 The United States vowed to accept the residents' claims to their lands and to accept them as full citizens with rights of suffrage.
+
+After Texas was admitted as a state to the Union, it continued to claim a northeastern portion of New Mexico. It was forced by the US government to drop these claims, in the Compromise of 1850, Texas ceded these claims to the United States of the area in New Mexico lying east of the Rio Grande, in exchange for $10 million from the federal government.[37]:135
+
+Congress established the separate New Mexico Territory in September 1850.[45] It included most of the present-day states of Arizona and New Mexico, and part of Colorado. When the boundary was fixed, a surveyor's error awarded the Permian Basin to the State of Texas.[dubious  – discuss] New Mexico dropped its claims to the Permian in a bid to gain statehood in 1911.
+
+In 1853, the United States acquired the mostly desert southwestern bootheel of the state and southern Arizona south of the Gila River in the Gadsden Purchase. It wanted to control lands needed for the right-of-way to encourage construction of a transcontinental railroad.[37]:136
+
+New Mexico played a role in the Trans-Mississippi Theater of the American Civil War. Both Confederate and Union governments claimed ownership and territorial rights over New Mexico Territory. In 1861, the Confederacy claimed the southern tract as its own Arizona Territory and waged the ambitious New Mexico Campaign in an attempt to control the American Southwest and open up access to Union California. Confederate power in the New Mexico Territory was effectively broken after the Battle of Glorieta Pass in 1862. However, the Confederate territorial government continued to operate out of Texas, and Confederate troops marched under the Arizona flag until the end of the war. Additionally, more than 8,000 men from New Mexico Territory served in the Union Army.[46]
+
+In the late 19th century, the majority of officially European-descended residents in New Mexico were ethnic Mexicans, many of whom had deep roots in the area from early Spanish colonial times. Politically, they still controlled most of the town and county offices through area elections, and wealthy sheepherder families commanded considerable influence. The Anglo-Americans tended to have more ties to the territorial governor and judges, who were appointed by officials out of the region. The two groups struggled for power and the future of the territory. The Anglo minority was "outnumbered, but well-organized and growing".[47] Anglo-Americans made distinctions between the wealthy Mexicans and poor, ill-educated laborers.
+
+The United States Congress admitted New Mexico as the 47th state on January 6, 1912.[37]:166
+
+European-American settlers in the state had an uneasy relationship with the large Native American tribes, most of whose members lived on reservations at the beginning of the 20th century. Although Congress passed a law in 1924 that granted all Native Americans U.S. citizenship, as well as the right to vote in federal and state elections, New Mexico was among several states with Jim Crow laws, e.g. those who do not pay taxes cannot vote.[48]
+
+A major oil discovery in 1928 brought wealth to the state, especially Lea County and the town of Hobbs. The town was named after James Hobbs, a homesteader there in 1907.[49] The Midwest State No. 1 well, begun in late 1927 with a standard cable-tool drilling rig, revealed the first signs of oil from the Hobbs field on June 13, 1928. Drilled to 4,330 feet and completed a few months later, the well produced 700 barrels of oil per day on state land. The Midwest Refining Company's Hobbs well produced oil until 2002. The New Mexico Bureau of Mines and Mineral Resources called it "the most important single discovery of oil in New Mexico's history".[50]
+
+During World War II, the first atomic bombs were designed and manufactured at Los Alamos, a site developed by the federal government specifically to support a high-intensity scientific effort to rapidly complete research and testing of this weapon. The first bomb was tested at Trinity site in the desert between Socorro and Alamogordo on what is now White Sands Missile Range.[37]:179–180
+
+Native Americans from New Mexico fought for the United States in both the First and Second World Wars. Veterans were disappointed to return and find their civil rights limited by state discrimination. In Arizona and New Mexico, veterans challenged state laws or practices prohibiting them from voting. In 1948, after veteran Miguel Trujillo, Sr. of Isleta Pueblo was told by the county registrar that he could not register to vote, he filed suit against the county in federal district court. A three-judge panel overturned as unconstitutional New Mexico's provisions that Indians who did not pay taxes (and could not document if they had paid taxes) could not vote.[48] Judge Phillips wrote:
+
+Any other citizen, regardless of race, in the State of New Mexico who has not paid one cent of tax of any kind or character, if he possesses the other qualifications, may vote. An Indian, and only an Indian, in order to meet the qualifications to vote must have paid a tax. How you can escape the conclusion that makes a requirement with respect to an Indian as a qualification to exercise the elective franchise and does not make that requirement with respect to the member of any race is beyond me.[48]
+
+New Mexico has received large amounts of federal government spending on major military and research institutions in the state. It is home to three Air Force bases, White Sands Missile Range, and the federal research laboratories Los Alamos National Laboratory and Sandia National Laboratories. The state's population grew rapidly after World War II, growing from 531,818 in 1940 to 1,819,046 in 2000.[53] Both residents and businesses moved to the state; some northerners came at first for the mild winters; others for retirement.
+
+On May 22, 1957, a B-36 accidentally dropped a nuclear bomb 4.5 miles from the control tower while landing at Kirtland Air Force Base. (Only its conventional "trigger" detonated.)[54][55]
+
+In the late 20th century, Native Americans were authorized by federal law to establish gaming casinos on their reservations under certain conditions, in states which had authorized such gaming. Such facilities have helped tribes close to population centers to generate revenues for reinvestment in economic development and welfare of their peoples.
+
+In the 21st century, employment growth areas in New Mexico include electronic circuitry, scientific research, call centers, and Indian casinos.[56]
+
+The United States Census Bureau estimates that the population of New Mexico was 2,096,829 on July 1, 2019, a 1.83% increase since the 2010 census.[52] The 2000 census recorded the population of New Mexico to be 1,819,046; ten years later it was 2,059,179—an 11.7% increase.[57]
+
+Of the people residing in New Mexico 51.4% were born there; 37.9% were born in another state; 1.1% were born in Puerto Rico, U.S. Island areas, or abroad to American parent(s); and 9.7% were foreign born.[58]
+
+As of May 1, 2010, 7.5% of New Mexico's population was reported as under 5 years of age, 25% under 18, and 13% were 65 or older.[59]
+
+As of 2000, 8% of the residents of the state were foreign-born.[59]
+
+Among U.S. states, New Mexico has the highest percentage of Hispanic ancestry, at 47% (as of July 1, 2012). This classification covers people of very different cultures and histories, including descendants of Spanish colonists with deep roots in the region, and recent immigrants from a variety of nations in Latin America, each with their own cultures.
+
+According to the United States Census Bureau Model-based Small Area Income and Poverty Estimates, the number of persons in poverty has increased to 400,779 (19.8% of the population) persons in 2010 from 2000. At that time, the estimated number of persons in poverty was recorded at 309,193 (17.3% of the population). The latest available data for 2014 estimate the number of persons in poverty at 420,388 (20.6% of the population).[57]
+
+Note: Births in table do not add up, because Hispanics are counted both by their ethnicity and by their race, giving a higher overall number.
+
+New Mexico is a majority-minority state.[67]
+
+The U.S. Census Bureau estimated that 48% of the total 2015 population was Hispanic or Latino of any race, the highest of any state. The majority of Hispanics in New Mexico claim to be descendants of Spanish colonists who settled here during the 16th, 17th, and 18th centuries. They speak New Mexican Spanish or English at home.[59]
+
+The state also has a large Native American population, second in percentage behind that of Alaska.[59][68] The 2018 racial composition of the population was estimated to be:[69]
+
+According to the United States Census Bureau, 1.5% of the population identifies as multiracial/mixed-race, a population larger than both the Asian and NHPI population groups.[59] In 2008, New Mexico had the highest percentage (47%) of Hispanics (of any race) of any state,[59] with 83% native-born and 17% foreign-born.[73]
+
+According to the 2000 United States Census,[74]:6
+the most commonly claimed ancestry groups in New Mexico were:
+
+According to the 2010 U.S. Census, 28.45% of the population age 5 and older speak Spanish at home, while 3.50% speak Navajo.[75] Some speakers of New Mexican Spanish are descendants of Spanish settlers who arrived in New Mexico in the 16th, 17th, and 18th centuries.[76] While it is a common folk belief that New Mexican Spanish is an archaic form of 17th-century Castilian Spanish, and archaisms do exist, research reveals that traditional New Mexican Spanish "is neither more Iberian nor more archaic than other New World Spanishes".[77][78]
+
+Besides Navajo, which is also spoken in Arizona, a few other Native American languages are spoken by smaller groups in New Mexico, most of which are only spoken in the state. Native New Mexican languages include Mescalero Apache, Jicarilla Apache, Tewa, Southern Tiwa, Northern Tiwa, Towa, Keres (Eastern and Western), and Zuni. Mescalero and Jicarilla Apache are closely related Southern Athabaskan languages, and both are also related to Navajo. Tewa, the Tiwa languages, and Towa belong to the Kiowa-Tanoan language family, and thus all descend from a common ancestor. Keres and Zuni are language isolates, and have no relatives outside of New Mexico.
+
+The original state constitution of 1912 provided for a bilingual government with laws being published in both English and Spanish;[79] this requirement was renewed twice, in 1931 and 1943.[80] Nonetheless, the constitution does not declare any language as "official".[81] While Spanish was permitted in the legislature until 1935, all state officials are required to have a good knowledge of English. Cobarrubias and Fishman therefore argue that New Mexico cannot be considered a bilingual state as not all laws are published in both languages.[80] Others, such as Juan Perea, claim that the state was officially bilingual until 1953.[82]
+
+With regard to the judiciary, witnesses have the right to testify in either of the two languages, and monolingual speakers of Spanish have the same right to be considered for jury duty as do speakers of English.[81][83] In public education, the state has the constitutional obligation to provide bilingual education and Spanish-speaking instructors in school districts where the majority of students are hispanophone.[81]
+
+In 1995, the state adopted an official bilingual song, "New Mexico – Mi Lindo Nuevo México".[84]:75,81 In 1989, New Mexico became the first state to officially adopt the English Plus resolution,[85] and in 2008, the first to officially adopt a Navajo textbook for use in public schools.[86]
+
+According to Association of Religion Data Archives (ARDA), the largest denominations in 2010 were the Catholic Church with 684,941; the Southern Baptist Convention with 113,452; The Church of Jesus Christ of Latter-day Saints with 67,637, and the United Methodist Church with 36,424 adherents.[88] According to a 2008 survey by the Pew Research Center, the most common self-reported religious affiliation of New Mexico residents are mentioned in reference.[citation needed]
+
+Within the hierarchy of the Catholic Church, New Mexico belongs to the Ecclesiastical Province of Santa Fe. New Mexico has three dioceses, one of which is an archdiocese:[89]
+Archdiocese of Santa Fe,
+Diocese of Gallup,
+Diocese of Las Cruces.
+
+Oil and gas production, tourism, and federal government spending are important drivers of the state economy. State government has an elaborate system of tax credits and technical assistance to promote job growth and business investment, especially in new technologies.
+
+In 2010, New Mexico's Gross Domestic Product was $80 billion, and an estimated $85 billion for 2013.[90] In 2007, the per capita personal income was $31,474 (rank 43rd in the nation).[91] In 2005, the percentage of persons below the poverty level was 18.4%.[92]
+The New Mexico Tourism Department estimates that in Fiscal Year 2006, the travel industry in New Mexico generated expenditures of $6.5 billion.[93] As of April 2012[update], the state's unemployment rate was 7.2%.[94] During the late-2000s recession, New Mexico's unemployment rate peaked at 8.0% for the period June–October 2010.[95]
+
+New Mexico is the third-largest crude oil and ninth-largest natural gas producer in the United States.[96] The Permian and San Juan Basins, which are located partly in New Mexico, account for some of these natural resources. In 2000 the value of oil and gas produced was $8.2 billion,[97] and in 2006, New Mexico accounted for 3.4% of the crude oil, 8.5% of the dry natural gas, and 10.2% of the natural gas liquids produced in the United States.[98] However, the boom in hydraulic fracturing and horizontal drilling beginning in the mid-2010s led to a large increase in the production of crude oil from the Permian Basin and other U.S. sources; these developments allowed the United States to again become the world's largest producer of crude oil, in 2018.[99][100][101][102] New Mexico's oil and gas operations contribute to the state's above-average release of the greenhouse gas methane, including from a national methane hot spot in the Four Corners area.[103][104][105][106]
+
+Federal government spending is a major driver of the New Mexico economy. In 2005, the federal government spent $2.03 on New Mexico for every dollar of tax revenue collected from the state. This rate of return is higher than any other state in the Union.[107]
+
+Many of the federal jobs relate to the military; the state hosts three air force bases (Kirtland Air Force Base, Holloman Air Force Base, and Cannon Air Force Base); a testing range (White Sands Missile Range); and an army proving ground (Fort Bliss's McGregor Range). A May 2005 estimate by New Mexico State University is that 11.65% of the state's total employment arises directly or indirectly from military spending.[108]
+Other federal installations include the technology labs of Los Alamos National Laboratory and Sandia National Laboratories.
+
+New Mexico provides a number of economic incentives to businesses operating in the state, including various types of tax credits and tax exemptions. Most of the incentives are based on job creation.[109]
+
+New Mexico law allows governments to provide land, buildings, and infrastructure to businesses to promote job creation. Several municipalities have imposed an Economic Development Gross Receipts Tax (a form of Municipal Infrastructure GRT) that is used to pay for these infrastructure improvements and for marketing their areas.[110]
+
+The state provides financial incentives for film production.[111][112] The New Mexico Film Office estimated at the end of 2007 that the incentive program had brought more than 85 film projects to the state since 2003 and had added $1.2 billion to the economy.[113]
+
+Since 2008, personal income tax rates for New Mexico have ranged from 1.7% to 4.9%, within four income brackets.[114] As of 2007, active-duty military salaries are exempt from state income tax.[115] New Mexico is one of the largest tax havens in the U.S., offering numerous economic incentives and tax breaks on personal and corporate income.[116][117] It does not have inheritance tax, estate tax, or sales taxes.[114][118]
+
+New Mexico imposes a Gross Receipts Tax (GRT) on many transactions, which may even include some governmental receipts. This resembles a sales tax but, unlike the sales taxes in many states, it applies to services as well as tangible goods. Normally, the provider or seller passes the tax on to the purchaser, however legal incidence and burden apply to the business, as an excise tax. GRT is imposed by the state and there may an additional locality component to produce a total tax rate.[119] As of July 1, 2013 the combined tax rate ranged from 5.125% to 8.6875%.[120]
+
+Property tax is imposed on real property by the state, by counties, and by school districts. In general, personal-use personal property is not subject to property taxation. On the other hand, property tax is levied on most business-use personal property. The taxable value of property is 1/3 of the assessed value. A tax rate of about 30 mills is applied to the taxable value, resulting in an effective tax rate of about 1%. In the 2005 tax year, the average millage was about 26.47 for residential property, and 29.80 for non-residential property. Assessed values of residences cannot be increased by more than 3% per year unless the residence is remodeled or sold. Property tax deductions are available for military veterans and heads of household.[121]
+
+New Mexico has long been an important corridor for trade and migration. The builders of the ruins at Chaco Canyon also created a radiating network of roads from the mysterious settlement.[122] Chaco Canyon's trade function shifted to Casas Grandes in the present-day Mexican state of Chihuahua, however, north–south trade continued. The pre-Columbian trade with Mesoamerican cultures included northbound exotic birds, seashells and copper. Turquoise, pottery, and salt were some of the goods transported south along the Rio Grande. Present-day New Mexico's pre-Columbian trade is especially remarkable for being undertaken on foot. The north–south trade route later became a path for colonists with horses arriving from New Spain as well as trade and communication. The route was called El Camino Real de Tierra Adentro.[123]
+
+The Santa Fe Trail was the 19th-century territory's vital commercial and military highway link to the Eastern United States.[124] All with termini in Northern New Mexico, the Camino Real, the Santa Fe Trail and the Old Spanish Trail are all recognized as National Historic Trails. New Mexico's latitude and low passes made it an attractive east–west transportation corridor.[125] As a territory, the Gadsden Purchase increased New Mexico's land area for the purpose of the construction of a southern transcontinental railroad, that of the Southern Pacific Railroad. Another transcontinental railroad was completed by the Atchison, Topeka and Santa Fe Railway. The railroads essentially replaced the earlier trails but brought on a population boom. Early transcontinental auto trails later crossed the state bringing more migrants. Railroads were later supplemented or replaced by a system of highways and airports. Today, New Mexico's Interstate Highways approximate the earlier land routes of the Camino Real, the Santa Fe Trail and the transcontinental railroads.
+
+New Mexico has only three Interstate Highways. In Albuquerque, I-25 and I-40 meet at a stack interchange called The Big I.
+
+Interstate 10 travels in the southwest portion of New Mexico starting from the Arizona stateline near Lordsburg to the Texas stateline south past Las Cruces, near El Paso, Texas.
+
+Interstate 25 is a major north–south interstate highway starting from Las Cruces, New Mexico to the Colorado stateline near Raton.
+
+Interstate 40 is a major east–west interstate highway starting from the Arizona stateline west of Gallup to the Texas stateline east from Tucumcari.
+
+New Mexico currently has 15 United States Highways. This includes US 54, US 56, US 60, US 62, US 64, US 70, US 82, US 84, US 87, US 160, US 180, US 285, US 380, US 491, and US 550.
+
+US 66, The Mother Road, was replaced by I-40 in 1985. US 85 is currently unsigned by the NMDOT, but the AASHTO still recognize it. It runs in the same trace with I-10 and I-25. US 666, The Devils Highway, was replaced by US 491 in 2003 because the number "666" is the "Number of the Beast".
+
+New Mexico has had a problem with drunk driving, but that has lessened. According to the Los Angeles Times, for years the state had the highest alcohol-related crash rates in the U.S., but ranked 25th in alcohol-related fatal crash rates, as of July 2009[update].[126]
+
+The automobile changed the character of New Mexico, marking the start of large-scale immigration to the state from elsewhere in the United States. Settlers moving West during the Great Depression and post-World War II American culture immortalized the National Old Trails Highway, later U.S. Route 66. Today, New Mexico relies heavily upon the automobile for transportation.
+
+New Mexico had 59,927 route miles of highway as of 2000[update], of which 7,037 receive federal aid.[127] In that same year there were 1,003 miles (1,614 km) of freeways, of which 1000 were the route miles of Interstate Highways 10, 25 and 40.[128] The former number has increased with the upgrading of roads near Pojoaque, Santa Fe and Las Cruces to freeways. The highway traffic fatality rate was 1.9 fatalities per million miles traveled in 2000, the 13th highest rate among U.S. states.[129] Notable bridges include the Rio Grande Gorge Bridge near Taos. As of 2001[update], 703 highway bridges, or one percent, were declared "structurally deficient" or "structurally obsolete".[130]
+
+Rural and intercity public transportation by road is provided by Americanos USA, LLC, Greyhound Lines and several government operators.
+
+The New Mexico Rail Runner Express is a commuter rail system serving the metropolitan area of Albuquerque, New Mexico. It began operation on July 14, 2006.[131] The system runs from Belen to downtown Santa Fe. Larger cities in New Mexico typically have some form of public transportation by road; ABQ RIDE is the largest such system in the state.[132]
+
+There were 2,354 route miles of railroads in the year 2000; this number increased with the opening of the Rail Runner's extension to Santa Fe.[133] In addition to local railroads and other tourist lines, the state jointly owns and operates a heritage narrow-gauge steam railroad, the Cumbres and Toltec Scenic Railway, with the state of Colorado. Narrow gauge railroads once connected many communities in the northern part of the state, from Farmington to Santa Fe.[134]:110 No fewer than 100 railroads of various names and lineage have operated in the jurisdiction at some point.[134]:8 New Mexico's rail transportation system reached its height in terms of length following admission as a state; in 1914 eleven railroads operated 3124 route miles.[134]:10
+
+Railroad surveyors arrived in New Mexico in the 1850s.[135] The first railroads incorporated in 1869.[134]:9 The first operational railroad, the Atchison, Topeka & Santa Fe Railway (ATSF), entered the territory by way of the lucrative and contested Raton Pass in 1878. It eventually reached El Paso, Texas in 1881 and with the Southern Pacific Railroad created the nation's second transcontinental railroad with a junction at Deming. The Southern Pacific Railroad entered the territory from the Territory of Arizona in 1880.[134]:9, 18, 58–59[135] The Denver & Rio Grande Railway, who would generally use narrow gauge equipment in New Mexico, entered the territory from Colorado and began service to Española on December 31, 1880.[134]:95–96[135] These first railroads were built as long-distance corridors, later railroad construction also targeted resource extraction.[134]:8–11
+
+New Mexico is served by two class I railroads, the BNSF Railway and the Union Pacific Railroad. Combined, they operate 2,200 route miles of railway in the state.[133]
+
+A commuter rail operation, the New Mexico Rail Runner Express, connects the state's capital, its largest city, and other communities.[136] The privately operated state owned railroad began operations in July 2006.[131] The BNSF Railway's entire line from Belen to Raton, New Mexico was sold to the state, partially for the construction of phase II of this operation, which opened in December 2008.[137] Phase II of Rail Runner extended the line northward to Santa Fe from the Sandoval County station, the northernmost station under Phase I service. The service now connects Santa Fe, Sandoval, Bernalillo, and Valencia counties. The trains connect Albuquerque's population base and central business district to downtown Santa Fe with up to eight roundtrips in a day. The section of the line running south to Belen is served less frequently.[138] Rail Runner operates scheduled service seven days per week.[139]
+
+With the rise of rail transportation many settlements grew or were founded and the territory became a tourist destination. As early as 1878, the ATSF promoted tourism in the region with emphasis on Native American imagery.[140]:64 Named trains often reflected the territory they traveled: Super Chief, the streamlined successor to the Chief;[140] Navajo, an early transcontinental tourist train; and Cavern, a through car operation connecting Clovis and Carlsbad (by the early 1950s as train 23–24),[134]:49–50[141]:51 were some of the named passenger trains of the ATSF that connoted New Mexico.
+
+Passenger train service once connected nine of New Mexico's present ten most populous cities (the exception is Rio Rancho), while today passenger train service connects two: Albuquerque and Santa Fe.[136] With the decline of most intercity rail service in the United States in the late 1960s, New Mexico was left with minimal services. No less than six daily long-distance roundtrip trains supplemented by many branch line and local trains served New Mexico in the early 1960s. Declines in passenger revenue, but not necessarily ridership, prompted many railroads to turn over their passenger services in truncated form to Amtrak, a state owned enterprise. Amtrak, also known as the National Passenger Railroad Corporation, began operating the two extant long-distance routes in May 1971.[134][140][141] Resurrection of passenger rail service from Denver to El Paso, a route once plied in part by the ATSF's El Pasoan,[141]:37 has been proposed over the years. As early as the 1980s, former Governor Toney Anaya proposed building a high-speed rail line connecting the two cities with New Mexico's major cities.[142] Front Range Commuter Rail is a project to connect Wyoming and New Mexico with high-speed rail.[143]
+
+Amtrak's Southwest Chief passes through daily at stations in Gallup, Albuquerque, Lamy, Las Vegas, and Raton, offering connections to Los Angeles, Chicago and intermediate points.[144] The Southwest Chief is a fast Amtrak long-distance train, being permitted a maximum speed of 90 mph (140 km/h) in various places on the tracks of the BNSF Railway.[145] It also operates on New Mexico Rail Runner Express trackage. The Southwest Chief is the successor to the Super Chief and El Capitan.[141]:115 The streamliner Super Chief, a favorite of early Hollywood stars, was one of the most famous named trains in the United States and one of the most esteemed for its luxury and exoticness—train cars were named for regional Native American tribes and outfitted with the artwork of many local artists—but also for its speed: as few as 39 hours 45 minutes westbound.[140]
+
+The Sunset Limited makes stops three times a week in both directions at Lordsburg, and Deming, serving Los Angeles, New Orleans and intermediate points.[146] The Sunset Limited is the successor to the Southern Pacific Railroad's train of the same name and operates exclusively on Union Pacific trackage in New Mexico.
+
+The Albuquerque International Sunport is the state's primary port of entry for air transportation.
+
+Upham, near Truth or Consequences, is the location of the world's first operational and purpose-built commercial spaceport, Spaceport America.[147][148][149] Rocket launches began in April 2007.[149] It is undeveloped and has one tenant, UP Aerospace, launching small payloads.[150] Virgin Galactic, a space tourism company, plans to make this their primary operating base.[148][151]
+
+The Constitution of New Mexico established New Mexico's governmental structure. The executive branch of government is fragmented as outlined in the state constitution. The executive is composed of the Governor and other statewide elected officials including the Lieutenant Governor (elected on the same ticket as the Governor), Attorney General, Secretary of State, State Auditor, State Treasurer, and Commissioner of Public Lands. The governor appoints a cabinet who lead agencies statutorily designated under their jurisdiction. The New Mexico Legislature consists of the House of Representatives and Senate. The judiciary is composed of the New Mexico Supreme Court and lower courts. There is also local government, consisting of counties, municipalities and special districts.[152]
+
+Current Governor Michelle Lujan Grisham (D) and Lieutenant Governor Howie Morales (D) were first elected in 2018. Terms for both the Governor and Lieutenant Governor expire in January 2023. Governors serve a term of four years, and may seek re-election for one additional term (limit of two terms). Other constitutional officers, all of whose terms also expire in January 2023, include Secretary of State Maggie Toulouse Oliver (D),[153] Attorney General Hector Balderas (D),[154] State Auditor Brian Colón (D),[155] State Land Commissioner Stephanie Garcia Richard (D),[156] and State Treasurer Tim Eichenberg (D).[157]
+
+Currently, both chambers of the New Mexico State Legislature have Democratic majorities. There are 26 Democrats and 16 Republicans in the Senate, and 47 Democrats and 23 Republicans in the House of Representatives.
+
+New Mexico's members of the United States Senate are Democrats Martin Heinrich and Tom Udall. Democrats represent the state's three United States House of Representatives congressional districts with Deb Haaland, Xochitl Torres Small, and Ben Ray Luján representing the first, second, and third districts respectively.[159][160] See New Mexico congressional map.
+
+New Mexico has traditionally been considered a swing state, whose population has favored both Democratic and Republican presidential candidates, but it has become more of a Democratic stronghold beginning with the presidential election of 2008. The governor is Michelle Lujan Grisham (D), who succeeded Susana Martinez (R) on January 1, 2019 after she served two terms as governor from 2011 to 2019. Gary Johnson served as governor from 1995 to 2003. Johnson served as a Republican, but in 2012 and 2016, he ran for president from the Libertarian Party. In previous presidential elections, Al Gore carried the state (by 366 votes) in 2000; George W. Bush won New Mexico's five electoral votes in 2004, and the state's electoral votes were won by Barack Obama and Hillary Clinton in 2008, 2012, and 2016. Since achieving statehood in 1912, New Mexico has been carried by the national popular vote victor in every presidential election of the past 104 years, except 1976, when Gerald Ford won the state by 2%, but lost the national popular vote by 2%.[161] It has also awarded its electoral votes to the candidate who would ultimately win, with the exception of 1976, 2000, and 2016.
+
+Democrats in the state are usually strongest in the Santa Fe Area, various areas of the Albuquerque Metro Area (such as the southeast and central areas, including the affluent Nob Hill neighborhood and the vicinity of the University of New Mexico), Northern and West Central New Mexico, and most of the Native American reservations, particularly the Navajo Nation. Republicans have traditionally had their strongholds in the eastern and southern parts of the state, the Farmington area, Rio Rancho, and the newly developed areas in the Northwest mesa. Albuquerque's Northeast Heights have historically leaned Republican, but have become a key swing area for Democrats in recent election cycles. While registered Democrats outnumber registered Republicans by nearly 200,000, New Mexico voters have favored moderate to conservative candidates of both parties at the state and federal levels.
+
+New Mexico abolished its death penalty statute, though not retroactively, effective July 1, 2009. This means individuals on New Mexico's Death Row can still be executed. On March 18, 2009, then Governor Bill Richardson signed the law abolishing the death penalty in New Mexico following the assembly and senate vote the week before, thus becoming the 15th U.S. state to abolish the penalty.[162]
+
+On gun control, New Mexico arguably has some of the least restrictive firearms laws in the country. State law pre-empts all local gun control ordinances. New Mexico residents may purchase any firearm deemed legal under federal law. There are no waiting periods under state law for picking up a firearm after it has been purchased, and there are no restrictions on magazine capacity. Additionally, New Mexico is a "shall-issue" state for concealed carry permits.
+
+Before December 2013, New Mexico law neither explicitly allowed nor prohibited same-sex marriage. Policy concerning the issuance of marriage licenses to same-sex couples was determined at the county level; that is, some county clerks issued marriage licenses to same-sex couples while others did not. In December 2013, the New Mexico Supreme Court issued a unanimous ruling directing all county clerks to issue marriage licenses to same-sex couples, thereby making New Mexico the 17th state to recognize same-sex marriage at the statewide level.
+
+Due to its relatively low population, in combination with numerous federally funded research facilities, New Mexico had the highest concentration of PhD holders of any state in 2000.[163] Despite this, the state routinely ranks near the bottom in surveys of the quality of primary and secondary school education.[164] In a landmark decision, a state judge ruled in 2018 that "New Mexico is violating the constitutional rights of at-risk students by failing to provide them with sufficient education,"[165] and ordered that the governor and Legislature provide an adequate system by April 2019.[165][166]
+
+New Mexico has a higher concentration of persons who do not finish high school or have some college without a degree than the nation as a whole. For the state, 23.9% of people over 25 have gone to college but not earned a degree.[57] This is compared with 21.0% of the nation as a whole according to United States Census Bureau 2014 American Community Survey estimates.[167] Los Alamos County has the highest number percent of post secondary degree holders of any county in New Mexico with 38.7% of the population (4,899 persons) estimated by the 2010-2014 American Community Survey.[168]
+
+The New Mexico Public Education Department oversees the operation of primary and secondary schools; individual school districts directly operate and staff said schools.
+
+New Mexico is one of eight states that funds college scholarships through the state lottery.[169][170][171] The state of New Mexico requires that the lottery put 30% of its gross sales into the scholarship fund.[172]
+The scholarship is available to residents who graduated from a state high school, and attend a state university full-time while maintaining a 2.5 GPA or higher.[173]
+It covered 100% of tuition when it was first instated in 1996,[174] decreased to 90%, then dropped to 60% in 2017.[170] The value slightly increased in 2018, and new legislation was passed to outline what funds are available per type of institution.[174]
+
+Zimmerman Library at The University of New Mexico
+
+Zuhl Library at New Mexico State University
+
+Walkway outside Golden Library at Eastern New Mexico University
+
+Donnelly Library at New Mexico Highlands University
+
+With a Native American population of 134,000 in 1990,[175] New Mexico still ranks as an important center of Native American culture. Both the Navajo and Apache share Athabaskan origin. The Apache and some Ute live on federal reservations within the state. With 16 million acres (6,500,000 ha), mostly in neighboring Arizona, the reservation of the Navajo Nation ranks as the largest in the United States. The prehistorically agricultural Pueblo Indians live in pueblos scattered throughout the state. Almost half of New Mexicans claim Hispanic origin; many are descendants of colonial settlers. They settled in the state's northern portion. Most of the Mexican immigrants reside in the southern part of the state. Also 10-15% of the population, mainly in the north, may contain Hispanic Jewish ancestry.[citation needed]
+
+Many New Mexicans speak a unique dialect of Spanish. Because of the historical isolation of New Mexico from other speakers of the Spanish language, some of the vocabulary of New Mexican Spanish is unknown to other Spanish speakers. It uses numerous Native American words for local features and includes anglicized words that express American concepts and modern inventions.
+
+Albuquerque has the New Mexico Museum of Natural History and Science, the National Hispanic Cultural Center, and the National Museum of Nuclear Science & History, as well as hosts the famed annual Albuquerque International Balloon Fiesta every fall.
+
+The earliest New Mexico artists whose work survives today are the Mimbres Indians, whose black and white pottery could be mistaken for modern art, except for the fact that it was produced before 1130 CE. See Mimbres culture. Many examples of this work can be seen at the Deming Luna Mimbres Museum[176] and at the Western New Mexico University Museum.[177]
+
+A large artistic community thrives in Santa Fe, and has included such people as Bruce Nauman, Richard Tuttle, John Connell and Steina Vasulka. The capital city has several art museums, including the New Mexico Museum of Art, Museum of Spanish Colonial Art, Museum of International Folk Art, Museum of Indian Arts and Culture, Museum of Contemporary Native Arts, SITE Santa Fe and others. Colonies for artists and writers thrive, and the small city teems with art galleries. In August, the city hosts the annual Santa Fe Indian Market, which is the oldest and largest juried Native American art showcase in the world. Performing arts include the renowned Santa Fe Opera which presents five operas in repertory each July to August, the Santa Fe Chamber Music Festival held each summer, and the restored Lensic Theater a principal venue for many kinds of performances. Santa Fe is also home to Frogville Records, an indie record label. The weekend after Labor Day boasts the burning of Zozobra, a 50 ft (15 m) marionette, during Fiestas de Santa Fe.
+
+Art is also a frequent theme in Albuquerque, New Mexico's largest city. The National Hispanic Cultural Center has held hundreds of performing arts events, art showcases, and other events related to Spanish culture in New Mexico and worldwide in the centerpiece Roy E Disney Center for the Performing Arts or in other venues at the 53 acre facility. New Mexico residents and visitors alike can enjoy performing art from around the world at Popejoy Hall on the campus of the University of New Mexico. Popejoy Hall hosts singers, dancers, Broadway shows, other types of acts, and Shakespeare.[178] Albuquerque also has the unique and memorable KiMo Theater built in 1927 in the Pueblo Revival Style architecture. The KiMo presents live theater and concerts as well as movies and simulcast operas.[179] In addition to other general interest theaters, Albuquerque also has the African American Performing Arts Center and Exhibit Hall which showcases achievements by people of African descent[180] and the Indian Pueblo Cultural Center which highlights the cultural heritage of the First Nations people of New Mexico.[181]
+
+New Mexico holds strong to its Spanish heritage. Old Spanish traditions such zarzuelas and flamenco are popular in New Mexico.[182][183] Flamenco dancer and native New Mexican María Benítez founded the Maria Benítez Institute for Spanish Arts "to present programs of the highest quality of the rich artistic heritage of Spain, as expressed through music, dance, visual arts, and other art forms". There is also the Festival Flamenco Internacional de Alburquerque held each year in which native Spanish and New Mexican flamenco dancers perform at the University of New Mexico.
+
+In the mid-20th century there was a thriving Hispano school of literature and scholarship being produced in both English and Spanish. Among the more notable authors were: Angélico Chávez, Nina Otero-Warren, Fabiola Cabeza de Baca, Aurelio Espinosa, Cleofas Jaramillo, Juan Bautista Rael, and Aurora Lucero-White Lea. As well, writer D. H. Lawrence lived near Taos in the 1920s, at the D. H. Lawrence Ranch, where there is a shrine said to contain his ashes.
+
+New Mexico's strong Spanish, Native American, and Wild West frontier motifs have provided material for many authors in the state, including internationally recognized Rudolfo Anaya and Tony Hillerman.[184]
+
+Silver City, in the southwestern mountains of the state, was originally a mining town, and at least one nearby mine still operates. It is perhaps better known now as the home of or exhibition center for large numbers of artists, visual and otherwise.[185] Another former mining town turned art haven is Madrid, New Mexico.[186] It was brought to national fame as the filming location for the movie Wild Hogs in 2007. The City of Las Cruces, in southern New Mexico, has a museum system that is affiliated with the Smithsonian Institution Affiliations Program.[187] Las Cruces also has a variety of cultural and artistic opportunities for residents and visitors.[188]
+
+Aside from the aforementioned Wild Hogs, other movies filmed in New Mexico include Sunshine Cleaning and Vampires.
+
+The various seasons of the A&E/Netflix series Longmire have been filmed in several New Mexico locations, including Las Vegas, Santa Fe, Eagle Nest, and Red River.[189]
+
+The widely acclaimed TV show Breaking Bad and its spin-off Better Call Saul were both set and filmed in and around Albuquerque.[190]
+
+No major league professional sports teams are based in New Mexico, but the Albuquerque Isotopes are a Pacific Coast League Triple-A baseball affiliate of the MLB Colorado Rockies. New Mexico is home to several baseball teams of the Pecos League: the Roswell Invaders, Ruidoso Osos, Santa Fe Fuego and the White Sands Pupfish. The Duke City Gladiators of the Indoor Football League (IFL) plays their home games at Tingley Coliseum in Albuquerque. New Mexico United, also based in Albuquerque, began play in the second tier of the American soccer pyramid, the USL Championship, in 2019. Another soccer team from that city, Albuquerque Sol FC, plays in the fourth-tier USL League Two.
+
+Collegiate athletics in New Mexico involve various New Mexico Lobos and New Mexico State Aggies teams in many sports. For many years the two universities have had a rivalry often referred to as the "Rio Grande Rivalry" or the "Battle of I-25" in recognition of the campuses' both being located along that highway. NMSU also has a rivalry with the University of Texas at El Paso that is called "The Battle of I-10". The winner of the NMSU-UTEP football game receives the Silver Spade trophy.
+
+Olympic gold medalist Tom Jager, who is an advocate of controversial high-altitude training for swimming, has conducted training camps in Albuquerque (elevation 5,312 ft (1,619.1 m)) and Los Alamos (7,320 ft (2,231 m)).[191]
+
+NRA Whittington Center in Raton is the United States' largest and most comprehensive competitive shooting range and training facility.[192]
+

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+
+
+
+The Americas (also collectively called America[4][5]) comprise the totality of the continents of North and South America.[6][7][8] Together, they make up most of the land in Earth's Western Hemisphere and comprise the New World.[4]
+
+Along with their associated islands, they cover 8% of Earth's total surface area and 28.4% of its land area. The topography is dominated by the American Cordillera, a long chain of mountains that runs the length of the west coast. The flatter eastern side of the Americas is dominated by large river basins, such as the Amazon, St. Lawrence River / Great Lakes basin, Mississippi, and La Plata. Since the Americas extend 14,000 km (8,700 mi) from north to south, the climate and ecology vary widely, from the arctic tundra of Northern Canada, Greenland, and Alaska, to the tropical rain forests in Central America and South America.
+
+Humans first settled the Americas from Asia between 42,000 and 17,000 years ago. A second migration of Na-Dene speakers followed later from Asia. The subsequent migration of the Inuit into the neoarctic around 3500 BCE completed what is generally regarded as the settlement by the indigenous peoples of the Americas.
+
+The first known European settlement in the Americas was by the Norse explorer Leif Erikson.[9] However, the colonization never became permanent and was later abandoned. The Spanish voyages of Christopher Columbus from 1492 to 1502 resulted in permanent contact with European (and subsequently, other Old World) powers, which eventually led to the Columbian exchange and inaugurated a period of exploration, conquest, and colonization whose effects and consequences persist to the present. The Spanish presence involved the enslavement of large numbers of the indigenous population of America.[10]
+
+Diseases introduced from Europe and West Africa devastated the indigenous peoples, and the European powers colonized the Americas.[11] Mass emigration from Europe, including large numbers of indentured servants, and importation of African slaves largely replaced the indigenous peoples.
+
+Decolonization of the Americas began with the American Revolution in the 1770s and largely ended with the Spanish–American War in the late 1890s. Currently, almost all of the population of the Americas resides in independent countries; however, the legacy of the colonization and settlement by Europeans is that the Americas share many common cultural traits, most notably Christianity and the use of Indo-European languages: primarily Spanish, English, Portuguese, French, and, to a lesser extent, Dutch.
+
+The Americas are home to over a billion inhabitants, two-thirds of whom reside in the United States, Brazil, and Mexico. It is home to eight megacities (metropolitan areas with ten million inhabitants or more): New York City (23.9 million), Mexico City (21.2 million), São Paulo (21.2 million), Los Angeles (18.8 million), Buenos Aires (15.6 million),[12] Rio de Janeiro (13.0 million), Bogotá (10.4 million), and Lima (10.1 million).
+
+The name America was first recorded in 1507. A two-dimensional globe created by Martin Waldseemüller was the earliest recorded use of the term.[14] The name was also used (together with the related term Amerigen) in the Cosmographiae Introductio, apparently written by Matthias Ringmann, in reference to South America.[15] It was applied to both North and South America by Gerardus Mercator in 1538. America derives from Americus, the Latin version of Italian explorer Amerigo Vespucci's first name. The feminine form America accorded with the feminine names of Asia, Africa, and Europa.[16]
+
+In modern English, North and South America are generally considered separate continents, and taken together are called the Americas, or more rarely America[17][18][4] When conceived as a unitary continent, the form is generally the continent of America in the singular. However, without a clarifying context, singular America in English commonly refers to the United States of America.[4]
+
+Historically, in the English-speaking world, the term America usually referred to a single continent until the 1950s (as in Van Loon's Geography of 1937): According to historians Kären Wigen and Martin W. Lewis,[19]
+
+While it might seem surprising to find North and South America still joined into a single continent in a book published in the United States in 1937, such a notion remained fairly common until World War II.  It cannot be coincidental that this idea served American geopolitical designs at the time, which sought both Western Hemispheric domination and disengagement from the "Old World" continents of Europe, Asia, and Africa. By the 1950s, however, virtually all American geographers had come to insist that the visually distinct landmasses of North and South America deserved separate designations.
+
+The first inhabitants migrated into the Americas from Asia. Habitation sites are known in Alaska and the Yukon from at least 20,000 years ago, with suggested ages of up to 40,000 years.[21][22][23]
+Beyond that, the specifics of the Paleo-Indian migration to and throughout the Americas, including the dates and routes traveled, are subject to ongoing research and discussion.[24] Widespread habitation of the Americas occurred during the late glacial maximum, from 16,000 to 13,000 years ago.[23][25]
+
+The traditional theory has been that these early migrants moved into the Beringia land bridge between eastern Siberia and present-day Alaska around 40,000–17,000 years ago,[26] when sea levels were significantly lowered during the Quaternary glaciation.[24][27] These people are believed to have followed herds of now-extinct pleistocene megafauna along ice-free corridors that stretched between the Laurentide and Cordilleran ice sheets.[28] Another route proposed is that, either on foot or using primitive boats, they migrated down the Pacific coast to South America.[29] Evidence of the latter would since have been covered by a sea level rise of hundreds of meters following the last ice age.[30] Both routes may have been taken, although the genetic evidences suggests a single founding population.[31] The micro-satellite diversity and distributions specific to South American Indigenous people indicates that certain populations have been isolated since the initial colonization of the region.[32]
+
+A second migration occurred after the initial peopling of the Americas;[33] Na Dene speakers found predominantly in North American groups at varying genetic rates with the highest frequency found among the Athabaskans at 42% derive from this second wave.[34] Linguists and biologists have reached a similar conclusion based on analysis of Amerindian language groups and ABO blood group system distributions.[33][35][36][37] Then the people of the Arctic small tool tradition, a broad cultural entity that developed along the Alaska Peninsula, around Bristol Bay, and on the eastern shores of the Bering Strait c. 2,500 BCE moved into North America.[38] The Arctic small tool tradition, a Paleo-Eskimo culture branched off into two cultural variants, including the Pre-Dorset, and the Independence traditions of Greenland.[39] The descendants of the Pre-Dorset cultural group, the Dorset culture was displaced by the final migrants from the Bering sea coast line the ancestors of modern Inuit, the Thule people by 1000 Common Era (CE).[39] Around the same time as the Inuit migrated into Greenland, Viking settlers began arriving in Greenland in 982 and Vinland shortly thereafter, establishing a settlement at L'Anse aux Meadows, near the northernmost tip of Newfoundland.[40] The Viking settlers quickly abandoned Vinland, and disappeared from Greenland by 1500.[41]
+
+The pre-Columbian era incorporates all period subdivisions in the history and prehistory of the Americas before the appearance of significant European influences on the American continents, spanning the time of the original settlement in the Upper Paleolithic to European colonization during the Early Modern period. The term Pre-Columbian is used especially often in the context of the great indigenous civilizations of the Americas, such as those of Mesoamerica (the Olmec, the Toltec, the Teotihuacano, the Zapotec, the Mixtec, the Aztec, and the Maya) and the Andes (Inca, Moche, Muisca, Cañaris).
+
+Many pre-Columbian civilizations established characteristics and hallmarks which included permanent or urban settlements, agriculture, civic and monumental architecture, and complex societal hierarchies. Some of these civilizations had long faded by the time of the first permanent European arrivals (c. late 15th–early 16th centuries), and are known only through archeological investigations. Others were contemporary with this period, and are also known from historical accounts of the time. A few, such as the Maya, had their own written records. However, most Europeans of the time viewed such texts as pagan, and much was destroyed in Christian pyres. Only a few hidden documents remain today, leaving modern historians with glimpses of ancient culture and knowledge.[42]
+
+Although there had been previous trans-oceanic contact, large-scale European colonization of the Americas began with the first voyage of Christopher Columbus in 1492. The first Spanish settlement in the Americas was La Isabela in northern Hispaniola. This town was abandoned shortly after in favor of Santo Domingo de Guzmán, founded in 1496, the oldest American city of European foundation. This was the base from which the Spanish monarchy administered its new colonies and their expansion. Santo Domingo was subject to frequent raids by English and French pirates. On the continent, Panama City on the Pacific coast of Central America, founded on August 15, 1519, played an important role, being the base for the Spanish conquest of South America. Conquistador Lucas Vázquez de Ayllón established San Miguel de Guadalupe, the first European settlement in what is now the United States, on the Pee Dee River in South Carolina.[43] During the first half of the 16th century, Spanish colonists conducted raids throughout the Caribbean Basin, bringing captives from Central America, northern South America, and Florida back to Hispaniola and other Spanish settlements.[44]
+
+France, led by Jacques Cartier and Giovanni da Verrazano,[45] focused primarily on North America. English explorations of the Americas were led by Giovanni Caboto[46] and Sir Walter Raleigh. The Dutch in New Netherland confined their operations to Manhattan Island, Long Island, the Hudson River Valley, and what later became New Jersey. The spread of new diseases brought by Europeans and African slaves killed many of the inhabitants of North America and South America,[47][48] with a general population crash of Native Americans occurring in the mid-16th century, often well ahead of European contact.[49] One of the most devastating diseases was smallpox.[50]
+
+European immigrants were often part of state-sponsored attempts to found colonies in the Americas. Migration continued as people moved to the Americas fleeing religious persecution or seeking economic opportunities. Millions of individuals were forcibly transported to the Americas as slaves, prisoners or indentured servants.
+
+Decolonization of the Americas began with the American Revolution and the Haitian Revolution in the late 1700s. This was followed by numerous Latin American wars of independence in the early 1800s. Between 1811 and 1825, Paraguay, Argentina, Chile, Gran Colombia, the United Provinces of Central America, Mexico, Brazil, Peru, and Bolivia gained independence from Spain and Portugal in armed revolutions. After the Dominican Republic won independence from Haiti, it was re-annexed by Spain in 1861, but reclaimed its independence in 1865 at the conclusion of the Dominican Restoration War. The last violent episode of decolonization was the Cuban War of Independence which became the Spanish–American War, which resulted in the independence of Cuba in 1898, and the transfer of sovereignty over Puerto Rico from Spain to the United States.
+
+Peaceful decolonization began with the purchase by the United States of Louisiana from France in 1803, Florida from Spain in 1819, of Alaska from Russia in 1867, and the Danish West Indies from Denmark in 1916. Canada became independent of the United Kingdom, starting with the Balfour Declaration of 1926, Statute of Westminster 1931, and ending with the patriation of the Canadian Constitution in 1982. The Dominion of Newfoundland similarly achieved partial independence under the Balfour Declaration and Statute of Westminster, but was re-absorbed into the United Kingdom in 1934. It was subsequently confederated with Canada in 1949.
+
+The remaining European colonies in the Caribbean began to achieve peaceful independence well after World War II. Jamaica and Trinidad and Tobago became independent in 1962, and Guyana and Barbados both achieved independence in 1966. In the 1970s, the Bahamas, Grenada, Dominica, St. Lucia, and St. Vincent and the Grenadines all became independent of the United Kingdom, and Suriname became independent of the Netherlands. Belize, Antigua and Barbuda, and Saint Kitts and Nevis achieved independence from the United Kingdom in the 1980s.
+
+The Americas make up most of the land in Earth's western hemisphere.[51] The northernmost point of the Americas is Kaffeklubben Island, which is the most northerly point of land on Earth.[52] The southernmost point is the islands of Southern Thule, although they are sometimes considered part of Antarctica.[53] The mainland of the Americas is the world's longest north-to-south landmass. The distance between its two polar extremities, the Boothia Peninsula in northern Canada and Cape Froward in Chilean Patagonia, is roughly 14,000 km (8,700 mi).[54] The mainland's most westerly point is the end of the Seward Peninsula in Alaska; Attu Island, further off the Alaskan coast to the west, is considered the westernmost point of the Americas. Ponta do Seixas in northeastern Brazil forms the easternmost extremity of the mainland,[54] while Nordostrundingen, in Greenland, is the most easterly point of the continental shelf.
+
+South America broke off from the west of the supercontinent Gondwana around 135 million years ago, forming its own continent.[55] Around 15 million years ago, the collision of the Caribbean Plate and the Pacific Plate resulted in the emergence of a series of volcanoes along the border that created a number of islands. The gaps in the archipelago of Central America filled in with material eroded off North America and South America, plus new land created by continued volcanism. By three million years ago, the continents of North America and South America were linked by the Isthmus of Panama, thereby forming the single landmass of the Americas.[56] The Great American Interchange resulted in many species being spread across the Americas, such as the cougar, porcupine, opossums, armadillos and hummingbirds.[57]
+
+The geography of the western Americas is dominated by the American cordillera, with the Andes running along the west coast of South America[58] and the Rocky Mountains and other North American Cordillera ranges running along the western side of North America.[59] The 2,300-kilometer-long (1,400 mi) Appalachian Mountains run along the east coast of North America from Alabama to Newfoundland.[60] North of the Appalachians, the Arctic Cordillera runs along the eastern coast of Canada.[61]
+
+The largest mountain ranges are the Andes and Rocky Mountains. The Sierra Nevada and the Cascade Range reach similar altitudes as the Rocky Mountains, but are significantly smaller. In North America, the greatest number of fourteeners are in the United States, and more specifically in the U.S. state of Colorado. The highest peaks of the Americas are located in the Andes, with Aconcagua of Argentina being the highest; in North America Denali (Mount McKinley) in the U.S. state of Alaska is the tallest.
+
+Between its coastal mountain ranges, North America has vast flat areas. The Interior Plains spread over much of the continent, with low relief.[62] The Canadian Shield covers almost 5 million km² of North America and is generally quite flat.[63] Similarly, the north-east of South America is covered by the flat Amazon Basin.[64] The Brazilian Highlands on the east coast are fairly smooth but show some variations in landform, while farther south the Gran Chaco and Pampas are broad lowlands.[65]
+
+The climate of the Americas varies significantly from region to region. Tropical rainforest climate occurs in the latitudes of the Amazon, American cloud forests, southeastern Florida and Darien Gap. In the Rocky Mountains and Andes, dry and continental climates are observed. Often the higher altitudes of these mountains are snow-capped.
+
+Southeastern North America is well known for its occurrence of tornadoes and hurricanes, of which the vast majority of tornadoes occur in the United States' Tornado Alley,[66] as well as in the southerly Dixie Alley in the North American late-winter and early spring seasons. Often parts of the Caribbean are exposed to the violent effects of hurricanes. These weather systems are formed by the collision of dry, cool air from Canada and wet, warm air from the Atlantic.
+
+With coastal mountains and interior plains, the Americas have several large river basins that drain the continents. The largest river basin in North America is that of the Mississippi, covering the second largest watershed on the planet.[67] The Mississippi-Missouri river system drains most of 31 states of the U.S., most of the Great Plains, and large areas between the Rocky and Appalachian mountains. This river is the fourth longest in the world and tenth most powerful in the world.
+
+In North America, to the east of the Appalachian Mountains, there are no major rivers but rather a series of rivers and streams that flow east with their terminus in the Atlantic Ocean, such as the Hudson River, Saint John River, and Savannah River. A similar instance arises with central Canadian rivers that drain into Hudson Bay; the largest being the Churchill River. On the west coast of North America, the main rivers are the Colorado River, Columbia River, Yukon River, Fraser River, and Sacramento River.
+
+The Colorado River drains much of the Southern Rockies and parts of the Great Basin and Range Province. The river flows approximately 1,450 miles (2,330 km) into the Gulf of California,[68] during which over time it has carved out natural phenomena such as the Grand Canyon and created phenomena such as the Salton Sea. The Columbia is a large river, 1,243 miles (2,000 km) long, in central western North America and is the most powerful river on the West Coast of the Americas. In the far northwest of North America, the Yukon drains much of the Alaskan peninsula and flows 1,980 miles (3,190 km)[69] from parts of Yukon and the Northwest Territory to the Pacific. Draining to the Arctic Ocean of Canada, the Mackenzie River drains waters from the Arctic Great Lakes of Arctic Canada, as opposed to the Saint-Lawrence River that drains the Great Lakes of Southern Canada into the Atlantic Ocean. The Mackenzie River is the largest in Canada and drains 1,805,200 square kilometers (697,000 sq mi).[70]
+
+The largest river basin in South America is that of the Amazon, which has the highest volume flow of any river on Earth.[71] The second largest watershed of South America is that of the Paraná River, which covers about 2.5 million km².[72]
+
+North America and South America began to develop a shared population of flora and fauna around 2.5 million years ago, when continental drift brought the two continents into contact via the Isthmus of Panama. Initially, the exchange of biota was roughly equal, with North American genera migrating into South America in about the same proportions as South American genera migrated into North America. This exchange is known as the Great American Interchange. The exchange became lopsided after roughly a million years, with the total spread of South American genera into North America far more limited in scope than the spread on North American genera into South America.[73]
+
+There are 35 sovereign states in the Americas, as well as an autonomous country of Denmark, three overseas departments of France, three overseas collectivities of France,[74] and one uninhabited territory of France, eight overseas territories of the United Kingdom, three constituent countries of the Netherlands, three public bodies of the Netherlands, two unincorporated territories of the United States, and one uninhabited territory of the United States.[75]
+
+In 2015 the total population of the Americas was about 985 million people, divided as follows:[note 1]
+
+There are three urban centers that each hold titles for being the largest population area based on the three main demographic concepts:[98]
+
+In accordance with these definitions, the three largest population centers in the Americas are: Mexico City, anchor to the largest metropolitan area in the Americas; New York City, anchor to the largest urban area in the Americas; and São Paulo, the largest city proper in the Americas. All three cities maintain Alpha classification and large scale influence.
+
+Mexico City – The largest metropolitan area in the Americas, with a population of 22,300,000 in 2017.
+
+São Paulo – Largest city with a population of 12,038,175 (city) in 2016.
+
+New York City – Largest urban area in the Americas, with a population of 18,351,295 in 2010.
+
+The population of the Americas is made up of the descendants of four large ethnic groups and their combinations.
+
+The majority of the population live in Latin America, named for its predominant cultures, rooted in Latin Europe (including the two dominant languages, Spanish and Portuguese, both Romance languages), more specifically in the Iberian nations of Portugal and Spain (hence the use of the term Ibero-America as a synonym). Latin America is typically contrasted with Anglo-America, where English, a Germanic language, is prevalent, and which comprises Canada (with the exception of francophone Canada rooted in Latin Europe [France]—see Québec and Acadia) and the United States. Both countries are located in North America, with cultures deriving predominantly from Anglo-Saxon and other Germanic roots.
+
+The most prevalent faiths in the Americas are as follows:
+
+Other faiths include Buddhism; Hinduism; Sikhism; Bahá'í Faith; a wide variety of indigenous religions, many of which can be categorized as animistic; new age religions and many African and African-derived religions. Syncretic faiths can also be found throughout the Americas.
+
+Various languages are spoken in the Americas. Some are of European origin, others are spoken by indigenous peoples or are the mixture of various languages like the different creoles.[125]
+
+The most widely spoken language in the Americas is Spanish.[137] The dominant language of Latin America is Spanish, though the most populous nation in Latin America, Brazil, speaks Portuguese. Small enclaves of French-, Dutch- and English-speaking regions also exist in Latin America, notably in French Guiana, Suriname, and Belize and Guyana respectively. Haitian Creole is dominant in the nation of Haiti, where French is also spoken. Native languages are more prominent in Latin America than in Anglo-America, with Nahuatl, Quechua, Aymara and Guaraní as the most common. Various other native languages are spoken with less frequency across both Anglo-America and Latin America. Creole languages other than Haitian Creole are also spoken in parts of Latin America.
+
+The dominant language of Anglo-America is English. French is also official in Canada, where it is the predominant language in Quebec and an official language in New Brunswick along with English. It is also an important language in Louisiana, and in parts of New Hampshire, Maine, and Vermont. Spanish has kept an ongoing presence in the Southwestern United States, which formed part of the Viceroyalty of New Spain, especially in California and New Mexico, where a distinct variety of Spanish spoken since the 17th century has survived. It has more recently become widely spoken in other parts of the United States because of heavy immigration from Latin America. High levels of immigration in general have brought great linguistic diversity to Anglo-America, with over 300 languages known to be spoken in the United States alone, but most languages are spoken only in small enclaves and by relatively small immigrant groups.
+
+The nations of Guyana, Suriname, and Belize are generally considered[by whom?] not to fall into either Anglo-America or Latin America because of their language differences from Latin America, geographic differences from Anglo-America, and cultural and historical differences from both regions; English is the primary language of Guyana and Belize, and Dutch is the primary language of Suriname.
+
+Most of the non-native languages have, to different degrees, evolved differently from the mother country, but are usually still mutually intelligible. Some have combined, however, which has even resulted in completely new languages, such as Papiamento, which is a combination of Portuguese, Spanish, Dutch (representing the respective colonizers), native Arawak, various African languages, and, more recently English. The lingua franca Portuñol, a mixture of Portuguese and Spanish, is spoken in the border regions of Brazil and neighboring Spanish-speaking countries.[138] More specifically, Riverense Portuñol is spoken by around 100,000 people in the border regions of Brazil and Uruguay. Because of immigration, there are many communities where other languages are spoken from all parts of the world, especially in the United States, Brazil, Argentina, Canada, Chile, Costa Rica and Uruguay—very important destinations for immigrants.[139][140][141]
+
+Northern America
+
+Speakers of English generally refer to the landmasses of North America and South America as the Americas, the Western Hemisphere, or the New World.[5] The adjective American may be used to indicate something pertains to the Americas,[2] but this term is primarily used in English to indicate something pertaining to the United States.[2][142][143] Some non-ambiguous alternatives exist, such as the adjective Pan-American,[144] or New Worlder as a demonym for a resident of the closely related New World.[3] Use of America in the hemispherical sense is sometimes retained, or can occur when translated from other languages.[145] For example, the Association of National Olympic Committees (ANOC) in Paris maintains a single continental association for "America", represented by one of the five Olympic rings.[146]
+
+American essayist H.L. Mencken said, "The Latin-Americans use Norteamericano in formal writing, but, save in Panama, prefer nicknames in colloquial speech."[147] To avoid "American" one can use constructed terms in their languages derived from "United States" or even "North America".[143][148][149] In Canada, its southern neighbor is often referred to as "the United States", "the U.S.A.", or (informally) "the States", while U.S. citizens are generally referred to as "Americans".[143] Most Canadians resent being referred to as "Americans".[143]
+
+In Spanish, América is a single continent composed of the subcontinents of América del Sur and América del Norte, the land bridge of América Central, and the islands of the Antillas. Americano or americana in Spanish refers to a person from América in a similar way that europeo or europea refers to a person from Europa. The terms sudamericano/a, centroamericano/a, antillano/a and norteamericano/a can be used to more specifically refer to the location where a person may live.
+
+Citizens of the United States of America are normally referred to by the term estadounidense (rough literal translation: "United Statesian") instead of americano or americana which is discouraged,[150][151] and the country's name itself is officially translated as Estados Unidos de América (United States of America), commonly abbreviated as Estados Unidos (EEUU).[151] Also, the term norteamericano (North American) may refer to a citizen of the United States. This term is primarily used to refer to citizens of the United States, and less commonly to those of other North American countries.[150]
+
+In Portuguese, América[152] is a single continent composed of América do Sul (South America), América Central (Central America) and América do Norte (North America).[153] It can be ambiguous, as América can be used to refer to the United States of America, but is avoided in print and formal environments.[154][155]
+
+In French the word américain may be used for things relating to the Americas; however, similar to English, it is most often used for things relating to the United States, with the term états-unien sometimes used for clarity. Panaméricain may be used as an adjective to refer to the Americas without ambiguity.[156] French speakers may use the noun Amérique to refer to the whole landmass as one continent, or two continents, Amérique du Nord and Amérique du Sud. In French, Amérique is seldom used to refer to the United States, leading to some ambiguity when it is. Similar to English usage, les Amériques or des Amériques is used to refer unambiguously to the Americas.
+
+In Dutch, the word Amerika mostly refers to the United States.[157][158] Although the United States is equally often referred to as de Verenigde Staten ("the United States") or de VS ("the US"), Amerika relatively rarely refers to the Americas, but it is the only commonly used Dutch word for the Americas. This often leads to ambiguity; and to stress that something concerns the Americas as a whole, Dutch uses a combination, namely Noord- en Zuid-Amerika (North and South America).
+
+Latin America is generally referred to as Latijns Amerika or Midden-Amerika for Central America.
+
+The adjective Amerikaans is most often used for things or people relating to the United States. There are no alternative words to distinguish between things relating to the United States or to the Americas. Dutch uses the local alternative for things relating to elsewhere in the Americas, such as Argentijns for Argentine, etc.
+
+The following is a list of multinational organizations in the Americas.
+
+Dominica, Panama and the Dominican Republic have the fastest-growing economy in the Americas according to the International Monetary Fund (IMF),[160]
+
+In 2016, five to seven countries in the southern part of the Americas had weakening economies in decline, compared to only three countries in the northern part of the Americas.[161][162] Haiti has the lowest GDP per capita in the Americas, although its economy was growing slightly as of 2016[update].[161][162]
+
+Coordinates: 19°N 96°W / 19°N 96°W / 19; -96
+
+Africa
+
+Antarctica
+
+Asia
+
+Australia
+
+Europe
+
+North America
+
+South America
+
+Afro-Eurasia
+
+America
+
+Eurasia
+
+Oceania

en/418.html.txt

@@ -0,0 +1,194 @@
+
+
+Asteroids are minor planets, especially of the inner Solar System. Larger asteroids have also been called planetoids. These terms have historically been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered that were found to have volatile-rich surfaces similar to comets, these came to be distinguished from the objects found in the main asteroid belt.[1]
+
+In this article, the term "asteroid" refers to the minor planets of the inner Solar System, including those co-orbital with Jupiter.
+
+Millions of asteroids exist, many the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets.[2] The vast majority of known asteroids orbit within the main asteroid belt located between the orbits of Mars and Jupiter, or are co-orbital with Jupiter (the Jupiter trojans). However, other orbital families exist with significant populations, including the near-Earth objects. Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, and S-type. These were named after and are generally identified with carbon-rich, metallic, and silicate (stony) compositions, respectively. The sizes of asteroids varies greatly; the largest, Ceres, is almost 1,000 km (600 mi) across and massive enough to qualify as a dwarf planet.
+
+Asteroids are somewhat arbitrarily differentiated from comets and meteoroids. In the case of comets, the difference is one of composition: while asteroids are mainly composed of mineral and rock, comets are primarily composed of dust and ice. Furthermore, asteroids formed closer to the sun, preventing the development of cometary ice.[3] The difference between asteroids and meteoroids is mainly one of size: meteoroids have a diameter of one meter or less, whereas asteroids have a diameter of greater than one meter.[4] Finally, meteoroids can be composed of either cometary or asteroidal materials.[5]
+
+Only one asteroid, 4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the naked eye for a short time.[6] As of March 2020[update], the Minor Planet Center had data on 930,000 minor planets in the inner and outer Solar System, of which about 545,000 had enough information to be given numbered designations.[7]
+
+The United Nations declared 30 June as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908.[8][9]
+
+In April 2018, the B612 Foundation reported "It is 100 percent certain we'll be hit [by a devastating asteroid], but we're not 100 percent sure when."[10] Also in 2018, physicist Stephen Hawking,
+in his final book Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet.[11][12][13] In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, and has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.[14][15][16][17][18] According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched.[19]
+
+The first asteroid to be discovered, Ceres, was originally considered to be a new planet.[a] This was followed by the discovery of other similar bodies, which, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though readily distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid",[b] coined in Greek as ἀστεροειδής, or asteroeidēs, meaning 'star-like, star-shaped', and derived from the Ancient Greek ἀστήρ astēr 'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" (not always qualified as "minor") were still used interchangeably.[c]
+
+Discovery timeline:[23]
+
+Asteroid discovery methods have dramatically improved over the past two centuries.
+
+In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law, partly because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law.[26] This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, be spotted. The expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers.
+
+The first object, Ceres, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily. He discovered a new star-like object in Taurus and followed the displacement of this object during several nights. Later that year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, which was found to be between the planets Mars and Jupiter. Piazzi named it after Ceres, the Roman goddess of agriculture.[26]
+
+Three other asteroids (2 Pallas, 3 Juno, and 4 Vesta) were discovered over the next few years, with Vesta found in 1807. After eight more years of fruitless searches, most astronomers assumed that there were no more and abandoned any further searches.[citation needed]
+
+However, Karl Ludwig Hencke persisted, and began searching for more asteroids in 1830. Fifteen years later, he found 5 Astraea, the first new asteroid in 38 years. He also found 6 Hebe less than two years later. After this, other astronomers joined in the search and at least one new asteroid was discovered every year after that (except the wartime year 1945). Notable asteroid hunters of this early era were J.R. Hind, A. de Gasparis, R. Luther, H.M.S. Goldschmidt, J. Chacornac, J. Ferguson, N.R. Pogson, E.W. Tempel, J.C. Watson, C.H.F. Peters, A. Borrelly, J. Palisa, the Henry brothers and A. Charlois.
+
+In 1891, Max Wolf pioneered the use of astrophotography to detect asteroids, which appeared as short streaks on long-exposure photographic plates. This dramatically increased the rate of detection compared with earlier visual methods: Wolf alone discovered 248 asteroids, beginning with 323 Brucia, whereas only slightly more than 300 had been discovered up to that point. It was known that there were many more, but most astronomers did not bother with them, some calling them "vermin of the skies",[27] a phrase variously attributed to E. Suess[28] and E. Weiss.[29] Even a century later, only a few thousand asteroids were identified, numbered and named.
+
+Until 1998, asteroids were discovered by a four-step process. First, a region of the sky was photographed by a wide-field telescope, or astrograph. Pairs of photographs were taken, typically one hour apart. Multiple pairs could be taken over a series of days. Second, the two films or plates of the same region were viewed under a stereoscope. Any body in orbit around the Sun would move slightly between the pair of films. Under the stereoscope, the image of the body would seem to float slightly above the background of stars. Third, once a moving body was identified, its location would be measured precisely using a digitizing microscope. The location would be measured relative to known star locations.[30]
+
+These first three steps do not constitute asteroid discovery: the observer has only found an apparition, which gets a provisional designation, made up of the year of discovery, a letter representing the half-month of discovery, and finally a letter and a number indicating the discovery's sequential number (example: 1998 FJ74).
+
+The last step of discovery is to send the locations and time of observations to the Minor Planet Center, where computer programs determine whether an apparition ties together earlier apparitions into a single orbit. If so, the object receives a catalogue number and the observer of the first apparition with a calculated orbit is declared the discoverer, and granted the honor of naming the object subject to the approval of the International Astronomical Union.
+
+There is increasing interest in identifying asteroids whose orbits cross Earth's, and that could, given enough time, collide with Earth (see Earth-crosser asteroids). The three most important groups of near-Earth asteroids are the Apollos, Amors, and Atens. Various asteroid deflection strategies have been proposed, as early as the 1960s.
+
+The near-Earth asteroid 433 Eros had been discovered as long ago as 1898, and the 1930s brought a flurry of similar objects. In order of discovery, these were: 1221 Amor, 1862 Apollo, 2101 Adonis, and finally 69230 Hermes, which approached within 0.005 AU of Earth in 1937. Astronomers began to realize the possibilities of Earth impact.
+
+Two events in later decades increased the alarm: the increasing acceptance of the Alvarez hypothesis that an impact event resulted in the Cretaceous–Paleogene extinction, and the 1994 observation of Comet Shoemaker-Levy 9 crashing into Jupiter. The U.S. military also declassified the information that its military satellites, built to detect nuclear explosions, had detected hundreds of upper-atmosphere impacts by objects ranging from one to ten meters across.
+
+All these considerations helped spur the launch of highly efficient surveys that consist of charge-coupled device (CCD) cameras and computers directly connected to telescopes. As of 2011[update], it was estimated that 89% to 96% of near-Earth asteroids one kilometer or larger in diameter had been discovered.[31] A list of teams using such systems includes:[32]
+[33]
+
+As of 29 October 2018[update], the LINEAR system alone has discovered 147,132 asteroids.[34] Among all the surveys, 19,266 near-Earth asteroids have been discovered[35] including almost 900 more than 1 km (0.6 mi) in diameter.[36]
+
+Traditionally, small bodies orbiting the Sun were classified as comets, asteroids, or meteoroids, with anything smaller than one meter across being called a meteoroid. Beech and Steel's 1995 paper proposed a meteoroid definition including size limits.[37][38] The term "asteroid", from the Greek word for "star-like", never had a formal definition, with the broader term minor planet being preferred by the International Astronomical Union.
+
+However, following the discovery of asteroids below ten meters in size, Rubin and Grossman's 2010 paper revised the previous definition of meteoroid to objects between 10 µm and 1 meter in size in order to maintain the distinction between asteroids and meteoroids.[4] The smallest asteroids discovered (based on absolute magnitude H) are 2008 TS26 with {{{1}}} and 2011 CQ1 with {{{1}}} both with an estimated size of about 1 meter.[39]
+
+In 2006, the term "small Solar System body" was also introduced to cover both most minor planets and comets.[40][d] Other languages prefer "planetoid" (Greek for "planet-like"), and this term is occasionally used in English especially for larger minor planets such as the dwarf planets as well as an alternative for asteroids since they are not star-like.[41] The word "planetesimal" has a similar meaning, but refers specifically to the small building blocks of the planets that existed when the Solar System was forming. The term "planetule" was coined by the geologist William Daniel Conybeare to describe minor planets,[42] but is not in common use. The three largest objects in the asteroid belt, Ceres, Pallas, and Vesta, grew to the stage of protoplanets. Ceres is a dwarf planet, the only one in the inner Solar System.
+
+When found, asteroids were seen as a class of objects distinct from comets, and there was no unified term for the two until "small Solar System body" was coined in 2006. The main difference between an asteroid and a comet is that a comet shows a coma due to sublimation of near surface ices by solar radiation. A few objects have ended up being dual-listed because they were first classified as minor planets but later showed evidence of cometary activity. Conversely, some (perhaps all) comets are eventually depleted of their surface volatile ices and become asteroid-like. A further distinction is that comets typically have more eccentric orbits than most asteroids; most "asteroids" with notably eccentric orbits are probably dormant or extinct comets.[43]
+
+For almost two centuries, from the discovery of Ceres in 1801 until the discovery of the first centaur, Chiron in 1977, all known asteroids spent most of their time at or within the orbit of Jupiter, though a few such as Hidalgo ventured far beyond Jupiter for part of their orbit. Those located between the orbits of Mars and Jupiter were known for many years simply as The Asteroids.[44] When astronomers started finding more small bodies that permanently resided further out than Jupiter, now called centaurs, they numbered them among the traditional asteroids, though there was debate over whether they should be considered asteroids or as a new type of object. Then, when the first trans-Neptunian object (other than Pluto), Albion, was discovered in 1992, and especially when large numbers of similar objects started turning up, new terms were invented to sidestep the issue: Kuiper-belt object, trans-Neptunian object, scattered-disc object, and so on. These inhabit the cold outer reaches of the Solar System where ices remain solid and comet-like bodies are not expected to exhibit much cometary activity; if centaurs or trans-Neptunian objects were to venture close to the Sun, their volatile ices would sublimate, and traditional approaches would classify them as comets and not asteroids.
+
+The innermost of these are the Kuiper-belt objects, called "objects" partly to avoid the need to classify them as asteroids or comets.[45] They are thought to be predominantly comet-like in composition, though some may be more akin to asteroids.[46] Furthermore, most do not have the highly eccentric orbits associated with comets, and the ones so far discovered are larger than traditional comet nuclei. (The much more distant Oort cloud is hypothesized to be the main reservoir of dormant comets.) Other recent observations, such as the analysis of the cometary dust collected by the Stardust probe, are increasingly blurring the distinction between comets and asteroids,[47] suggesting "a continuum between asteroids and comets" rather than a sharp dividing line.[48]
+
+The minor planets beyond Jupiter's orbit are sometimes also called "asteroids", especially in popular presentations.[e] However, it is becoming increasingly common for the term "asteroid" to be restricted to minor planets of the inner Solar System.[45] Therefore, this article will restrict itself for the most part to the classical asteroids: objects of the asteroid belt, Jupiter trojans, and near-Earth objects.
+
+When the IAU introduced the class small Solar System bodies in 2006 to include most objects previously classified as minor planets and comets, they created the class of dwarf planets for the largest minor planets – those that have enough mass to have become ellipsoidal under their own gravity. According to the IAU, "the term 'minor planet' may still be used, but generally the term 'Small Solar System Body' will be preferred."[49] Currently only the largest object in the asteroid belt, Ceres, at about 975 km (606 mi) across, has been placed in the dwarf planet category.
+
+It is thought that planetesimals in the asteroid belt evolved much like the rest of the solar nebula until Jupiter neared its current mass, at which point excitation from orbital resonances with Jupiter ejected over 99% of planetesimals in the belt. Simulations and a discontinuity in spin rate and spectral properties suggest that asteroids larger than approximately 120 km (75 mi) in diameter accreted during that early era, whereas smaller bodies are fragments from collisions between asteroids during or after the Jovian disruption.[51] Ceres and Vesta grew large enough to melt and differentiate, with heavy metallic elements sinking to the core, leaving rocky minerals in the crust.[52]
+
+In the Nice model, many Kuiper-belt objects are captured in the outer asteroid belt, at distances greater than 2.6 AU. Most were later ejected by Jupiter, but those that remained may be the D-type asteroids, and possibly include Ceres.[53]
+
+Various dynamical groups of asteroids have been discovered orbiting in the inner Solar System. Their orbits are perturbed by the gravity of other bodies in the Solar System and by the Yarkovsky effect. Significant populations include:
+
+The majority of known asteroids orbit within the asteroid belt between the orbits of Mars and Jupiter, generally in relatively low-eccentricity (i.e. not very elongated) orbits. This belt is now estimated to contain between 1.1 and 1.9 million asteroids larger than 1 km (0.6 mi) in diameter,[54] and millions of smaller ones. These asteroids may be remnants of the protoplanetary disk, and in this region the accretion of planetesimals into planets during the formative period of the Solar System was prevented by large gravitational perturbations by Jupiter.
+
+Trojans are populations that share an orbit with a larger planet or moon, but do not collide with it because they orbit in one of the two Lagrangian points of stability, L4 and L5, which lie 60° ahead of and behind the larger body.
+The most significant population of trojans are the Jupiter trojans. Although fewer Jupiter trojans have been discovered (As of 2010[update]), it is thought that they are as numerous as the asteroids in the asteroid belt. Trojans have been found in the orbits of other planets, including Venus, Earth, Mars, Uranus, and Neptune.
+
+Near-Earth asteroids, or NEAs, are asteroids that have orbits that pass close to that of Earth. Asteroids that actually cross Earth's orbital path are known as Earth-crossers. As of June 2016[update], 14,464 near-Earth asteroids are known[31] and the number over one kilometer in diameter is estimated to be 900–1,000.
+
+Asteroids vary greatly in size, from almost 1000 km for the largest down to rocks just 1 meter across.[f] The three largest are very much like miniature planets: they are roughly spherical, have at least partly differentiated interiors,[55] and are thought to be surviving protoplanets. The vast majority, however, are much smaller and are irregularly shaped; they are thought to be either battered planetesimals or fragments of larger bodies.
+
+The dwarf planet Ceres is by far the largest asteroid, with a diameter of 940 km (580 mi). The next largest are 4 Vesta and 2 Pallas, both with diameters of just over 500 km (300 mi). Vesta is the only main-belt asteroid that can, on occasion, be visible to the naked eye. On some rare occasions, a near-Earth asteroid may briefly become visible without technical aid; see 99942 Apophis.
+
+The mass of all the objects of the asteroid belt, lying between the orbits of Mars and Jupiter, is estimated to be in the range of (2.8–3.2)×1021 kg, about 4% of the mass of the Moon. Of this, Ceres comprises 0.938×1021 kg, about a third of the total. Adding in the next three most massive objects, Vesta (9%), Pallas (7%), and Hygiea (3%), brings this figure up to half, whereas the three most-massive asteroids after that, 511 Davida (1.2%), 704 Interamnia (1.0%), and 52 Europa (0.9%), constitute only another 3%. The number of asteroids increases rapidly as their individual masses decrease.
+
+The number of asteroids decreases markedly with size. Although this generally follows a power law, there are 'bumps' at 5 km and 100 km, where more asteroids than expected from a logarithmic distribution are found.[56]
+
+Although their location in the asteroid belt excludes them from planet status, the three largest objects, Ceres, Vesta, and Pallas, are intact protoplanets that share many characteristics common to planets, and are atypical compared to the majority of irregularly shaped asteroids. The fourth largest asteroid, Hygiea, appears nearly spherical although it may have an undifferentiated interior[citation needed], like the majority of asteroids. Between them, the four largest asteroids constitute half the mass of the asteroid belt.
+
+Ceres is the only asteroid with a fully ellipsoidal shape and hence the only one that is a dwarf planet.[40] It has a much higher absolute magnitude than the other asteroids, of around 3.32,[57] and may possess a surface layer of ice.[58] Like the planets, Ceres is differentiated: it has a crust, a mantle and a core.[58] No meteorites from Ceres have been found on Earth.
+
+Vesta, too, has a differentiated interior, though it formed inside the Solar System's frost line, and so is devoid of water;[59][60] its composition is mainly of basaltic rock with minerals such as olivine.[61] Aside from the large crater at its southern pole, Rheasilvia, Vesta also has an ellipsoidal shape. Vesta is the parent body of the Vestian family and other V-type asteroids, and is the source of the HED meteorites, which constitute 5% of all meteorites on Earth.
+
+Pallas is unusual in that, like Uranus, it rotates on its side, with its axis of rotation tilted at high angles to its orbital plane.[62] Its composition is similar to that of Ceres: high in carbon and silicon, and perhaps partially differentiated.[63] Pallas is the parent body of the Palladian family of asteroids.
+
+Hygiea is the largest carbonaceous asteroid[64] and, unlike the other largest asteroids, lies relatively close to the plane of the ecliptic.[65] It is the largest member and presumed parent body of the Hygiean family of asteroids. Because there is no sufficiently large crater on the surface to be the source of that family, as there is on Vesta, it is thought that Hygiea may have been completely disrupted in the collision that formed the Hygiean family, and recoalesced after losing a bit less than 2% of its mass. Observations taken with the Very Large Telescope's SPHERE imager in 2017 and 2018, and announced in late 2019, revealed that Hygiea has a nearly spherical shape, which is at consistent both with it being in hydrostatic equilibrium (and thus a dwarf planet), or formerly being in hydrostatic equilibrium, or with being disrupted and recoalescing.[66][67]
+
+Measurements of the rotation rates of large asteroids in the asteroid belt show that there is an upper limit. Very few asteroids with a diameter larger than 100 meters have a rotation period smaller than 2.2 hours.[70] For asteroids rotating faster than approximately this rate, the inertial force at the surface is greater than the gravitational force, so any loose surface material would be flung out. However, a solid object should be able to rotate much more rapidly. This suggests that most asteroids with a diameter over 100 meters are rubble piles formed through accumulation of debris after collisions between asteroids.[71]
+
+The physical composition of asteroids is varied and in most cases poorly understood. Ceres appears to be composed of a rocky core covered by an icy mantle, where Vesta is thought to have a nickel-iron core, olivine mantle, and basaltic crust.[72] 10 Hygiea, however, which appears to have a uniformly primitive composition of carbonaceous chondrite, is thought to be the largest undifferentiated asteroid. Most of the smaller asteroids are thought to be piles of rubble held together loosely by gravity, though the largest are probably solid. Some asteroids have moons or are co-orbiting binaries: Rubble piles, moons, binaries, and scattered asteroid families are thought to be the results of collisions that disrupted a parent asteroid, or, possibly, a planet.[73]
+
+Asteroids contain traces of amino acids and other organic compounds, and some speculate that asteroid impacts may have seeded the early Earth with the chemicals necessary to initiate life, or may have even brought life itself to Earth (also see panspermia).[74][75] In August 2011, a report, based on NASA studies with meteorites found on Earth, was published suggesting DNA and RNA components (adenine, guanine and related organic molecules) may have been formed on asteroids and comets in outer space.[76][77][78]
+
+Composition is calculated from three primary sources: albedo, surface spectrum, and density. The last can only be determined accurately by observing the orbits of moons the asteroid might have. So far, every asteroid with moons has turned out to be a rubble pile, a loose conglomeration of rock and metal that may be half empty space by volume. The investigated asteroids are as large as 280 km in diameter, and include 121 Hermione (268×186×183 km), and 87 Sylvia (384×262×232 km). Only half a dozen asteroids are larger than 87 Sylvia, though none of them have moons; however, some smaller asteroids are thought to be more massive, suggesting they may not have been disrupted, and indeed 511 Davida, the same size as Sylvia to within measurement error, is estimated to be two and a half times as massive, though this is highly uncertain. The fact that such large asteroids as Sylvia can be rubble piles, presumably due to disruptive impacts, has important consequences for the formation of the Solar System: Computer simulations of collisions involving solid bodies show them destroying each other as often as merging, but colliding rubble piles are more likely to merge. This means that the cores of the planets could have formed relatively quickly.[79]
+
+On 7 October 2009, the presence of water ice was confirmed on the surface of 24 Themis using NASA's Infrared Telescope Facility. The surface of the asteroid appears completely covered in ice. As this ice layer is sublimating, it may be getting replenished by a reservoir of ice under the surface. Organic compounds were also detected on the surface.[80][81][82][83] Scientists hypothesize that some of the first water brought to Earth was delivered by asteroid impacts after the collision that produced the Moon. The presence of ice on 24 Themis supports this theory.[82]
+
+In October 2013, water was detected on an extrasolar body for the first time, on an asteroid orbiting the white dwarf GD 61.[84] On 22 January 2014, European Space Agency (ESA) scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt.[85] The detection was made by using the far-infrared abilities of the Herschel Space Observatory.[86] The finding is unexpected because comets, not asteroids, are typically considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids."[86]
+
+In May 2016, significant asteroid data arising from the Wide-field Infrared Survey Explorer and NEOWISE missions have been questioned.[87][88][89] Although the early original criticism had not undergone peer review,[90] a more recent peer-reviewed study was subsequently published.[91][18]
+
+In November 2019, scientists reported detecting, for the first time, sugar molecules, including ribose, in meteorites, suggesting that chemical processes on asteroids can produce some fundamentally essential bio-ingredients important to life, and supporting the notion of an RNA world prior to a DNA-based origin of life on Earth, and possibly, as well, the notion of panspermia.[92][93]
+
+Most asteroids outside the "big four" (Ceres, Pallas, Vesta, and Hygiea) are likely to be broadly similar in appearance, if irregular in shape. 50 km (31 mi) 253 Mathilde is a rubble pile saturated with craters with diameters the size of the asteroid's radius, and Earth-based observations of 300 km (186 mi) 511 Davida, one of the largest asteroids after the big four, reveal a similarly angular profile, suggesting it is also saturated with radius-size craters.[94] Medium-sized asteroids such as Mathilde and 243 Ida that have been observed up close also reveal a deep regolith covering the surface. Of the big four, Pallas and Hygiea are practically unknown. Vesta has compression fractures encircling a radius-size crater at its south pole but is otherwise a spheroid. Ceres seems quite different in the glimpses Hubble has provided, with surface features that are unlikely to be due to simple craters and impact basins, but details will be expanded with the Dawn spacecraft, which entered Ceres orbit on 6 March 2015.[95]
+
+Asteroids become darker and redder with age due to space weathering.[96] However evidence suggests most of the color change occurs rapidly, in the first hundred thousands years, limiting the usefulness of spectral measurement for determining the age of asteroids.[97]
+
+Asteroids are commonly categorized according to two criteria: the characteristics of their orbits, and features of their reflectance spectrum.
+
+Many asteroids have been placed in groups and families based on their orbital characteristics. Apart from the broadest divisions, it is customary to name a group of asteroids after the first member of that group to be discovered. Groups are relatively loose dynamical associations, whereas families are tighter and result from the catastrophic break-up of a large parent asteroid sometime in the past.[98] Families are more common and easier to identify within the main asteroid belt, but several small families have been reported among the Jupiter trojans.[99] Main belt families were first recognized by Kiyotsugu Hirayama in 1918 and are often called Hirayama families in his honor.
+
+About 30–35% of the bodies in the asteroid belt belong to dynamical families each thought to have a common origin in a past collision between asteroids. A family has also been associated with the plutoid dwarf planet Haumea.
+
+Some asteroids have unusual horseshoe orbits that are co-orbital with Earth or some other planet. Examples are 3753 Cruithne and 2002 AA29. The first instance of this type of orbital arrangement was discovered between Saturn's moons Epimetheus and Janus.
+
+Sometimes these horseshoe objects temporarily become quasi-satellites for a few decades or a few hundred years, before returning to their earlier status. Both Earth and Venus are known to have quasi-satellites.
+
+Such objects, if associated with Earth or Venus or even hypothetically Mercury, are a special class of Aten asteroids. However, such objects could be associated with outer planets as well.
+
+In 1975, an asteroid taxonomic system based on color, albedo, and spectral shape was developed by Chapman, Morrison, and Zellner.[100] These properties are thought to correspond to the composition of the asteroid's surface material. The original classification system had three categories: C-types for dark carbonaceous objects (75% of known asteroids), S-types for stony (silicaceous) objects (17% of known asteroids) and U for those that did not fit into either C or S. This classification has since been expanded to include many other asteroid types. The number of types continues to grow as more asteroids are studied.
+
+The two most widely used taxonomies now used are the Tholen classification and SMASS classification. The former was proposed in 1984 by David J. Tholen, and was based on data collected from an eight-color asteroid survey performed in the 1980s. This resulted in 14 asteroid categories.[101] In 2002, the Small Main-Belt Asteroid Spectroscopic Survey resulted in a modified version of the Tholen taxonomy with 24 different types. Both systems have three broad categories of C, S, and X asteroids, where X consists of mostly metallic asteroids, such as the M-type. There are also several smaller classes.[102]
+
+The proportion of known asteroids falling into the various spectral types does not necessarily reflect the proportion of all asteroids that are of that type; some types are easier to detect than others, biasing the totals.
+
+Originally, spectral designations were based on inferences of an asteroid's composition.[103] However, the correspondence between spectral class and composition is not always very good, and a variety of classifications are in use. This has led to significant confusion. Although asteroids of different spectral classifications are likely to be composed of different materials, there are no assurances that asteroids within the same taxonomic class are composed of the same (or similar) materials.
+
+A newly discovered asteroid is given a provisional designation (such as 2002 AT4) consisting of the year of discovery and an alphanumeric code indicating the half-month of discovery and the sequence within that half-month. Once an asteroid's orbit has been confirmed, it is given a number, and later may also be given a name (e.g. 433 Eros). The formal naming convention uses parentheses around the number – e.g. (433) Eros – but dropping the parentheses is quite common. Informally, it is common to drop the number altogether, or to drop it after the first mention when a name is repeated in running text.[104] In addition, names can be proposed by the asteroid's discoverer, within guidelines established by the International Astronomical Union.[105]
+
+The first asteroids to be discovered were assigned iconic symbols like the ones traditionally used to designate the planets. By 1855 there were two dozen asteroid symbols, which often occurred in multiple variants.[106]
+
+In 1851,[111] after the fifteenth asteroid (Eunomia) had been discovered, Johann Franz Encke made a major change in the upcoming 1854 edition of the Berliner Astronomisches Jahrbuch (BAJ, Berlin Astronomical Yearbook). He introduced a disk (circle), a traditional symbol for a star, as the generic symbol for an asteroid. The circle was then numbered in order of discovery to indicate a specific asteroid (although he assigned ① to the fifth, Astraea, while continuing to designate the first four only with their existing iconic symbols). The numbered-circle convention was quickly adopted by astronomers, and the next asteroid to be discovered (16 Psyche, in 1852) was the first to be designated in that way at the time of its discovery. However, Psyche was given an iconic symbol as well, as were a few other asteroids discovered over the next few years (see chart above). 20 Massalia was the first asteroid that was not assigned an iconic symbol, and no iconic symbols were created after the 1855 discovery of 37 Fides.[h] That year Astraea's number was increased to ⑤, but the first four asteroids, Ceres to Vesta, were not listed by their numbers until the 1867 edition. The circle was soon abbreviated to a pair of parentheses, which were easier to typeset and sometimes omitted altogether over the next few decades, leading to the modern convention.[107]
+
+Until the age of space travel, objects in the asteroid belt were merely pinpricks of light in even the largest telescopes and their shapes and terrain remained a mystery. The best modern ground-based telescopes and the Earth-orbiting Hubble Space Telescope can resolve a small amount of detail on the surfaces of the largest asteroids, but even these mostly remain little more than fuzzy blobs. Limited information about the shapes and compositions of asteroids can be inferred from their light curves (their variation in brightness as they rotate) and their spectral properties, and asteroid sizes can be estimated by timing the lengths of star occulations (when an asteroid passes directly in front of a star). Radar imaging can yield good information about asteroid shapes and orbital and rotational parameters, especially for near-Earth asteroids. In terms of delta-v and propellant requirements, NEOs are more easily accessible than the Moon.[112]
+
+The first close-up photographs of asteroid-like objects were taken in 1971, when the Mariner 9 probe imaged Phobos and Deimos, the two small moons of Mars, which are probably captured asteroids. These images revealed the irregular, potato-like shapes of most asteroids, as did later images from the Voyager probes of the small moons of the gas giants.
+
+The first true asteroid to be photographed in close-up was 951 Gaspra in 1991, followed in 1993 by 243 Ida and its moon Dactyl, all of which were imaged by the Galileo probe en route to Jupiter.
+
+The first dedicated asteroid probe was NEAR Shoemaker, which photographed 253 Mathilde in 1997, before entering into orbit around 433 Eros, finally landing on its surface in 2001.
+
+Other asteroids briefly visited by spacecraft en route to other destinations include 9969 Braille (by Deep Space 1 in 1999), and 5535 Annefrank (by Stardust in 2002).
+
+From September to November 2005, the Japanese Hayabusa probe studied 25143 Itokawa in detail and was plagued with difficulties, but returned samples of its surface to Earth on 13 June 2010.
+
+The European Rosetta probe (launched in 2004) flew by 2867 Šteins in 2008 and 21 Lutetia, the third-largest asteroid visited to date, in 2010.
+
+In September 2007, NASA launched the Dawn spacecraft, which orbited 4 Vesta from July 2011 to September 2012, and has been orbiting the dwarf planet 1 Ceres since 2015. 4 Vesta is the second-largest asteroid visited to date.
+
+On 13 December 2012, China's lunar orbiter Chang'e 2 flew within 3.2 km (2 mi) of the asteroid 4179 Toutatis on an extended mission.
+
+The Japan Aerospace Exploration Agency (JAXA) launched the Hayabusa2 probe in December 2014, and plans to return samples from 162173 Ryugu in December 2020.
+
+In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, and has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.[14][15][16][18]
+
+In September 2016, NASA launched the OSIRIS-REx sample return mission to asteroid 101955 Bennu, which it reached in December 2018. As of June 2019[update], the probe is in orbit around the asteroid.[113]
+
+In early 2013, NASA announced the planning stages of a mission to capture a near-Earth asteroid and move it into lunar orbit where it could possibly be visited by astronauts and later impacted into the Moon.[114] On 19 June 2014, NASA reported that asteroid 2011 MD was a prime candidate for capture by a robotic mission, perhaps in the early 2020s.[115]
+
+It has been suggested that asteroids might be used as a source of materials that may be rare or exhausted on Earth (asteroid mining), or materials for constructing space habitats (see Colonization of the asteroids). Materials that are heavy and expensive to launch from Earth may someday be mined from asteroids and used for space manufacturing and construction.
+
+In the U.S. Discovery program the Psyche spacecraft proposal to 16 Psyche and Lucy spacecraft to Jupiter trojans made it to the semi-finalist stage of mission selection.
+
+In January 2017, Lucy and Psyche mission were both selected as NASA's Discovery Program missions 13 and 14 respectively.[116]
+
+Location of Ceres (within asteroid belt) compared to other bodies of the Solar System
+
+Distances of selected bodies of the Solar System from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively, hence long bars denote high orbital eccentricity. The radius of the Sun is 0.7 million km, and the radius of Jupiter (the largest planet) is 0.07 million km, both too small to resolve on this image.
+
+Asteroids and the asteroid belt are a staple of science fiction stories. Asteroids play several potential roles in science fiction: as places human beings might colonize, resources for extracting minerals, hazards encountered by spacecraft traveling between two other points, and as a threat to life on Earth or other inhabited planets, dwarf planets, and natural satellites by potential impact.
+
+951 Gaspra is the first asteroid to be imaged in close-up, imaged by Galileo on 29 October 1991 (enhanced color)
+
+Several views of 433 Eros in natural color, imaged by NEAR on 12 February 2000
+
+Vesta imaged by Dawn on 9 July 2011
+
+Ceres imaged by Dawn on 4 February 2015
+
+"We include Trojans (bodies captured in Jupiter's 4th and 5th Lagrange points), Centaurs (bodies in orbit between Jupiter and Neptune), and trans-Neptunian objects (orbiting beyond Neptune) in our definition of "asteroid" as used on this site, even though they may more correctly be called "minor planets" instead of asteroids."[citation needed]
+
+Further information about asteroids
+
+Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Observable universe → UniverseEach arrow (→) may be read as "within" or "part of".

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+The New Testament (Ancient Greek: Ἡ Καινὴ Διαθήκη, transl. Hē Kainḕ Diathḗkē; Latin: Novum Testamentum) is the second part of the Christian biblical canon, the first being the Old Testament. The New Testament discusses the teachings and person of Jesus, as well as events in first-century Christianity. Christians regard both the Old and New Testaments together as sacred scripture.
+
+The New Testament is a collection of Christian texts originally written in the Koine Greek language, at different times by various different authors. While the Old Testament canon varies somewhat between different Christian denominations, the 27-book canon of the New Testament has been almost universally recognized within Christianity since at least Late Antiquity. Thus, in almost all Christian traditions today, the New Testament consists of 27 books:
+
+The earliest known complete list of the 27 books of the New Testament is found in a letter written by Athanasius, a 4th-century bishop of Alexandria, dated to 367 AD.[1] The 27-book New Testament was first formally canonized during the councils of Hippo (393) and Carthage (397) in North Africa. Pope Innocent I ratified the same canon in 405, but it is probable that a Council in Rome in 382 under Pope Damasus I gave the same list first. These councils also provided the canon of the Old Testament, which included the apocryphal books.[2]
+
+There is no scholarly consensus on the date of composition of the latest New Testament texts. Conservative scholars John A. T. Robinson, Dan Wallace, and William F. Albright dated all the books of the New Testament before 70 AD.[3] But most[citation needed] scholars date some New Testament texts much later than this.[4] For example, Richard Pervo dates Luke-Acts to c. AD 115,[5] and David Trobisch places Acts in the mid- to late second century, contemporaneous with the publication of the first New Testament canon.[6][note 1]
+
+The use of the phrase New Testament (Koine Greek: Ἡ Καινὴ Διαθήκη, Hē Kainḕ Diathḗkē) to describe a collection of first and second-century Christian Greek scriptures can be traced back to Tertullian in his work Against Praxeas.[7][8][9] Irenaeus uses the phrase "New Testament" several times, but does not use it in reference to any written text.[8] In Against Marcion, written c. 208 AD, Tertullian writes of:[10]
+
+the Divine Word, who is doubly edged with the two testaments of the law and the gospel.
+
+And Tertullian continues later in the book, writing:[11][note 2]
+
+it is certain that the whole aim at which he [Marcion] has strenuously laboured, even in the drawing up of his Antitheses, centres in this, that he may establish a diversity between the Old and the New Testaments, so that his own Christ may be separate from the Creator, as belonging to this rival god, and as alien from the law and the prophets.
+
+By the 4th century, the existence—even if not the exact contents—of both an Old and New Testament had been established. Lactantius, a 3rd–4th century Christian author wrote in his early-4th-century Latin Institutiones Divinae (Divine Institutes):[12]
+
+But all scripture is divided into two Testaments. That which preceded the advent and passion of Christ—that is, the law and the prophets—is called the Old; but those things which were written after His resurrection are named the New Testament. The Jews make use of the Old, we of the New: but yet they are not discordant, for the New is the fulfilling of the Old, and in both there is the same testator, even Christ, who, having suffered death for us, made us heirs of His everlasting kingdom, the people of the Jews being deprived and disinherited. As the prophet Jeremiah testifies when he speaks such things: "Behold, the days come, saith the Lord, that I will make a new testament to the house of Israel and the house of Judah, not according to the testament which I made to their fathers, in the day that I took them by the hand to bring them out of the land of Egypt; for they continued not in my testament, and I disregarded them, saith the Lord."[Jer 31:31–32]  ... For that which He said above, that He would make a new testament to the house of Judah, shows that the old testament which was given by Moses was not perfect; but that which was to be given by Christ would be complete.
+
+Eusebius describes the collection of Christian writings as "covenanted" (ἐνδιαθήκη) books in Hist. Eccl. 3.3.1–7; 3.25.3; 5.8.1; 6.25.1.
+
+Each of the four gospels in the New Testament narrates the life, death, and resurrection of Jesus of Nazareth, with the exception of Mark which in the original text ends with the empty tomb and has no account of the post-resurrection appearances. The word "gospel" derives from the Old English gōd-spell[13] (rarely godspel), meaning "good news" or "glad tidings". The gospel was considered the "good news" of the coming Kingdom of Messiah, and the redemption through the life and death of Jesus, the central Christian message.[14] Gospel is a calque (word-for-word translation) of the Greek word εὐαγγέλιον, euangelion (eu- "good", -angelion "message").
+
+Starting in the late second century, the four narrative accounts of the life and work of Jesus Christ have been referred to as "The Gospel of ..." or "The Gospel according to ..." followed by the name of the supposed author. The first author to explicitly name the canonical gospels is Irenaeus of Lyon,[8][15] who promoted the four canonical gospels in his book Against Heresies, written around 180.[16] Whatever these admittedly early ascriptions may imply about the sources behind or the perception of these gospels, they are anonymous compositions.
+
+The first three gospels listed above are classified as the Synoptic Gospels. They contain similar accounts of the events in Jesus's life and his teaching, due to their literary interdependence. The Gospel of John is structured differently and includes stories of several miracles of Jesus and sayings not found in the other three.
+
+These four gospels that were eventually included in the New Testament were only a few among many other early Christian gospels. The existence of such texts is even mentioned at the beginning of the Gospel of Luke.[Luke 1:1–4] Other early Christian gospels, such as the so-called "Jewish-Christian Gospels" or the Gospel of Thomas, also offer both a window into the context of early Christianity and may provide some assistance in the reconstruction of the historical Jesus.
+
+The Acts of the Apostles is a narrative of the apostles' ministry and activity after Christ's death and resurrection, from which point it resumes and functions as a sequel to the Gospel of Luke. Examining style, phraseology, and other evidence, modern scholarship generally concludes that Acts and the Gospel of Luke share the same author, referred to as Luke–Acts. Luke-Acts does not name its author.[18] Church tradition identified him as Luke the Evangelist, the companion of Paul, but the majority of scholars reject this due to the many differences between Acts and the authentic Pauline letters.[19] The most probable date of composition is around 80–100 AD, although some scholars date it significantly later,[5][6] and there is evidence that it was still being substantially revised well into the 2nd century.[20]
+
+The epistles of the New Testament are considered by Christians to be divinely inspired and holy letters, written by the apostles and disciples of Christ, to either local congregations with specific needs, or to New Covenant Christians in general, scattered about; or "catholic epistles."
+
+The Pauline letters to churches are the thirteen New Testament books that present Paul the Apostle as their author.[note 3] Six of the letters are disputed. Four are thought by most modern scholars to be pseudepigraphic, i.e., not actually written by Paul even if attributed to him within the letters themselves.  Opinion is more divided on the other two disputed letters (2 Thessalonians and Colossians).[22] These letters were written to Christian communities in specific cities or geographical regions, often to address issues faced by that particular community. Prominent themes include the relationship both to broader "pagan" society, to Judaism, and to other Christians.[23]
+
+[Disputed letters are marked with an asterisk (*).]
+
+The last four Pauline letters in the New Testament are addressed to individual persons. They include the following:
+
+[Disputed letters are marked with an asterisk (*).]
+
+All of the above except for Philemon are known as the Pastoral epistles. They are addressed to individuals charged with pastoral oversight of churches and discuss issues of Christian living, doctrine and leadership. They often address different concerns to those of the preceding epistles. These letters are believed by many to be pseudepigraphic. Some scholars (e.g., Bill Mounce, Ben Witherington) will argue that the letters are genuinely Pauline, or at least written under Paul's supervision.
+
+The Epistle to the Hebrews addresses a Jewish audience who had come to believe that Jesus was the anointed one (Hebrew: מָשִׁיחַ—transliterated in English as "Moshiach", or "Messiah"; Greek: Χριστός—transliterated in English as "Christos", for "Christ") who was predicted in the writings of the Hebrew Scriptures. The author discusses the superiority of the new covenant and the ministry of Jesus, to the Mosaic covenant [Heb. 1:1–10:18] and urges the readers in the practical implications of this conviction through the end of the epistle.[Heb. 10:19–13:25]
+
+The book has been widely accepted by the Christian church as inspired by God and thus authoritative, despite the acknowledgment of uncertainties about who its human author was. Regarding authorship, although the Epistle to the Hebrews does not internally claim to have been written by the Apostle Paul, some similarities in wordings to some of the Pauline Epistles have been noted and inferred. In antiquity, some began to ascribe it to Paul in an attempt to provide the anonymous work an explicit apostolic pedigree.[24]
+
+In the 4th century, Jerome and Augustine of Hippo supported Paul's authorship. The Church largely agreed to include Hebrews as the fourteenth letter of Paul, and affirmed this authorship until the Reformation. The letter to the Hebrews had difficulty in being accepted as part of the Christian canon because of its anonymity.[25] As early as the 3rd century, Origen wrote of the letter, "Men of old have handed it down as Paul's, but who wrote the Epistle God only knows."[26]
+
+Contemporary scholars often reject Pauline authorship for the epistle to the Hebrews,[27] based on its distinctive style and theology, which are considered to set it apart from Paul's writings.[28]
+
+The Catholic epistles (or "general epistles") consist of both letters and treatises in the form of letters written to the church at large. The term "catholic" (Greek: καθολική, katholikē), used to describe these letters in the oldest manuscripts containing them, here simply means "general" or "universal". The authorship of a number of these is disputed.
+
+The final book of the New Testament is the Book of Revelation, also known as the Apocalypse of John. In the New Testament canon, it is considered prophetical or apocalyptic literature. Its authorship has been attributed either to John the Apostle (in which case it is often thought that John the Apostle is John the Evangelist, i.e. author of the Gospel of John) or to another John designated "John of Patmos" after the island where the text says the revelation was received (1:9). Some ascribe the writership date as circa 81–96 AD, and others at around 68 AD.[30] The work opens with letters to seven local congregations of Asia Minor and thereafter takes the form of an apocalypse, a "revealing" of divine prophecy and mysteries, a literary genre popular in ancient Judaism and Christianity.[31]
+
+The order in which the books of the New Testament appear differs between some collections and ecclesiastical traditions. In the Latin West, prior to the Vulgate (an early 5th-century Latin version of the Bible), the four Gospels were arranged in the following order: Matthew, John, Luke, and Mark.[note 4] The Syriac Peshitta places the major Catholic epistles (James, 1 Peter, and 1 John) immediately after Acts and before the Pauline epistles.
+
+The order of an early edition of the letters of Paul is based on the size of the letters: longest to shortest, though keeping 1 and 2 Corinthians and 1 and 2 Thessalonians together. The Pastoral epistles were apparently not part of the Corpus Paulinum in which this order originated and were later inserted after 2 Thessalonians and before Philemon. Hebrews was variously incorporated into the Corpus Paulinum either after 2 Thessalonians, after Philemon (i.e. at the very end), or after Romans.
+
+The New Testament of the 16th-century Luther Bible continues, to this day, to place Hebrews, James, Jude, and the Apocalypse last. This reflects the thoughts of the Reformer Martin Luther on the canonicity of these books.[36][note 5][citation needed]
+
+The books that eventually found a permanent place in the New Testament were not the only works of Christian literature produced in the earliest Christian centuries. The long process of canonization began early, sometimes with tacit reception of traditional texts, sometimes with explicit selection or rejection of particular texts as either acceptable or unacceptable for use in a given context (e.g., not all texts that were acceptable for private use were considered appropriate for use in the liturgy).
+
+Over the course of history, those works of early Christian literature that survived but that did not become part of the New Testament have been variously grouped by theologians and scholars. Drawing upon, though redefining, an older term used in early Christianity and among Protestants when referring to those books found in the Christian Old Testament although not in the Jewish Bible, modern scholars began to refer to these works of early Christian literature not included in the New Testament as "apocryphal", by which was meant non-canonical.
+
+Collected editions of these works were then referred to as the "New Testament apocrypha". Typically excluded from such published collections are the following groups of works: The Apostolic Fathers, the 2nd-century Christian apologists, the Alexandrians, Tertullian, Methodius of Olympus, Novatian, Cyprian, martyrdoms, and the Desert Fathers. Almost all other Christian literature from the period, and sometimes including works composed well into Late Antiquity, are relegated to the so-called New Testament apocrypha.
+
+Although not considered to be inspired by God, these "apocryphal" works were produced in the same ancient context and often using the same language as those books that would eventually form the New Testament. Some of these later works are dependent (either directly or indirectly) upon books that would later come to be in the New Testament or upon the ideas expressed in them. There is even an example of a pseudepigraphical letter composed under the guise of a presumably lost letter of the Apostle Paul, the Epistle to the Laodiceans.
+
+The books of the New Testament were all or nearly all written by Jewish Christians—that is, Jewish disciples of Christ, who lived in the Roman Empire, and under Roman occupation.[37] Luke, who wrote the Gospel of Luke and the Book of Acts, is frequently thought of as an exception; scholars are divided as to whether Luke was a Gentile or a Hellenistic Jew.[38] A few scholars identify the author of the Gospel of Mark as probably a Gentile, and similarly for the Gospel of Matthew, though most assert Jewish-Christian authorship.[39][40][41][verification needed]
+
+According to the large majority of critical scholars, none of the authors of the Gospels were eyewitnesses or even explicitly claimed to be eyewitnesses.[42][43][44] Bart D. Ehrman of the University of North Carolina has argued for a scholarly consensus that many New Testament books were not written by the individuals whose names are attached to them.[44][45] He further argues that names were not ascribed to the gospels until around 185 AD.[46][47] Other scholars concur.[48][49][50] Many scholars believe that none of the gospels were written in the region of Palestine.[51]
+
+Christian tradition identifies John the Apostle with John the Evangelist, the supposed author of the Gospel of John. Traditionalists tend to support the idea that the writer of the Gospel of John himself claimed to be an eyewitness in their commentaries of John 21:24 and therefore the gospel was written by an eyewitness;[52][53] however, this idea is rejected by the majority of modern scholars.[54]
+
+Most[citation needed] scholars hold to the two-source hypothesis, which posits that the Gospel of Mark was the first gospel to be written. On this view, the authors of the Gospel of Matthew and the Gospel of Luke used as sources the Gospel of Mark and a hypothetical Q document to write their individual gospel accounts.[55][56][57][58][59] These three gospels are called the Synoptic Gospels, because they include many of the same stories, often in the same sequence, and sometimes in exactly the same wording. Scholars agree that the Gospel of John was written last, by using a different tradition and body of testimony. In addition, most scholars agree that the author of Luke also wrote the Acts of the Apostles. Scholars hold that these books constituted two-halves of a single work, Luke-Acts.[citation needed]
+
+All four gospels and the Acts of the Apostles are anonymous works.[60] The Gospel of John claims to be based on eyewitness testimony from the Disciple whom Jesus loved, but never names this character.[61]
+
+The same author appears to have written the Gospel of Luke and the Acts of the Apostles, and most refer to them as the Lucan texts.[62][63] The most direct evidence comes from the prefaces of each book; both were addressed to Theophilus, and the preface to the Acts of the Apostles references "my former book" about the ministry of Jesus.[64] Furthermore, there are linguistic and theological similarities between the two works, suggesting that they have a common author.[65][66][67][68]
+
+The Pauline epistles are the thirteen books in the New Testament traditionally attributed to Paul of Tarsus. The anonymous Epistle to the Hebrews is, despite unlikely Pauline authorship, often functionally grouped with these thirteen to form a corpus of fourteen "Pauline" epistles.[note 6]
+
+Seven letters are generally classified as "undisputed", expressing contemporary scholarly near consensus that they are the work of Paul: Romans, 1 Corinthians, 2 Corinthians, Galatians, Philippians, 1 Thessalonians and Philemon. Six additional letters bearing Paul's name do not currently enjoy the same academic consensus: Ephesians, Colossians, 2 Thessalonians, 1 Timothy, 2 Timothy and Titus.[note 7]
+
+While many scholars uphold the traditional view, some question whether the first three, called the "Deutero-Pauline Epistles", are authentic letters of Paul. As for the latter three, the "Pastoral epistles", some scholars uphold the traditional view of these as the genuine writings of the Apostle Paul;[note 7] most, however, regard them as pseudepigrapha.[71]
+
+One might refer to the Epistle to the Laodiceans and the Third Epistle to the Corinthians as examples of works identified as pseudonymous. Since the early centuries of the church, there has been debate concerning the authorship of the anonymous Epistle to the Hebrews, and contemporary scholars generally reject Pauline authorship.[27]
+
+The epistles all share common themes, emphasis, vocabulary and style; they exhibit a uniformity of doctrine concerning the Mosaic Law, Jesus, faith, and various other issues. All of these letters easily fit into the chronology of Paul's journeys depicted in Acts of the Apostles.
+
+The author of the Epistle of James identifies himself in the opening verse as "James, a servant of God and of the Lord Jesus Christ". From the middle of the 3rd century, patristic authors cited the Epistle as written by James the Just.[72] Ancient and modern scholars have always been divided on the issue of authorship. Many consider the epistle to be written in the late 1st or early 2nd centuries.[73]
+
+The author of the First Epistle of Peter identifies himself in the opening verse as "Peter, an apostle of Jesus Christ", and the view that the epistle was written by St. Peter is attested to by a number of Church Fathers: Irenaeus (140–203), Tertullian (150–222), Clement of Alexandria (155–215) and Origen of Alexandria (185–253). Unlike The Second Epistle of Peter, the authorship of which was debated in antiquity, there was little debate about Peter's authorship of this first epistle until the 18th century. Although 2 Peter internally purports to be a work of the apostle, many biblical scholars have concluded that Peter is not the author.[74] For an early date and (usually) for a defense of the Apostle Peter's authorship see Kruger,[75] Zahn,[76] Spitta,[77] Bigg,[78] and Green.[79]
+
+The Epistle of Jude title is written as follows: "Jude, a servant of Jesus Christ and a brother of James" (NRSV). The debate has continued over the author's identity as the apostle, the brother of Jesus, both, or neither.[80]
+
+The Gospel of John, the three Johannine epistles, and the Book of Revelation, exhibit marked similarities, although more so between the gospel and the epistles (especially the gospel and 1 John) than between those and Revelation.[81] Most scholars therefore treat the five as a single corpus of Johannine literature, albeit not from the same author.[82]
+
+The gospel went through two or three "editions" before reaching its current form around AD 90–110.[83][84] It speaks of an unnamed "disciple whom Jesus loved" as the source of its traditions, but does not say specifically that he is its author;[85] Christian tradition identifies this disciple as the apostle John, but while this idea still has supporters, for a variety of reasons the majority of modern scholars have abandoned it or hold it only tenuously.[86] It is significantly different from the synoptic gospels, with major variations in material, theological emphasis, chronology, and literary style, sometimes amounting to contradictions.[87]
+
+The author of the Book of Revelation identifies himself several times as "John".[Rev. 1:1, 4, 9; 22:8] and states that he was on Patmos when he received his first vision.[Rev. 1:9; 4:1–2] As a result, the author is sometimes referred to as John of Patmos. The author has traditionally been identified with John the Apostle to whom the Gospel and the epistles of John were attributed. It was believed that he was exiled to the island of Patmos during the reign of the Roman emperor Domitian, and there wrote Revelation. Justin Martyr (c. 100–165 AD) who was acquainted with Polycarp, who had been mentored by John, makes a possible allusion to this book, and credits John as the source.[88] Irenaeus (c. 115–202) assumes it as a conceded point. According to the Zondervan Pictorial Encyclopedia of the Bible, modern scholars are divided between the apostolic view and several alternative hypotheses put forth in the last hundred years or so.[89] Ben Witherington points out that linguistic evidence makes it unlikely that the books were written by the same person.[90]
+
+The earliest manuscripts of New Testament books date from the late second to early third centuries (although see Papyrus 52 for a possible exception).[27]:479–480 These manuscripts place a clear upper limit on the dating of New Testament texts. Explicit references to NT books in extra-biblical documents can push this upper limit down a bit further. Irenaeus of Lyon names and quotes from most of the books in the New Testament in his book Against Heresies, written around 180 AD. The Epistle of Polycarp to the Philippians, written some time between 110 and Polycarp's death in 155-167 AD, quotes or alludes to most New Testament texts. Ignatius of Antioch wrote letters referencing much of the New Testament. He lived from about 35AD to 107AD and is rumored to have been a disciple of the Apostle John. His writings reference the Gospels of John, Matthew, and Luke, as well as Peter, James, and Paul's Epistles. His writing is usually attributed to the end of his lifetime, which places the Gospels as First Century writings.
+
+Literary analysis of the New Testament texts themselves can be used to date many of the books of the New Testament to the mid- to late first century. The earliest works of the New Testament are the letters of the Apostle Paul. It can be determined that 1 Thessalonians is likely the earliest of these letters, written around 52 AD.[91]
+
+The major languages spoken by both Jews and Greeks in the Holy Land at the time of Jesus were Aramaic and Koine Greek, and also a colloquial dialect of Mishnaic Hebrew. It is generally agreed by most scholars that the historical Jesus primarily spoke Aramaic,[92] perhaps also some Hebrew and Koine Greek. The majority view is that all of the books that would eventually form the New Testament were written in the Koine Greek language.[93][94]
+
+As Christianity spread, these books were later translated into other languages, most notably, Latin, Syriac, and Egyptian Coptic. However, some of the Church Fathers[95] imply or claim that Matthew was originally written in Hebrew or Aramaic, and then soon after was written in Koine Greek. Nevertheless, some scholars believe the Gospel of Matthew known today was composed in Greek and is neither directly dependent upon nor a translation of a text in a Semitic language.[96]
+
+The process of canonization of the New Testament was complex and lengthy. In the initial centuries of early Christianity, there were many books widely considered by the church to be inspired, but there was no single formally recognized New Testament canon.[97] The process was characterized by a compilation of books that apostolic tradition considered authoritative in worship and teaching, relevant to the historical situations in which they lived, and consonant with the Old Testament.[98] Writings attributed to the apostles circulated among the earliest Christian communities and the Pauline epistles were circulating, perhaps in collected forms, by the end of the 1st century AD.[99]
+
+One of the earliest attempts at solidifying a canon was made by Marcion, circa 140 AD, who accepted only a modified version of Luke (the Gospel of Marcion) and ten of Paul's letters, while rejecting the Old Testament entirely. His canon was largely rejected by other groups of Christians, notably the proto-orthodox Christians, as was his theology, Marcionism. Adolf von Harnack,[100] John Knox,[101] and David Trobisch,[6] among other scholars, have argued that the church formulated its New Testament canon partially in response to the challenge posed by Marcion.
+
+Polycarp,[102] Irenaeus[103] and Tertullian[104] held the epistles of Paul to be divinely inspired "scripture." Other books were held in high esteem but were gradually relegated to the status of New Testament apocrypha. Justin Martyr, in the mid 2nd century, mentions "memoirs of the apostles" as being read on Sunday alongside the "writings of the prophets".[105]
+
+The Muratorian fragment, dated at between 170 and as late as the end of the 4th century (according to the Anchor Bible Dictionary), may be the earliest known New Testament canon attributed to mainstream Christianity. It is similar, but not identical, to the modern New Testament canon.
+
+The oldest clear endorsement of Matthew, Mark, Luke, and John being the only legitimate gospels was written circa 180 AD. A four gospel canon (the Tetramorph) was asserted by Irenaeus, who refers to it directly[106][107] in his polemic Against Heresies:
+
+"It is not possible that the gospels can be either more or fewer in number than they are. For, since there are four zones of the world in which we live, and four principal winds, while the church is scattered throughout all the world, and the 'pillar and ground' of the church is the gospel and the spirit of life; it is fitting that she should have four pillars, breathing out immortality on every side, and vivifying men afresh." (emphasis added)[107]
+
+The books considered to be authoritative by Irenaeus included the four gospels and many of the letters of Paul, although, based on the arguments Irenaeus made in support of only four authentic gospels, some interpreters deduce that the fourfold Gospel must have still been a novelty in Irenaeus's time.[108]
+
+By the early 200s, Origen may have been using the same twenty-seven books as in the Catholic New Testament canon, though there were still disputes over the canonicity of the Letter to the Hebrews, Epistle of James, II Peter, II John and III John and the Book of Revelation,[109] known as the Antilegomena. Likewise, the Muratorian fragment is evidence that, perhaps as early as 200, there existed a set of Christian writings somewhat similar to the twenty-seven book NT canon, which included four gospels and argued against objections to them.[110] Thus, while there was a good measure of debate in the Early Church over the New Testament canon, the major writings are claimed to have been accepted by almost all Christians by the middle of the 3rd century.[111]
+
+Origen was largely responsible for the collection of usage information regarding the texts that became the New Testament. The information used to create the late-4th-century Easter Letter, which declared accepted Christian writings, was probably based on the Ecclesiastical History [HE] of Eusebius of Caesarea, wherein he uses the information passed on to him by Origen to create both his list at HE 3:25 and Origen's list at HE 6:25. Eusebius got his information about what texts were then accepted and what were then disputed, by the third-century churches throughout the known world, a great deal of which Origen knew of firsthand from his extensive travels, from the library and writings of Origen.[112]
+
+In fact, Origen would have possibly included in his list of "inspired writings" other texts kept out by the likes of Eusebius—including the Epistle of Barnabas, Shepherd of Hermas, and 1 Clement. Notwithstanding these facts, "Origen is not the originator of the idea of biblical canon, but he certainly gives the philosophical and literary-interpretative underpinnings for the whole notion."[113]
+
+Eusebius, circa 300, gave a detailed list of New Testament writings in his Ecclesiastical History Book 3, Chapter XXV:
+
+The Book of Revelation is counted as both accepted (Kirsopp Lake translation: "Recognized") and disputed, which has caused some confusion over what exactly Eusebius meant by doing so. From other writings of the church fathers, it was disputed with several canon lists rejecting its canonicity. EH 3.3.5 adds further detail on Paul: "Paul's fourteen epistles are well known and undisputed. It is not indeed right to overlook the fact that some have rejected the Epistle to the Hebrews, saying that it is disputed by the church of Rome, on the ground that it was not written by Paul." EH 4.29.6 mentions the Diatessaron: "But their original founder, Tatian, formed a certain combination and collection of the gospels, I know not how, to which he gave the title Diatessaron, and which is still in the hands of some. But they say that he ventured to paraphrase certain words of the apostle Paul, in order to improve their style."
+
+In his Easter letter of 367, Athanasius, Bishop of Alexandria, gave a list of the books that would become the twenty-seven-book NT canon,[1] and he used the word "canonized" (kanonizomena) in regards to them.[114] The first council that accepted the present canon of the New Testament may have been the Synod of Hippo Regius in North Africa (393 AD); the acts of this council, however, are lost. A brief summary of the acts was read at and accepted by the Council of Carthage (397) and the Council of Carthage (419).[115] These councils were under the authority of St. Augustine, who regarded the canon as already closed.[116][117][118]
+
+Pope Damasus I's Council of Rome in 382, if the Decretum Gelasianum is correctly associated with it, issued a biblical canon identical to that mentioned above,[1] or, if not, the list is at least a 6th-century compilation.[119] Likewise, Damasus' commissioning of the Latin Vulgate edition of the Bible, c. 383, was instrumental in the fixation of the canon in the West.[120] In c. 405, Pope Innocent I sent a list of the sacred books to a Gallic bishop, Exsuperius of Toulouse. Christian scholars assert that, when these bishops and councils spoke on the matter, however, they were not defining something new but instead "were ratifying what had already become the mind of the Church."[116][121][122]
+
+The New Testament canon as it is now was first listed by St. Athanasius, Bishop of Alexandria, in 367, in a letter written to his churches in Egypt, Festal Letter 39. Also cited is the Council of Rome, but not without controversy. That canon gained wider and wider recognition until it was accepted at the Third Council of Carthage in 397 and 419.[note 8]
+
+Even this council did not settle the matter, however. Certain books, referred to as Antilegomena, continued to be questioned, especially James and Revelation. Even as late as the 16th century, the Reformer Martin Luther questioned (but in the end did not reject) the Epistle of James, the Epistle of Jude, the Epistle to the Hebrews and the Book of Revelation. To this day, German-language Luther Bibles are printed with these four books at the end of the canon, rather than in their traditional order as in other editions of the Bible.
+
+In light of this questioning of the canon of Scripture by Protestants in the 16th century, the (Roman Catholic) Council of Trent reaffirmed the traditional western canon (i.e., the canon accepted at the 4th-century Council of Rome and Council of Carthage), thus making the Canon of Trent and the Vulgate Bible dogma in the Catholic Church. Later, Pope Pius XI on 2 June 1927 decreed the Comma Johanneum was open to dispute and Pope Pius XII on 3 September 1943 issued the encyclical Divino afflante Spiritu, which allowed translations based on other versions than just the Latin Vulgate, notably in English the New American Bible.
+
+Thus, some claim that, from the 4th century, there existed unanimity in the West concerning the New Testament canon (as it is today),[123] and that, by the 5th century, the Eastern Church, with a few exceptions, had come to accept the Book of Revelation and thus had come into harmony on the matter of the canon.[124] Nonetheless, full dogmatic articulations of the canon were not made until the Canon of Trent of 1546 for Roman Catholicism, the Thirty-Nine Articles of 1563 for the Church of England, the Westminster Confession of Faith of 1647 for Calvinism, and the Synod of Jerusalem of 1672 for the Greek Orthodox.
+
+On the question of NT Canon formation generally, New Testament scholar Lee Martin McDonald has written that:[125]
+
+Although a number of Christians have thought that church councils determined what books were to be included in the biblical canons, a more accurate reflection of the matter is that the councils recognized or acknowledged those books that had already obtained prominence from usage among the various early Christian communities.
+
+Christian scholars assert that when these bishops and councils spoke on the matter, they were not defining something new, but instead "were ratifying what had already become the mind of the Church".[121][122]
+
+Some synods of the 4th century published lists of canonical books (e.g. Hippo and Carthage). The existing 27-book canon of the New Testament was reconfirmed (for Roman Catholicism) in the 16th century with the Council of Trent (also called the Tridentine Council) of 1546,[126] the Thirty-Nine Articles of 1563 for the Church of England, the Westminster Confession of Faith of 1647 for Calvinism, and the Synod of Jerusalem of 1672 for Eastern Orthodoxy. Although these councils did include statements about the canon, when it came to the New Testament they were only reaffirming the existing canon, including the Antilegomena.
+
+According to the Catholic Encyclopedia article on the Canon of the New Testament: "The idea of a complete and clear-cut canon of the New Testament existing from the beginning, that is from Apostolic times, has no foundation in history. The Canon of the New Testament, like that of the Old, is the result of a development, of a process at once stimulated by disputes with doubters, both within and without the Church, and retarded by certain obscurities and natural hesitations, and which did not reach its final term until the dogmatic definition of the Tridentine Council."[127]
+
+In 331, Constantine I commissioned Eusebius to deliver fifty Bibles for the Church of Constantinople. Athanasius (Apol. Const. 4) recorded Alexandrian scribes around 340 preparing Bibles for Constans. Little else is known, though there is plenty of speculation. For example, it is speculated that this may have provided motivation for canon lists, and that Codex Vaticanus and Codex Sinaiticus may be examples of these Bibles. Together with the Peshitta and Codex Alexandrinus, these are the earliest extant Christian Bibles.[128] There is no evidence among the canons of the First Council of Nicaea of any determination on the canon.
+
+Like other literature from antiquity, the text of the New Testament was (prior to the advent of the printing press) preserved and transmitted in manuscripts. Manuscripts containing at least a part of the New Testament number in the thousands. The earliest of these (like manuscripts containing other literature) are often very fragmentarily preserved. Some of these fragments have even been thought to date as early as the 2nd century (i.e., Papyrus 90, Papyrus 98, Papyrus 104, and famously Rylands Library Papyrus P52, though the early date of the latter has recently been called into question).[129]
+
+For each subsequent century, more and more manuscripts survive that contain a portion or all of the books that were held to be part of the New Testament at that time (for example, the New Testament of the 4th-century Codex Sinaiticus, once a complete Bible, contains the Epistle of Barnabas and the Shepherd of Hermas), though occasionally these manuscripts contain other works as well (e.g., Papyrus 72 and the Crosby-Schøyen Codex). The date when a manuscript was written, however, does not necessarily reflect the date of the form of text it contains. That is, later manuscripts can, and occasionally do, contain older forms of text or older readings.
+
+Some of the more important manuscripts containing an early text of books of the New Testament are:
+
+Textual criticism deals with the identification and removal of transcription errors in the texts of manuscripts. Ancient scribes made errors or alterations (such as including non-authentic additions).[130] The New Testament has been preserved in more than 5,800 Greek manuscripts, 10,000 Latin manuscripts and 9,300 manuscripts in various other ancient languages including Syriac, Slavic, Ethiopic and Armenian. Even if the original Greek versions were lost, the entire New Testament could still be assembled from the translations.[131]
+
+In addition, there are so many quotes from the New Testament in early church documents and commentaries that the entire New Testament could also be assembled from these alone.[131] Not all biblical manuscripts come from orthodox Christian writers. For example, the Gnostic writings of Valentinus come from the 2nd century AD, and these Christians were regarded as heretics by the mainstream church.[132] The sheer number of witnesses presents unique difficulties, but it also gives scholars a better idea of how close modern Bibles are to the original versions.[132]
+
+On noting the large number of surviving ancient manuscripts, Bruce Metzger sums up the view on the issue by saying "The more often you have copies that agree with each other, especially if they emerge from different geographical areas, the more you can cross-check them to figure out what the original document was like. The only way they'd agree would be where they went back genealogically in a family tree that represents the descent of the manuscripts.[131]
+
+In attempting to determine the original text of the New Testament books, some modern textual critics have identified sections as additions of material, centuries after the gospel was written. These are called interpolations. In modern translations of the Bible, the results of textual criticism have led to certain verses, words and phrases being left out or marked as not original. According to Bart D. Ehrman, "These scribal additions are often found in late medieval manuscripts of the New Testament, but not in the manuscripts of the earlier centuries."[133]
+
+Most modern Bibles have footnotes to indicate passages that have disputed source documents. Bible Commentaries also discuss these, sometimes in great detail. While many variations have been discovered between early copies of biblical texts, almost all have no importance, as they are variations in spelling, punctuation, or grammar. Also, many of these variants are so particular to the Greek language that they would not appear in translations into other languages. For example, order of words (i.e. "man bites dog" versus "dog bites man") often does not matter in Greek, so textual variants that flip the order of words often have no consequences.[131]
+
+Outside of these unimportant variants, there are a couple variants of some importance. The two most commonly cited examples are the last verses of the Gospel of Mark[134][135][136] and the story of the adulterous woman in the Gospel of John.[137][138][139] Many scholars and critics also believe that the Comma Johanneum reference supporting the Trinity doctrine in 1 John to have been a later addition.[140][141] According to Norman Geisler and William Nix, "The New Testament, then, has not only survived in more manuscripts than any other book from antiquity, but it has survived in a purer form than any other great book—a form that is 99.5% pure"[142]
+
+The often referred to Interpreter's Dictionary of the Bible, a book written to prove the validity of the New Testament, says: " A study of 150 Greek [manuscripts] of the Gospel of Luke has revealed more than 30,000 different readings... It is safe to say that there is not one sentence in the New Testament in which the [manuscript] is wholly uniform."[143] Most of the variation took place within the first three Christian centuries.
+
+By the 4th century, textual "families" or types of text become discernible among New Testament manuscripts. A "text-type" is the name given to a family of texts with similar readings due to common ancestors and mutual correction. Many early manuscripts, however, contain individual readings from several different earlier forms of text. Modern texual critics have identified the following text-types among textual witnesses to the New Testament: The Alexandrian text-type is usually considered to generally preserve many early readings. It is represented, e.g., by Codex Vaticanus, Codex Sinaiticus and the Bodmer Papyri.
+
+The Western text-type is generally longer and can be paraphrastic, but can also preserve early readings. The Western version of the Acts of the Apostles is, notably, 8.5% longer than the Alexandrian form of the text. Examples of the Western text are found in Codex Bezae, Codex Claromontanus, Codex Washingtonianus, the Old Latin (i.e., Latin translations made prior to the Vulgate), as well as in quotations by Marcion, Tatian, Irenaeus, Tertullian and Cyprian.
+
+A text-type referred to as the "Caesarean text-type" and thought to have included witnesses such as Codex Koridethi and minuscule 565, can today be described neither as "Caesarean" nor as a text-type as was previously thought. However, the Gospel of Mark in Papyrus 45, Codex Washingtonianus and in Family 13 does indeed reflect a distinct type of text.
+
+Increasing standardization of distinct (and once local) text-types eventually gave rise to the Byzantine text-type. Since most manuscripts of the New Testament do not derive from the first several centuries, that is, they were copied after the rise of the Byzantine text-type, this form of text is found the majority of extant manuscripts and is therefore often called the "Majority Text." As with all of the other (earlier) text-types, the Byzantine can also occasionally preserve early readings.
+
+Biblical criticism is the scholarly "study and investigation of biblical writings that seeks to make discerning judgments about these writings." Viewing biblical texts as having human rather than supernatural origins, it asks when and where a particular text originated; how, why, by whom, for whom, and in what circumstances it was produced; what influences were at work in its production; what sources were used in its composition; and what message it was intended to convey.
+
+It will vary slightly depending on whether the focus is on the Old Testament, the letters of the New Testament, or the Canonical Gospels. It also plays an important role in the quest for the historical Jesus. It also addresses the physical text, including the meaning of the words and the way in which they are used, its preservation, history, and integrity. Biblical criticism draws upon a wide range of scholarly disciplines including archaeology, anthropology, folklore, linguistics, Oral Tradition studies, history, and religious studies.
+
+The textual variation among manuscript copies of books in the New Testament prompted attempts to discern the earliest form of text already in antiquity (e.g., by the 3rd-century Christian author Origen). The efforts began in earnest again during the Renaissance, which saw a revival of the study of ancient Greek texts. During this period, modern textual criticism was born. In this context, Christian humanists such as Lorenzo Valla and Erasmus promoted a return to the original Greek of the New Testament. This was the beginning of modern New Testament textual criticism, which over subsequent centuries would increasingly incorporate more and more manuscripts, in more languages (i.e., versions of the New Testament), as well as citations of the New Testament by ancient authors and the New Testament text in lectionaries in order to reconstruct the earliest recoverable form of the New Testament text and the history of changes to it.[144]
+
+Books that later formed the New Testament, like other Christian literature of the period, originated in a literary context that reveals relationships not only to other Christian writings, but also to Graeco-Roman and Jewish works. Of singular importance is the extensive use of and interaction with the Jewish Bible and what would become the Christian Old Testament. Both implicit and explicit citations, as well as countless allusions, appear throughout the books of the New Testament, from the Gospels and Acts, to the Epistles, to the Apocalypse.[145]
+
+The first translations (usually called "versions") of the New Testament were made beginning already at the end of 2nd century. The earliest versions of the New Testament are the translations into the Syriac, Latin, and Coptic languages.[146] These three versions were made directly from the Greek, and are frequently cited in the apparatuses of modern critical editions.
+
+Syriac was spoken in Syria, and Mesopotamia, and with dialect in Roman and Byzantine Palestine where it was known as Jewish Palestinian Aramaic. Several Syriac translations were made and have come to us. Most of the Old Syriac, however, as well as the Philoxonian version have been lost.
+
+Tatian, the Assyrian, created the Diatessaron, a gospel harmony written in Syriac around 170 AD and the earliest form of the gospel not only in Syriac but probably also in Armenian.
+
+In the 19th century, manuscript evidence was discovered for an "Old Syriac" version of the four distinct (i.e., not harmonized) gospels. These "separated" (Syriac: da-Mepharreshe) gospels, though old, have been shown to be later than the Diatessaron. The Old Syriac gospels are fragmentarily preserved in two manuscripts: the 5th-century Curetonian Syriac and the Sinaitic Syriac from the 4th or 5th century.
+
+No Old Syriac manuscripts of other portions of the New Testament survive, though Old Syriac readings, e.g. from the Pauline Epistles, can be discerned in citations made by Eastern fathers and in later Syriac versions. The Old Syriac version is a representative of the Western text-type. The Peshitta version was prepared in the beginning of the 5th century. It contains only 22 books (neither the Minor Catholic Epistles of 2 Peter, 2 and 3 John, and Jude, nor the Book of Revelation were part of this translation).
+
+The Philoxenian probably was produced in 508 for Philoxenus, Bishop of Mabung.[147]
+
+The Gospels were likely translated into Latin as early as the last quarter of the 2nd century in North Africa (Afra). Not much later, there were also European Latin translations (Itala). There are about 80 Old Latin mansucripts. The Vetus Latina ("Old Latin") versions often contain readings with a Western type of text. (For the avoidance of confusion, these texts were written in Late Latin, not the early version of the Latin language known as Old Latin, pre 75 BC.)
+
+The bewildering diversity of the Old Latin versions prompted Jerome to prepare another translation into Latin—the Vulgate. In many respects it was merely a revision of the Old Latin. There are currently around 8,000 manuscripts of the Vulgate.
+
+There are several dialects of the Coptic language: Bohairic (northern dialect), Fayyumic, Sahidic (southern dialect), Akhmimic, and others. The first translation was made by at least the 3rd century into the Sahidic dialect (copsa). This translation represents a mixed text, mostly Alexandrian, though also with Western readings.[148]
+
+A Bohairic translation was made later, but existed already in the 4th century. Though the translation makes less use of Greek words than the Sahidic, it does employ some Greek grammar (e.g., in word-order and the use of particles such as the syntactic construction μεν—δε). For this reason, the Bohairic translation can be helpful in the reconstruction of the early Greek text of the New Testament.[149]
+
+The continued spread of Christianity, and the foundation of national churches, led to the translation of the Bible—often beginning with books from the New Testament—into a variety of other languages at a relatively early date: Armenian, Georgian, Ethiopic, Persian, Sogdian, and eventually Gothic, Old Church Slavonic, Arabic, and Nubian.[150]
+
+Historically, throughout the Christian world and in the context of Christian missionary activity, the New Testament (or portions thereof) has been that part of the Christian Bible first translated into the vernacular. The production of such translations grew out of the insertion of vernacular glosses in biblical texts, as well as out of the production of biblical paraphrases and poetic renditions of stories from the life of Christ (e.g., the Heliand).
+
+The 16th century saw the rise of Protestantism and an explosion of translations of the New (and Old) Testament into the vernacular. Notable are those of Martin Luther (1522), Jacques Lefèvre d'Étaples (1523), the Froschau Bible (1525–1529, revised in 1574), William Tyndale (1526, revised in 1534, 1535 and 1536), the Brest Bible (1563), and the Authorized Version (also called the "King James Version") (1611).
+
+Most of these translations relied (though not always exclusively) upon one of the printed editions of the Greek New Testament edited by Erasmus, the Novum Instrumentum omne; a form of this Greek text emerged as the standard and is known as the Textus Receptus. This text, based on the majority of manuscripts is also used in the majority of translations that were made in the years 100 to 400 AD.
+
+Translations of the New Testament made since the appearance of critical editions of the Greek text (notably those of Tischendorf, Westcott and Hort, and von Soden) have largely used them as their base text. Unlike the Textus Receptus, these have a pronounced Alexandrian character. Standard critical editions are those of Nestle-Åland (the text, though not the full critical apparatus of which is reproduced in the United Bible Societies' "Greek New Testament"), Souter, Vogels, Bover and Merk.
+
+Notable translations of the New Testament based on these most recent critical editions include the Revised Standard Version (1946, revised in 1971), La Bible de Jérusalem (1961, revised in 1973 and 2000), the Einheitsübersetzung (1970, final edition 1979), the New American Bible (1970, revised in 1986), the Traduction Oecuménique de la Bible (1988, revised in 2004), and the New Revised Standard Version (1989).
+
+Though all Christian churches accept the New Testament as scripture, they differ in their understanding of the nature, extent, and relevance of its authority. Views of the authoritativeness of the New Testament often depend on the concept of inspiration, which relates to the role of God in the formation of the New Testament. Generally, the greater the role of God in one's doctrine of inspiration, the more one accepts the doctrine of biblical inerrancy or authoritativeness of the Bible. One possible source of confusion is that these terms are difficult to define, because many people use them interchangeably or with very different meanings. This article will use the terms in the following manner:
+
+The self-witness of the Bible to its inspiration demands a commitment to its unity. The ultimate basis for unity is contained in the claim of divine inspiration in 2 Timothy 3:16 that "all Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness" (KJV). The term "inspiration" renders the Greek word theopneustos. This term only occurs here in the New Testament and literally means "God-breathed" (the chosen translation of the NIV).[151]
+
+All of these concepts depend for their meaning on the supposition that the text of Bible has been properly interpreted, with consideration for the intention of the text, whether literal history, allegory or poetry, etc. Especially the doctrine of inerrancy is variously understood according to the weight given by the interpreter to scientific investigations of the world.
+
+The notion of unity in diversity of Scripture claims that the Bible presents a noncontradictory and consistent message concerning God and redemptive history. The fact of diversity is observed in comparing the diversity of time, culture, authors' perspectives, literary genre, and the theological themes.[151]
+
+Studies from many theologians considering the "unity in diversity" to be found in the New Testament (and the Bible as a whole) have been collected and summarized by New Testament theologian Frank Stagg. He describes them as some basic presuppositions, tenets, and concerns common among the New Testament writers, giving to the New Testament its "unity in diversity":
+
+For the Roman Catholic Church, there are two modes of Revelation: Scripture and Tradition. Both of them are interpreted by the teachings of the Church. The Roman Catholic view is expressed clearly in the Catechism of the Catholic Church (1997):
+
+§ 82: As a result the Church, to whom the transmission and interpretation of Revelation is entrusted, does not derive her certainty about all revealed truths from the holy Scriptures alone. Both Scripture and Tradition must be accepted and honoured with equal sentiments of devotion and reverence.
+
+§ 107: The inspired books teach the truth. Since therefore all that the inspired authors or sacred writers affirm should be regarded as affirmed by the Holy Spirit, we must acknowledge that the books of Scripture firmly, faithfully, and without error teach that truth which God, for the sake of our salvation, wished to see confided to the Sacred Scriptures.
+
+In Catholic terminology the teaching office is called the Magisterium.  The Catholic view should not be confused with the two-source theory.  As the Catechism states in §§ 80 and 81, Revelation has "one common source ... two distinct modes of transmission."[153]
+
+While many Eastern Orthodox writers distinguish between Scripture and Tradition, Bishop Kallistos Ware says that for the Orthodox there is only one source of the Christian faith, Holy Tradition, within which Scripture exists.[154]
+
+Traditional Anglicans believe that "Holy Scripture containeth all things necessary to salvation", (Article VI), but also that the Catholic Creeds "ought thoroughly to be received and believed" (Article VIII), and that the Church "hath authority in Controversies of Faith" and is "a witness and keeper of Holy Writ" (Article XX).[155] Classical Anglicanism, therefore, like Orthodoxy, holds that Holy Tradition is the only safe guardian against perversion and innovation in the interpretation of Scripture.
+
+In the famous words of Thomas Ken, Bishop of Bath and Wells: "As for my religion, I dye in the holy catholic and apostolic faith professed by the whole Church before the disunion of East and West, more particularly in the communion of the Church of England, as it stands distinguished from all Papal and Puritan innovations, and as it adheres to the doctrine of the Cross."
+
+Following the doctrine of sola scriptura, Protestants believe that their traditions of faith, practice and interpretations carry forward what the scriptures teach, and so tradition is not a source of authority in itself. Their traditions derive authority from the Bible, and are therefore always open to reevaluation. This openness to doctrinal revision has extended in Liberal Protestant traditions even to the reevaluation of the doctrine of Scripture upon which the Reformation was founded, and members of these traditions may even question whether the Bible is infallible in doctrine, inerrant in historical and other factual statements, and whether it has uniquely divine authority. However, the adjustments made by modern Protestants to their doctrine of scripture vary widely.
+
+Within the US, the Chicago Statement on Biblical Inerrancy (1978) is a statement, articulating evangelical views on this issue. Paragraph four of its summary states: "Being wholly and verbally God-given, Scripture is without error or fault in all its teaching, no less in what it states about God's acts in creation, about the events of world history, and about its own literary origins under God, than in its witness to God's saving grace in individual lives."[156]
+
+Mainline American Protestant denominations, including the United Methodist Church, Presbyterian Church USA, The Episcopal Church, and Evangelical Lutheran Church in America, do not teach the doctrine of inerrancy as set forth in the Chicago Statement. All of these churches have more ancient doctrinal statements asserting the authority of scripture, but may interpret these statements in such a way as to allow for a very broad range of teaching—from evangelicalism to skepticism. It is not an impediment to ordination in these denominations to teach that the scriptures contain errors, or that the authors follow a more or less unenlightened ethics that, however appropriate it may have seemed in the authors' time, moderns would be very wrong to follow blindly.
+
+For example, ordination of women is universally accepted in the mainline churches, abortion is condemned as a grievous social tragedy but not always a personal sin or a crime against an unborn person, and homosexuality is sometimes recognized as a genetic propensity or morally neutral preference that should be neither encouraged nor condemned. In North America, the most contentious of these issues among these churches at the present time is how far the ordination of gay men and lesbians should be accepted.
+
+Officials of the Presbyterian Church USA report: "We acknowledge the role of scriptural authority in the Presbyterian Church, but Presbyterians generally do not believe in biblical inerrancy. Presbyterians do not insist that every detail of chronology or sequence or prescientific description in scripture be true in literal form. Our confessions do teach biblical infallibility. Infallibility affirms the entire truthfulness of scripture without depending on every exact detail."[157]
+
+Those who hold a more liberal view of the Bible as a human witness to the glory of God, the work of fallible humans who wrote from a limited experience unusual only for the insight they have gained through their inspired struggle to know God in the midst of a troubled world. Therefore, they tend not to accept such doctrines as inerrancy. These churches also tend to retain the social activism of their evangelical forebears of the 19th century, placing particular emphasis on those teachings of scripture that teach compassion for the poor and concern for social justice.
+
+The message of personal salvation is, generally speaking, of the good that comes to oneself and the world through following the New Testament's Golden Rule admonition to love others without hypocrisy or prejudice. Toward these ends, the "spirit" of the New Testament, more than the letter, is infallible and authoritative.
+
+There are some movements that believe the Bible contains the teachings of Jesus but who reject the churches that were formed following its publication. These people believe all individuals can communicate directly with God and therefore do not need guidance or doctrines from a church. These people are known as Christian anarchists.
+
+Messianic Judaism generally holds the same view of New Testament authority as evangelical Protestants.[158] According to the view of some Messianic Jewish congregations, Jesus did not annul the Torah, but that its interpretation is revised and ultimately explained through the Apostolic Scriptures.[159]
+
+Jehovah's Witnesses accept the New Testament as divinely inspired Scripture, and as infallible in every detail, with equal authority as the Hebrew Scriptures. They view it as the written revelation and good news of the Messiah, the ransom sacrifice of Jesus, and the Kingdom of God, explaining and expounding the Hebrew Bible, not replacing but vitally supplementing it. They also view the New Testament as the primary instruction guide for Christian living, and church discipline. They generally call the New Testament the "Christian Greek Scriptures", and see only the "covenants" as "old" or "new", but not any part of the actual Scriptures themselves.[160]
+
+Oneness Pentecostalism subscribes to the common Protestant doctrine of sola scriptura. They view the Bible as the inspired Word of God, and as absolutely inerrant in its contents (though not necessarily in every translation).[161][162] They regard the New Testament as perfect and inerrant in every way, revealing the Lord Jesus Christ in the Flesh, and his Atonement, and which also explains and illuminates the Old Testament perfectly, and is part of the Bible canon, not because church councils or decrees claimed it so, but by witness of the Holy Spirit.[163][164]
+
+The Seventh-day Adventist Church holds the New Testament as the inspired Word of God, with God influencing the "thoughts" of the Apostles in the writing, not necessarily every word though.  The first fundamental belief of the Seventh-Day Adventist church stated that "The Holy Scriptures are the infallible revelation of [God's] will." Adventist theologians generally reject the "verbal inspiration" position on Scripture held by many conservative evangelical Christians. They believe instead that God inspired the thoughts of the biblical authors and apostles, and that the writers then expressed these thoughts in their own words.[165] This view is popularly known as "thought inspiration", and most Adventist members hold to that view. According to Ed Christian, former JATS editor, "few if any ATS members believe in verbal inerrancy".[166]
+
+Regarding the teachings of the New Testament compared to the Old, and the application in the New Covenant, Adventists have traditionally taught that the Decalogue is part of the moral law of God, which was not abrogated by the ministry and death of Jesus Christ. Therefore, the fourth commandment concerning the Sabbath is as applicable to Christian believers as the other nine. Adventists have often taught a distinction between "moral law" and "ceremonial law". According to Adventist beliefs, the moral law continues into the "New Testament era", but the ceremonial law was done away with by Jesus.
+
+How the Mosaic law should be applied came up at Adventist conferences in the past, and Adventist theologians such as A. T. Jones and E. J. Waggoner looked at the problem addressed by Paul in Galatians as not the ceremonial law, but rather the wrong use of the law (legalism). They were opposed by Uriah Smith and George Butler at the 1888 Conference. Smith in particular thought the Galatians issue had been settled by Ellen White already, yet in 1890 she claimed justification by faith is "the third angel's message in verity."[citation needed]
+
+Ellen White interpreted Colossians 2:14 as saying that the ceremonial law was nailed to the cross.[167]
+
+Members of The Church of Jesus Christ of Latter-day Saints (LDS Church) believe that the New Testament, as part of the Christian biblical canon, is accurate "as far as it is translated correctly".[168] They believe the Bible as originally revealed is the word of God, but that the processes of transcription and translation have introduced errors into the texts as currently available, and therefore they cannot be regarded as completely inerrant.[169][170] In addition to the Old and New Testaments, the Book of Mormon, the Doctrine and Covenants and the Pearl of Great Price are considered part of their scriptural canon.[171][172]
+
+Despite the wide variety among Christian liturgies, texts from the New Testament play a role in almost all forms of Christian worship. In addition to some language derived from the New Testament in the liturgy itself (e.g., the Trisagion may be based on Apocalypse 4:8, and the beginning of the "Hymn of Praise" draws upon Luke 2:14), the reading of extended passages from the New Testament is a practice common to almost all Christian worship, liturgical or not.
+
+These readings are most often part of an established lectionary (i.e., selected texts to be read at church services on specific days), and (together with an Old Testament reading and a Psalm) include a non-gospel reading from the New Testament and culminate with a Gospel reading. No readings from the Book of Revelation, however, are included in the standard lectionary of the Eastern Orthodox churches.
+
+Central to the Christian liturgy is the celebration of the Eucharist or "Holy Communion". The Words of Institution that begin this rite are drawn directly from 1 Corinthians 11:23–26. In addition, the communal recitation of the Lord's Prayer (in the form found in the Gospel of Matthew 6:9–13) is also a standard feature of Christian worship.
+
+Most of the influence of the New Testament upon the arts has come from the Gospels and the Book of Revelation.[citation needed] Literary expansion of the Nativity of Jesus found in the Gospels of Matthew and Luke began already in the 2nd century, and the portrayal of the Nativity has continued in various art forms to this day. The earliest Christian art would often depict scenes from the New Testament such as the raising of Lazarus, the baptism of Jesus or the motif of the Good Shepherd.
+
+Biblical paraphrases and poetic renditions of stories from the life of Christ (e.g., the Heliand) became popular in the Middle Ages, as did the portrayal of the arrest, trial and execution of Jesus in Passion plays. Indeed, the Passion became a central theme in Christian art and music. The ministry and Passion of Jesus, as portrayed in one or more of the New Testament Gospels, has also been a theme in film, almost since the inception of the medium (e.g., La Passion, France, 1903).

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+The New Testament (Ancient Greek: Ἡ Καινὴ Διαθήκη, transl. Hē Kainḕ Diathḗkē; Latin: Novum Testamentum) is the second part of the Christian biblical canon, the first being the Old Testament. The New Testament discusses the teachings and person of Jesus, as well as events in first-century Christianity. Christians regard both the Old and New Testaments together as sacred scripture.
+
+The New Testament is a collection of Christian texts originally written in the Koine Greek language, at different times by various different authors. While the Old Testament canon varies somewhat between different Christian denominations, the 27-book canon of the New Testament has been almost universally recognized within Christianity since at least Late Antiquity. Thus, in almost all Christian traditions today, the New Testament consists of 27 books:
+
+The earliest known complete list of the 27 books of the New Testament is found in a letter written by Athanasius, a 4th-century bishop of Alexandria, dated to 367 AD.[1] The 27-book New Testament was first formally canonized during the councils of Hippo (393) and Carthage (397) in North Africa. Pope Innocent I ratified the same canon in 405, but it is probable that a Council in Rome in 382 under Pope Damasus I gave the same list first. These councils also provided the canon of the Old Testament, which included the apocryphal books.[2]
+
+There is no scholarly consensus on the date of composition of the latest New Testament texts. Conservative scholars John A. T. Robinson, Dan Wallace, and William F. Albright dated all the books of the New Testament before 70 AD.[3] But most[citation needed] scholars date some New Testament texts much later than this.[4] For example, Richard Pervo dates Luke-Acts to c. AD 115,[5] and David Trobisch places Acts in the mid- to late second century, contemporaneous with the publication of the first New Testament canon.[6][note 1]
+
+The use of the phrase New Testament (Koine Greek: Ἡ Καινὴ Διαθήκη, Hē Kainḕ Diathḗkē) to describe a collection of first and second-century Christian Greek scriptures can be traced back to Tertullian in his work Against Praxeas.[7][8][9] Irenaeus uses the phrase "New Testament" several times, but does not use it in reference to any written text.[8] In Against Marcion, written c. 208 AD, Tertullian writes of:[10]
+
+the Divine Word, who is doubly edged with the two testaments of the law and the gospel.
+
+And Tertullian continues later in the book, writing:[11][note 2]
+
+it is certain that the whole aim at which he [Marcion] has strenuously laboured, even in the drawing up of his Antitheses, centres in this, that he may establish a diversity between the Old and the New Testaments, so that his own Christ may be separate from the Creator, as belonging to this rival god, and as alien from the law and the prophets.
+
+By the 4th century, the existence—even if not the exact contents—of both an Old and New Testament had been established. Lactantius, a 3rd–4th century Christian author wrote in his early-4th-century Latin Institutiones Divinae (Divine Institutes):[12]
+
+But all scripture is divided into two Testaments. That which preceded the advent and passion of Christ—that is, the law and the prophets—is called the Old; but those things which were written after His resurrection are named the New Testament. The Jews make use of the Old, we of the New: but yet they are not discordant, for the New is the fulfilling of the Old, and in both there is the same testator, even Christ, who, having suffered death for us, made us heirs of His everlasting kingdom, the people of the Jews being deprived and disinherited. As the prophet Jeremiah testifies when he speaks such things: "Behold, the days come, saith the Lord, that I will make a new testament to the house of Israel and the house of Judah, not according to the testament which I made to their fathers, in the day that I took them by the hand to bring them out of the land of Egypt; for they continued not in my testament, and I disregarded them, saith the Lord."[Jer 31:31–32]  ... For that which He said above, that He would make a new testament to the house of Judah, shows that the old testament which was given by Moses was not perfect; but that which was to be given by Christ would be complete.
+
+Eusebius describes the collection of Christian writings as "covenanted" (ἐνδιαθήκη) books in Hist. Eccl. 3.3.1–7; 3.25.3; 5.8.1; 6.25.1.
+
+Each of the four gospels in the New Testament narrates the life, death, and resurrection of Jesus of Nazareth, with the exception of Mark which in the original text ends with the empty tomb and has no account of the post-resurrection appearances. The word "gospel" derives from the Old English gōd-spell[13] (rarely godspel), meaning "good news" or "glad tidings". The gospel was considered the "good news" of the coming Kingdom of Messiah, and the redemption through the life and death of Jesus, the central Christian message.[14] Gospel is a calque (word-for-word translation) of the Greek word εὐαγγέλιον, euangelion (eu- "good", -angelion "message").
+
+Starting in the late second century, the four narrative accounts of the life and work of Jesus Christ have been referred to as "The Gospel of ..." or "The Gospel according to ..." followed by the name of the supposed author. The first author to explicitly name the canonical gospels is Irenaeus of Lyon,[8][15] who promoted the four canonical gospels in his book Against Heresies, written around 180.[16] Whatever these admittedly early ascriptions may imply about the sources behind or the perception of these gospels, they are anonymous compositions.
+
+The first three gospels listed above are classified as the Synoptic Gospels. They contain similar accounts of the events in Jesus's life and his teaching, due to their literary interdependence. The Gospel of John is structured differently and includes stories of several miracles of Jesus and sayings not found in the other three.
+
+These four gospels that were eventually included in the New Testament were only a few among many other early Christian gospels. The existence of such texts is even mentioned at the beginning of the Gospel of Luke.[Luke 1:1–4] Other early Christian gospels, such as the so-called "Jewish-Christian Gospels" or the Gospel of Thomas, also offer both a window into the context of early Christianity and may provide some assistance in the reconstruction of the historical Jesus.
+
+The Acts of the Apostles is a narrative of the apostles' ministry and activity after Christ's death and resurrection, from which point it resumes and functions as a sequel to the Gospel of Luke. Examining style, phraseology, and other evidence, modern scholarship generally concludes that Acts and the Gospel of Luke share the same author, referred to as Luke–Acts. Luke-Acts does not name its author.[18] Church tradition identified him as Luke the Evangelist, the companion of Paul, but the majority of scholars reject this due to the many differences between Acts and the authentic Pauline letters.[19] The most probable date of composition is around 80–100 AD, although some scholars date it significantly later,[5][6] and there is evidence that it was still being substantially revised well into the 2nd century.[20]
+
+The epistles of the New Testament are considered by Christians to be divinely inspired and holy letters, written by the apostles and disciples of Christ, to either local congregations with specific needs, or to New Covenant Christians in general, scattered about; or "catholic epistles."
+
+The Pauline letters to churches are the thirteen New Testament books that present Paul the Apostle as their author.[note 3] Six of the letters are disputed. Four are thought by most modern scholars to be pseudepigraphic, i.e., not actually written by Paul even if attributed to him within the letters themselves.  Opinion is more divided on the other two disputed letters (2 Thessalonians and Colossians).[22] These letters were written to Christian communities in specific cities or geographical regions, often to address issues faced by that particular community. Prominent themes include the relationship both to broader "pagan" society, to Judaism, and to other Christians.[23]
+
+[Disputed letters are marked with an asterisk (*).]
+
+The last four Pauline letters in the New Testament are addressed to individual persons. They include the following:
+
+[Disputed letters are marked with an asterisk (*).]
+
+All of the above except for Philemon are known as the Pastoral epistles. They are addressed to individuals charged with pastoral oversight of churches and discuss issues of Christian living, doctrine and leadership. They often address different concerns to those of the preceding epistles. These letters are believed by many to be pseudepigraphic. Some scholars (e.g., Bill Mounce, Ben Witherington) will argue that the letters are genuinely Pauline, or at least written under Paul's supervision.
+
+The Epistle to the Hebrews addresses a Jewish audience who had come to believe that Jesus was the anointed one (Hebrew: מָשִׁיחַ—transliterated in English as "Moshiach", or "Messiah"; Greek: Χριστός—transliterated in English as "Christos", for "Christ") who was predicted in the writings of the Hebrew Scriptures. The author discusses the superiority of the new covenant and the ministry of Jesus, to the Mosaic covenant [Heb. 1:1–10:18] and urges the readers in the practical implications of this conviction through the end of the epistle.[Heb. 10:19–13:25]
+
+The book has been widely accepted by the Christian church as inspired by God and thus authoritative, despite the acknowledgment of uncertainties about who its human author was. Regarding authorship, although the Epistle to the Hebrews does not internally claim to have been written by the Apostle Paul, some similarities in wordings to some of the Pauline Epistles have been noted and inferred. In antiquity, some began to ascribe it to Paul in an attempt to provide the anonymous work an explicit apostolic pedigree.[24]
+
+In the 4th century, Jerome and Augustine of Hippo supported Paul's authorship. The Church largely agreed to include Hebrews as the fourteenth letter of Paul, and affirmed this authorship until the Reformation. The letter to the Hebrews had difficulty in being accepted as part of the Christian canon because of its anonymity.[25] As early as the 3rd century, Origen wrote of the letter, "Men of old have handed it down as Paul's, but who wrote the Epistle God only knows."[26]
+
+Contemporary scholars often reject Pauline authorship for the epistle to the Hebrews,[27] based on its distinctive style and theology, which are considered to set it apart from Paul's writings.[28]
+
+The Catholic epistles (or "general epistles") consist of both letters and treatises in the form of letters written to the church at large. The term "catholic" (Greek: καθολική, katholikē), used to describe these letters in the oldest manuscripts containing them, here simply means "general" or "universal". The authorship of a number of these is disputed.
+
+The final book of the New Testament is the Book of Revelation, also known as the Apocalypse of John. In the New Testament canon, it is considered prophetical or apocalyptic literature. Its authorship has been attributed either to John the Apostle (in which case it is often thought that John the Apostle is John the Evangelist, i.e. author of the Gospel of John) or to another John designated "John of Patmos" after the island where the text says the revelation was received (1:9). Some ascribe the writership date as circa 81–96 AD, and others at around 68 AD.[30] The work opens with letters to seven local congregations of Asia Minor and thereafter takes the form of an apocalypse, a "revealing" of divine prophecy and mysteries, a literary genre popular in ancient Judaism and Christianity.[31]
+
+The order in which the books of the New Testament appear differs between some collections and ecclesiastical traditions. In the Latin West, prior to the Vulgate (an early 5th-century Latin version of the Bible), the four Gospels were arranged in the following order: Matthew, John, Luke, and Mark.[note 4] The Syriac Peshitta places the major Catholic epistles (James, 1 Peter, and 1 John) immediately after Acts and before the Pauline epistles.
+
+The order of an early edition of the letters of Paul is based on the size of the letters: longest to shortest, though keeping 1 and 2 Corinthians and 1 and 2 Thessalonians together. The Pastoral epistles were apparently not part of the Corpus Paulinum in which this order originated and were later inserted after 2 Thessalonians and before Philemon. Hebrews was variously incorporated into the Corpus Paulinum either after 2 Thessalonians, after Philemon (i.e. at the very end), or after Romans.
+
+The New Testament of the 16th-century Luther Bible continues, to this day, to place Hebrews, James, Jude, and the Apocalypse last. This reflects the thoughts of the Reformer Martin Luther on the canonicity of these books.[36][note 5][citation needed]
+
+The books that eventually found a permanent place in the New Testament were not the only works of Christian literature produced in the earliest Christian centuries. The long process of canonization began early, sometimes with tacit reception of traditional texts, sometimes with explicit selection or rejection of particular texts as either acceptable or unacceptable for use in a given context (e.g., not all texts that were acceptable for private use were considered appropriate for use in the liturgy).
+
+Over the course of history, those works of early Christian literature that survived but that did not become part of the New Testament have been variously grouped by theologians and scholars. Drawing upon, though redefining, an older term used in early Christianity and among Protestants when referring to those books found in the Christian Old Testament although not in the Jewish Bible, modern scholars began to refer to these works of early Christian literature not included in the New Testament as "apocryphal", by which was meant non-canonical.
+
+Collected editions of these works were then referred to as the "New Testament apocrypha". Typically excluded from such published collections are the following groups of works: The Apostolic Fathers, the 2nd-century Christian apologists, the Alexandrians, Tertullian, Methodius of Olympus, Novatian, Cyprian, martyrdoms, and the Desert Fathers. Almost all other Christian literature from the period, and sometimes including works composed well into Late Antiquity, are relegated to the so-called New Testament apocrypha.
+
+Although not considered to be inspired by God, these "apocryphal" works were produced in the same ancient context and often using the same language as those books that would eventually form the New Testament. Some of these later works are dependent (either directly or indirectly) upon books that would later come to be in the New Testament or upon the ideas expressed in them. There is even an example of a pseudepigraphical letter composed under the guise of a presumably lost letter of the Apostle Paul, the Epistle to the Laodiceans.
+
+The books of the New Testament were all or nearly all written by Jewish Christians—that is, Jewish disciples of Christ, who lived in the Roman Empire, and under Roman occupation.[37] Luke, who wrote the Gospel of Luke and the Book of Acts, is frequently thought of as an exception; scholars are divided as to whether Luke was a Gentile or a Hellenistic Jew.[38] A few scholars identify the author of the Gospel of Mark as probably a Gentile, and similarly for the Gospel of Matthew, though most assert Jewish-Christian authorship.[39][40][41][verification needed]
+
+According to the large majority of critical scholars, none of the authors of the Gospels were eyewitnesses or even explicitly claimed to be eyewitnesses.[42][43][44] Bart D. Ehrman of the University of North Carolina has argued for a scholarly consensus that many New Testament books were not written by the individuals whose names are attached to them.[44][45] He further argues that names were not ascribed to the gospels until around 185 AD.[46][47] Other scholars concur.[48][49][50] Many scholars believe that none of the gospels were written in the region of Palestine.[51]
+
+Christian tradition identifies John the Apostle with John the Evangelist, the supposed author of the Gospel of John. Traditionalists tend to support the idea that the writer of the Gospel of John himself claimed to be an eyewitness in their commentaries of John 21:24 and therefore the gospel was written by an eyewitness;[52][53] however, this idea is rejected by the majority of modern scholars.[54]
+
+Most[citation needed] scholars hold to the two-source hypothesis, which posits that the Gospel of Mark was the first gospel to be written. On this view, the authors of the Gospel of Matthew and the Gospel of Luke used as sources the Gospel of Mark and a hypothetical Q document to write their individual gospel accounts.[55][56][57][58][59] These three gospels are called the Synoptic Gospels, because they include many of the same stories, often in the same sequence, and sometimes in exactly the same wording. Scholars agree that the Gospel of John was written last, by using a different tradition and body of testimony. In addition, most scholars agree that the author of Luke also wrote the Acts of the Apostles. Scholars hold that these books constituted two-halves of a single work, Luke-Acts.[citation needed]
+
+All four gospels and the Acts of the Apostles are anonymous works.[60] The Gospel of John claims to be based on eyewitness testimony from the Disciple whom Jesus loved, but never names this character.[61]
+
+The same author appears to have written the Gospel of Luke and the Acts of the Apostles, and most refer to them as the Lucan texts.[62][63] The most direct evidence comes from the prefaces of each book; both were addressed to Theophilus, and the preface to the Acts of the Apostles references "my former book" about the ministry of Jesus.[64] Furthermore, there are linguistic and theological similarities between the two works, suggesting that they have a common author.[65][66][67][68]
+
+The Pauline epistles are the thirteen books in the New Testament traditionally attributed to Paul of Tarsus. The anonymous Epistle to the Hebrews is, despite unlikely Pauline authorship, often functionally grouped with these thirteen to form a corpus of fourteen "Pauline" epistles.[note 6]
+
+Seven letters are generally classified as "undisputed", expressing contemporary scholarly near consensus that they are the work of Paul: Romans, 1 Corinthians, 2 Corinthians, Galatians, Philippians, 1 Thessalonians and Philemon. Six additional letters bearing Paul's name do not currently enjoy the same academic consensus: Ephesians, Colossians, 2 Thessalonians, 1 Timothy, 2 Timothy and Titus.[note 7]
+
+While many scholars uphold the traditional view, some question whether the first three, called the "Deutero-Pauline Epistles", are authentic letters of Paul. As for the latter three, the "Pastoral epistles", some scholars uphold the traditional view of these as the genuine writings of the Apostle Paul;[note 7] most, however, regard them as pseudepigrapha.[71]
+
+One might refer to the Epistle to the Laodiceans and the Third Epistle to the Corinthians as examples of works identified as pseudonymous. Since the early centuries of the church, there has been debate concerning the authorship of the anonymous Epistle to the Hebrews, and contemporary scholars generally reject Pauline authorship.[27]
+
+The epistles all share common themes, emphasis, vocabulary and style; they exhibit a uniformity of doctrine concerning the Mosaic Law, Jesus, faith, and various other issues. All of these letters easily fit into the chronology of Paul's journeys depicted in Acts of the Apostles.
+
+The author of the Epistle of James identifies himself in the opening verse as "James, a servant of God and of the Lord Jesus Christ". From the middle of the 3rd century, patristic authors cited the Epistle as written by James the Just.[72] Ancient and modern scholars have always been divided on the issue of authorship. Many consider the epistle to be written in the late 1st or early 2nd centuries.[73]
+
+The author of the First Epistle of Peter identifies himself in the opening verse as "Peter, an apostle of Jesus Christ", and the view that the epistle was written by St. Peter is attested to by a number of Church Fathers: Irenaeus (140–203), Tertullian (150–222), Clement of Alexandria (155–215) and Origen of Alexandria (185–253). Unlike The Second Epistle of Peter, the authorship of which was debated in antiquity, there was little debate about Peter's authorship of this first epistle until the 18th century. Although 2 Peter internally purports to be a work of the apostle, many biblical scholars have concluded that Peter is not the author.[74] For an early date and (usually) for a defense of the Apostle Peter's authorship see Kruger,[75] Zahn,[76] Spitta,[77] Bigg,[78] and Green.[79]
+
+The Epistle of Jude title is written as follows: "Jude, a servant of Jesus Christ and a brother of James" (NRSV). The debate has continued over the author's identity as the apostle, the brother of Jesus, both, or neither.[80]
+
+The Gospel of John, the three Johannine epistles, and the Book of Revelation, exhibit marked similarities, although more so between the gospel and the epistles (especially the gospel and 1 John) than between those and Revelation.[81] Most scholars therefore treat the five as a single corpus of Johannine literature, albeit not from the same author.[82]
+
+The gospel went through two or three "editions" before reaching its current form around AD 90–110.[83][84] It speaks of an unnamed "disciple whom Jesus loved" as the source of its traditions, but does not say specifically that he is its author;[85] Christian tradition identifies this disciple as the apostle John, but while this idea still has supporters, for a variety of reasons the majority of modern scholars have abandoned it or hold it only tenuously.[86] It is significantly different from the synoptic gospels, with major variations in material, theological emphasis, chronology, and literary style, sometimes amounting to contradictions.[87]
+
+The author of the Book of Revelation identifies himself several times as "John".[Rev. 1:1, 4, 9; 22:8] and states that he was on Patmos when he received his first vision.[Rev. 1:9; 4:1–2] As a result, the author is sometimes referred to as John of Patmos. The author has traditionally been identified with John the Apostle to whom the Gospel and the epistles of John were attributed. It was believed that he was exiled to the island of Patmos during the reign of the Roman emperor Domitian, and there wrote Revelation. Justin Martyr (c. 100–165 AD) who was acquainted with Polycarp, who had been mentored by John, makes a possible allusion to this book, and credits John as the source.[88] Irenaeus (c. 115–202) assumes it as a conceded point. According to the Zondervan Pictorial Encyclopedia of the Bible, modern scholars are divided between the apostolic view and several alternative hypotheses put forth in the last hundred years or so.[89] Ben Witherington points out that linguistic evidence makes it unlikely that the books were written by the same person.[90]
+
+The earliest manuscripts of New Testament books date from the late second to early third centuries (although see Papyrus 52 for a possible exception).[27]:479–480 These manuscripts place a clear upper limit on the dating of New Testament texts. Explicit references to NT books in extra-biblical documents can push this upper limit down a bit further. Irenaeus of Lyon names and quotes from most of the books in the New Testament in his book Against Heresies, written around 180 AD. The Epistle of Polycarp to the Philippians, written some time between 110 and Polycarp's death in 155-167 AD, quotes or alludes to most New Testament texts. Ignatius of Antioch wrote letters referencing much of the New Testament. He lived from about 35AD to 107AD and is rumored to have been a disciple of the Apostle John. His writings reference the Gospels of John, Matthew, and Luke, as well as Peter, James, and Paul's Epistles. His writing is usually attributed to the end of his lifetime, which places the Gospels as First Century writings.
+
+Literary analysis of the New Testament texts themselves can be used to date many of the books of the New Testament to the mid- to late first century. The earliest works of the New Testament are the letters of the Apostle Paul. It can be determined that 1 Thessalonians is likely the earliest of these letters, written around 52 AD.[91]
+
+The major languages spoken by both Jews and Greeks in the Holy Land at the time of Jesus were Aramaic and Koine Greek, and also a colloquial dialect of Mishnaic Hebrew. It is generally agreed by most scholars that the historical Jesus primarily spoke Aramaic,[92] perhaps also some Hebrew and Koine Greek. The majority view is that all of the books that would eventually form the New Testament were written in the Koine Greek language.[93][94]
+
+As Christianity spread, these books were later translated into other languages, most notably, Latin, Syriac, and Egyptian Coptic. However, some of the Church Fathers[95] imply or claim that Matthew was originally written in Hebrew or Aramaic, and then soon after was written in Koine Greek. Nevertheless, some scholars believe the Gospel of Matthew known today was composed in Greek and is neither directly dependent upon nor a translation of a text in a Semitic language.[96]
+
+The process of canonization of the New Testament was complex and lengthy. In the initial centuries of early Christianity, there were many books widely considered by the church to be inspired, but there was no single formally recognized New Testament canon.[97] The process was characterized by a compilation of books that apostolic tradition considered authoritative in worship and teaching, relevant to the historical situations in which they lived, and consonant with the Old Testament.[98] Writings attributed to the apostles circulated among the earliest Christian communities and the Pauline epistles were circulating, perhaps in collected forms, by the end of the 1st century AD.[99]
+
+One of the earliest attempts at solidifying a canon was made by Marcion, circa 140 AD, who accepted only a modified version of Luke (the Gospel of Marcion) and ten of Paul's letters, while rejecting the Old Testament entirely. His canon was largely rejected by other groups of Christians, notably the proto-orthodox Christians, as was his theology, Marcionism. Adolf von Harnack,[100] John Knox,[101] and David Trobisch,[6] among other scholars, have argued that the church formulated its New Testament canon partially in response to the challenge posed by Marcion.
+
+Polycarp,[102] Irenaeus[103] and Tertullian[104] held the epistles of Paul to be divinely inspired "scripture." Other books were held in high esteem but were gradually relegated to the status of New Testament apocrypha. Justin Martyr, in the mid 2nd century, mentions "memoirs of the apostles" as being read on Sunday alongside the "writings of the prophets".[105]
+
+The Muratorian fragment, dated at between 170 and as late as the end of the 4th century (according to the Anchor Bible Dictionary), may be the earliest known New Testament canon attributed to mainstream Christianity. It is similar, but not identical, to the modern New Testament canon.
+
+The oldest clear endorsement of Matthew, Mark, Luke, and John being the only legitimate gospels was written circa 180 AD. A four gospel canon (the Tetramorph) was asserted by Irenaeus, who refers to it directly[106][107] in his polemic Against Heresies:
+
+"It is not possible that the gospels can be either more or fewer in number than they are. For, since there are four zones of the world in which we live, and four principal winds, while the church is scattered throughout all the world, and the 'pillar and ground' of the church is the gospel and the spirit of life; it is fitting that she should have four pillars, breathing out immortality on every side, and vivifying men afresh." (emphasis added)[107]
+
+The books considered to be authoritative by Irenaeus included the four gospels and many of the letters of Paul, although, based on the arguments Irenaeus made in support of only four authentic gospels, some interpreters deduce that the fourfold Gospel must have still been a novelty in Irenaeus's time.[108]
+
+By the early 200s, Origen may have been using the same twenty-seven books as in the Catholic New Testament canon, though there were still disputes over the canonicity of the Letter to the Hebrews, Epistle of James, II Peter, II John and III John and the Book of Revelation,[109] known as the Antilegomena. Likewise, the Muratorian fragment is evidence that, perhaps as early as 200, there existed a set of Christian writings somewhat similar to the twenty-seven book NT canon, which included four gospels and argued against objections to them.[110] Thus, while there was a good measure of debate in the Early Church over the New Testament canon, the major writings are claimed to have been accepted by almost all Christians by the middle of the 3rd century.[111]
+
+Origen was largely responsible for the collection of usage information regarding the texts that became the New Testament. The information used to create the late-4th-century Easter Letter, which declared accepted Christian writings, was probably based on the Ecclesiastical History [HE] of Eusebius of Caesarea, wherein he uses the information passed on to him by Origen to create both his list at HE 3:25 and Origen's list at HE 6:25. Eusebius got his information about what texts were then accepted and what were then disputed, by the third-century churches throughout the known world, a great deal of which Origen knew of firsthand from his extensive travels, from the library and writings of Origen.[112]
+
+In fact, Origen would have possibly included in his list of "inspired writings" other texts kept out by the likes of Eusebius—including the Epistle of Barnabas, Shepherd of Hermas, and 1 Clement. Notwithstanding these facts, "Origen is not the originator of the idea of biblical canon, but he certainly gives the philosophical and literary-interpretative underpinnings for the whole notion."[113]
+
+Eusebius, circa 300, gave a detailed list of New Testament writings in his Ecclesiastical History Book 3, Chapter XXV:
+
+The Book of Revelation is counted as both accepted (Kirsopp Lake translation: "Recognized") and disputed, which has caused some confusion over what exactly Eusebius meant by doing so. From other writings of the church fathers, it was disputed with several canon lists rejecting its canonicity. EH 3.3.5 adds further detail on Paul: "Paul's fourteen epistles are well known and undisputed. It is not indeed right to overlook the fact that some have rejected the Epistle to the Hebrews, saying that it is disputed by the church of Rome, on the ground that it was not written by Paul." EH 4.29.6 mentions the Diatessaron: "But their original founder, Tatian, formed a certain combination and collection of the gospels, I know not how, to which he gave the title Diatessaron, and which is still in the hands of some. But they say that he ventured to paraphrase certain words of the apostle Paul, in order to improve their style."
+
+In his Easter letter of 367, Athanasius, Bishop of Alexandria, gave a list of the books that would become the twenty-seven-book NT canon,[1] and he used the word "canonized" (kanonizomena) in regards to them.[114] The first council that accepted the present canon of the New Testament may have been the Synod of Hippo Regius in North Africa (393 AD); the acts of this council, however, are lost. A brief summary of the acts was read at and accepted by the Council of Carthage (397) and the Council of Carthage (419).[115] These councils were under the authority of St. Augustine, who regarded the canon as already closed.[116][117][118]
+
+Pope Damasus I's Council of Rome in 382, if the Decretum Gelasianum is correctly associated with it, issued a biblical canon identical to that mentioned above,[1] or, if not, the list is at least a 6th-century compilation.[119] Likewise, Damasus' commissioning of the Latin Vulgate edition of the Bible, c. 383, was instrumental in the fixation of the canon in the West.[120] In c. 405, Pope Innocent I sent a list of the sacred books to a Gallic bishop, Exsuperius of Toulouse. Christian scholars assert that, when these bishops and councils spoke on the matter, however, they were not defining something new but instead "were ratifying what had already become the mind of the Church."[116][121][122]
+
+The New Testament canon as it is now was first listed by St. Athanasius, Bishop of Alexandria, in 367, in a letter written to his churches in Egypt, Festal Letter 39. Also cited is the Council of Rome, but not without controversy. That canon gained wider and wider recognition until it was accepted at the Third Council of Carthage in 397 and 419.[note 8]
+
+Even this council did not settle the matter, however. Certain books, referred to as Antilegomena, continued to be questioned, especially James and Revelation. Even as late as the 16th century, the Reformer Martin Luther questioned (but in the end did not reject) the Epistle of James, the Epistle of Jude, the Epistle to the Hebrews and the Book of Revelation. To this day, German-language Luther Bibles are printed with these four books at the end of the canon, rather than in their traditional order as in other editions of the Bible.
+
+In light of this questioning of the canon of Scripture by Protestants in the 16th century, the (Roman Catholic) Council of Trent reaffirmed the traditional western canon (i.e., the canon accepted at the 4th-century Council of Rome and Council of Carthage), thus making the Canon of Trent and the Vulgate Bible dogma in the Catholic Church. Later, Pope Pius XI on 2 June 1927 decreed the Comma Johanneum was open to dispute and Pope Pius XII on 3 September 1943 issued the encyclical Divino afflante Spiritu, which allowed translations based on other versions than just the Latin Vulgate, notably in English the New American Bible.
+
+Thus, some claim that, from the 4th century, there existed unanimity in the West concerning the New Testament canon (as it is today),[123] and that, by the 5th century, the Eastern Church, with a few exceptions, had come to accept the Book of Revelation and thus had come into harmony on the matter of the canon.[124] Nonetheless, full dogmatic articulations of the canon were not made until the Canon of Trent of 1546 for Roman Catholicism, the Thirty-Nine Articles of 1563 for the Church of England, the Westminster Confession of Faith of 1647 for Calvinism, and the Synod of Jerusalem of 1672 for the Greek Orthodox.
+
+On the question of NT Canon formation generally, New Testament scholar Lee Martin McDonald has written that:[125]
+
+Although a number of Christians have thought that church councils determined what books were to be included in the biblical canons, a more accurate reflection of the matter is that the councils recognized or acknowledged those books that had already obtained prominence from usage among the various early Christian communities.
+
+Christian scholars assert that when these bishops and councils spoke on the matter, they were not defining something new, but instead "were ratifying what had already become the mind of the Church".[121][122]
+
+Some synods of the 4th century published lists of canonical books (e.g. Hippo and Carthage). The existing 27-book canon of the New Testament was reconfirmed (for Roman Catholicism) in the 16th century with the Council of Trent (also called the Tridentine Council) of 1546,[126] the Thirty-Nine Articles of 1563 for the Church of England, the Westminster Confession of Faith of 1647 for Calvinism, and the Synod of Jerusalem of 1672 for Eastern Orthodoxy. Although these councils did include statements about the canon, when it came to the New Testament they were only reaffirming the existing canon, including the Antilegomena.
+
+According to the Catholic Encyclopedia article on the Canon of the New Testament: "The idea of a complete and clear-cut canon of the New Testament existing from the beginning, that is from Apostolic times, has no foundation in history. The Canon of the New Testament, like that of the Old, is the result of a development, of a process at once stimulated by disputes with doubters, both within and without the Church, and retarded by certain obscurities and natural hesitations, and which did not reach its final term until the dogmatic definition of the Tridentine Council."[127]
+
+In 331, Constantine I commissioned Eusebius to deliver fifty Bibles for the Church of Constantinople. Athanasius (Apol. Const. 4) recorded Alexandrian scribes around 340 preparing Bibles for Constans. Little else is known, though there is plenty of speculation. For example, it is speculated that this may have provided motivation for canon lists, and that Codex Vaticanus and Codex Sinaiticus may be examples of these Bibles. Together with the Peshitta and Codex Alexandrinus, these are the earliest extant Christian Bibles.[128] There is no evidence among the canons of the First Council of Nicaea of any determination on the canon.
+
+Like other literature from antiquity, the text of the New Testament was (prior to the advent of the printing press) preserved and transmitted in manuscripts. Manuscripts containing at least a part of the New Testament number in the thousands. The earliest of these (like manuscripts containing other literature) are often very fragmentarily preserved. Some of these fragments have even been thought to date as early as the 2nd century (i.e., Papyrus 90, Papyrus 98, Papyrus 104, and famously Rylands Library Papyrus P52, though the early date of the latter has recently been called into question).[129]
+
+For each subsequent century, more and more manuscripts survive that contain a portion or all of the books that were held to be part of the New Testament at that time (for example, the New Testament of the 4th-century Codex Sinaiticus, once a complete Bible, contains the Epistle of Barnabas and the Shepherd of Hermas), though occasionally these manuscripts contain other works as well (e.g., Papyrus 72 and the Crosby-Schøyen Codex). The date when a manuscript was written, however, does not necessarily reflect the date of the form of text it contains. That is, later manuscripts can, and occasionally do, contain older forms of text or older readings.
+
+Some of the more important manuscripts containing an early text of books of the New Testament are:
+
+Textual criticism deals with the identification and removal of transcription errors in the texts of manuscripts. Ancient scribes made errors or alterations (such as including non-authentic additions).[130] The New Testament has been preserved in more than 5,800 Greek manuscripts, 10,000 Latin manuscripts and 9,300 manuscripts in various other ancient languages including Syriac, Slavic, Ethiopic and Armenian. Even if the original Greek versions were lost, the entire New Testament could still be assembled from the translations.[131]
+
+In addition, there are so many quotes from the New Testament in early church documents and commentaries that the entire New Testament could also be assembled from these alone.[131] Not all biblical manuscripts come from orthodox Christian writers. For example, the Gnostic writings of Valentinus come from the 2nd century AD, and these Christians were regarded as heretics by the mainstream church.[132] The sheer number of witnesses presents unique difficulties, but it also gives scholars a better idea of how close modern Bibles are to the original versions.[132]
+
+On noting the large number of surviving ancient manuscripts, Bruce Metzger sums up the view on the issue by saying "The more often you have copies that agree with each other, especially if they emerge from different geographical areas, the more you can cross-check them to figure out what the original document was like. The only way they'd agree would be where they went back genealogically in a family tree that represents the descent of the manuscripts.[131]
+
+In attempting to determine the original text of the New Testament books, some modern textual critics have identified sections as additions of material, centuries after the gospel was written. These are called interpolations. In modern translations of the Bible, the results of textual criticism have led to certain verses, words and phrases being left out or marked as not original. According to Bart D. Ehrman, "These scribal additions are often found in late medieval manuscripts of the New Testament, but not in the manuscripts of the earlier centuries."[133]
+
+Most modern Bibles have footnotes to indicate passages that have disputed source documents. Bible Commentaries also discuss these, sometimes in great detail. While many variations have been discovered between early copies of biblical texts, almost all have no importance, as they are variations in spelling, punctuation, or grammar. Also, many of these variants are so particular to the Greek language that they would not appear in translations into other languages. For example, order of words (i.e. "man bites dog" versus "dog bites man") often does not matter in Greek, so textual variants that flip the order of words often have no consequences.[131]
+
+Outside of these unimportant variants, there are a couple variants of some importance. The two most commonly cited examples are the last verses of the Gospel of Mark[134][135][136] and the story of the adulterous woman in the Gospel of John.[137][138][139] Many scholars and critics also believe that the Comma Johanneum reference supporting the Trinity doctrine in 1 John to have been a later addition.[140][141] According to Norman Geisler and William Nix, "The New Testament, then, has not only survived in more manuscripts than any other book from antiquity, but it has survived in a purer form than any other great book—a form that is 99.5% pure"[142]
+
+The often referred to Interpreter's Dictionary of the Bible, a book written to prove the validity of the New Testament, says: " A study of 150 Greek [manuscripts] of the Gospel of Luke has revealed more than 30,000 different readings... It is safe to say that there is not one sentence in the New Testament in which the [manuscript] is wholly uniform."[143] Most of the variation took place within the first three Christian centuries.
+
+By the 4th century, textual "families" or types of text become discernible among New Testament manuscripts. A "text-type" is the name given to a family of texts with similar readings due to common ancestors and mutual correction. Many early manuscripts, however, contain individual readings from several different earlier forms of text. Modern texual critics have identified the following text-types among textual witnesses to the New Testament: The Alexandrian text-type is usually considered to generally preserve many early readings. It is represented, e.g., by Codex Vaticanus, Codex Sinaiticus and the Bodmer Papyri.
+
+The Western text-type is generally longer and can be paraphrastic, but can also preserve early readings. The Western version of the Acts of the Apostles is, notably, 8.5% longer than the Alexandrian form of the text. Examples of the Western text are found in Codex Bezae, Codex Claromontanus, Codex Washingtonianus, the Old Latin (i.e., Latin translations made prior to the Vulgate), as well as in quotations by Marcion, Tatian, Irenaeus, Tertullian and Cyprian.
+
+A text-type referred to as the "Caesarean text-type" and thought to have included witnesses such as Codex Koridethi and minuscule 565, can today be described neither as "Caesarean" nor as a text-type as was previously thought. However, the Gospel of Mark in Papyrus 45, Codex Washingtonianus and in Family 13 does indeed reflect a distinct type of text.
+
+Increasing standardization of distinct (and once local) text-types eventually gave rise to the Byzantine text-type. Since most manuscripts of the New Testament do not derive from the first several centuries, that is, they were copied after the rise of the Byzantine text-type, this form of text is found the majority of extant manuscripts and is therefore often called the "Majority Text." As with all of the other (earlier) text-types, the Byzantine can also occasionally preserve early readings.
+
+Biblical criticism is the scholarly "study and investigation of biblical writings that seeks to make discerning judgments about these writings." Viewing biblical texts as having human rather than supernatural origins, it asks when and where a particular text originated; how, why, by whom, for whom, and in what circumstances it was produced; what influences were at work in its production; what sources were used in its composition; and what message it was intended to convey.
+
+It will vary slightly depending on whether the focus is on the Old Testament, the letters of the New Testament, or the Canonical Gospels. It also plays an important role in the quest for the historical Jesus. It also addresses the physical text, including the meaning of the words and the way in which they are used, its preservation, history, and integrity. Biblical criticism draws upon a wide range of scholarly disciplines including archaeology, anthropology, folklore, linguistics, Oral Tradition studies, history, and religious studies.
+
+The textual variation among manuscript copies of books in the New Testament prompted attempts to discern the earliest form of text already in antiquity (e.g., by the 3rd-century Christian author Origen). The efforts began in earnest again during the Renaissance, which saw a revival of the study of ancient Greek texts. During this period, modern textual criticism was born. In this context, Christian humanists such as Lorenzo Valla and Erasmus promoted a return to the original Greek of the New Testament. This was the beginning of modern New Testament textual criticism, which over subsequent centuries would increasingly incorporate more and more manuscripts, in more languages (i.e., versions of the New Testament), as well as citations of the New Testament by ancient authors and the New Testament text in lectionaries in order to reconstruct the earliest recoverable form of the New Testament text and the history of changes to it.[144]
+
+Books that later formed the New Testament, like other Christian literature of the period, originated in a literary context that reveals relationships not only to other Christian writings, but also to Graeco-Roman and Jewish works. Of singular importance is the extensive use of and interaction with the Jewish Bible and what would become the Christian Old Testament. Both implicit and explicit citations, as well as countless allusions, appear throughout the books of the New Testament, from the Gospels and Acts, to the Epistles, to the Apocalypse.[145]
+
+The first translations (usually called "versions") of the New Testament were made beginning already at the end of 2nd century. The earliest versions of the New Testament are the translations into the Syriac, Latin, and Coptic languages.[146] These three versions were made directly from the Greek, and are frequently cited in the apparatuses of modern critical editions.
+
+Syriac was spoken in Syria, and Mesopotamia, and with dialect in Roman and Byzantine Palestine where it was known as Jewish Palestinian Aramaic. Several Syriac translations were made and have come to us. Most of the Old Syriac, however, as well as the Philoxonian version have been lost.
+
+Tatian, the Assyrian, created the Diatessaron, a gospel harmony written in Syriac around 170 AD and the earliest form of the gospel not only in Syriac but probably also in Armenian.
+
+In the 19th century, manuscript evidence was discovered for an "Old Syriac" version of the four distinct (i.e., not harmonized) gospels. These "separated" (Syriac: da-Mepharreshe) gospels, though old, have been shown to be later than the Diatessaron. The Old Syriac gospels are fragmentarily preserved in two manuscripts: the 5th-century Curetonian Syriac and the Sinaitic Syriac from the 4th or 5th century.
+
+No Old Syriac manuscripts of other portions of the New Testament survive, though Old Syriac readings, e.g. from the Pauline Epistles, can be discerned in citations made by Eastern fathers and in later Syriac versions. The Old Syriac version is a representative of the Western text-type. The Peshitta version was prepared in the beginning of the 5th century. It contains only 22 books (neither the Minor Catholic Epistles of 2 Peter, 2 and 3 John, and Jude, nor the Book of Revelation were part of this translation).
+
+The Philoxenian probably was produced in 508 for Philoxenus, Bishop of Mabung.[147]
+
+The Gospels were likely translated into Latin as early as the last quarter of the 2nd century in North Africa (Afra). Not much later, there were also European Latin translations (Itala). There are about 80 Old Latin mansucripts. The Vetus Latina ("Old Latin") versions often contain readings with a Western type of text. (For the avoidance of confusion, these texts were written in Late Latin, not the early version of the Latin language known as Old Latin, pre 75 BC.)
+
+The bewildering diversity of the Old Latin versions prompted Jerome to prepare another translation into Latin—the Vulgate. In many respects it was merely a revision of the Old Latin. There are currently around 8,000 manuscripts of the Vulgate.
+
+There are several dialects of the Coptic language: Bohairic (northern dialect), Fayyumic, Sahidic (southern dialect), Akhmimic, and others. The first translation was made by at least the 3rd century into the Sahidic dialect (copsa). This translation represents a mixed text, mostly Alexandrian, though also with Western readings.[148]
+
+A Bohairic translation was made later, but existed already in the 4th century. Though the translation makes less use of Greek words than the Sahidic, it does employ some Greek grammar (e.g., in word-order and the use of particles such as the syntactic construction μεν—δε). For this reason, the Bohairic translation can be helpful in the reconstruction of the early Greek text of the New Testament.[149]
+
+The continued spread of Christianity, and the foundation of national churches, led to the translation of the Bible—often beginning with books from the New Testament—into a variety of other languages at a relatively early date: Armenian, Georgian, Ethiopic, Persian, Sogdian, and eventually Gothic, Old Church Slavonic, Arabic, and Nubian.[150]
+
+Historically, throughout the Christian world and in the context of Christian missionary activity, the New Testament (or portions thereof) has been that part of the Christian Bible first translated into the vernacular. The production of such translations grew out of the insertion of vernacular glosses in biblical texts, as well as out of the production of biblical paraphrases and poetic renditions of stories from the life of Christ (e.g., the Heliand).
+
+The 16th century saw the rise of Protestantism and an explosion of translations of the New (and Old) Testament into the vernacular. Notable are those of Martin Luther (1522), Jacques Lefèvre d'Étaples (1523), the Froschau Bible (1525–1529, revised in 1574), William Tyndale (1526, revised in 1534, 1535 and 1536), the Brest Bible (1563), and the Authorized Version (also called the "King James Version") (1611).
+
+Most of these translations relied (though not always exclusively) upon one of the printed editions of the Greek New Testament edited by Erasmus, the Novum Instrumentum omne; a form of this Greek text emerged as the standard and is known as the Textus Receptus. This text, based on the majority of manuscripts is also used in the majority of translations that were made in the years 100 to 400 AD.
+
+Translations of the New Testament made since the appearance of critical editions of the Greek text (notably those of Tischendorf, Westcott and Hort, and von Soden) have largely used them as their base text. Unlike the Textus Receptus, these have a pronounced Alexandrian character. Standard critical editions are those of Nestle-Åland (the text, though not the full critical apparatus of which is reproduced in the United Bible Societies' "Greek New Testament"), Souter, Vogels, Bover and Merk.
+
+Notable translations of the New Testament based on these most recent critical editions include the Revised Standard Version (1946, revised in 1971), La Bible de Jérusalem (1961, revised in 1973 and 2000), the Einheitsübersetzung (1970, final edition 1979), the New American Bible (1970, revised in 1986), the Traduction Oecuménique de la Bible (1988, revised in 2004), and the New Revised Standard Version (1989).
+
+Though all Christian churches accept the New Testament as scripture, they differ in their understanding of the nature, extent, and relevance of its authority. Views of the authoritativeness of the New Testament often depend on the concept of inspiration, which relates to the role of God in the formation of the New Testament. Generally, the greater the role of God in one's doctrine of inspiration, the more one accepts the doctrine of biblical inerrancy or authoritativeness of the Bible. One possible source of confusion is that these terms are difficult to define, because many people use them interchangeably or with very different meanings. This article will use the terms in the following manner:
+
+The self-witness of the Bible to its inspiration demands a commitment to its unity. The ultimate basis for unity is contained in the claim of divine inspiration in 2 Timothy 3:16 that "all Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness" (KJV). The term "inspiration" renders the Greek word theopneustos. This term only occurs here in the New Testament and literally means "God-breathed" (the chosen translation of the NIV).[151]
+
+All of these concepts depend for their meaning on the supposition that the text of Bible has been properly interpreted, with consideration for the intention of the text, whether literal history, allegory or poetry, etc. Especially the doctrine of inerrancy is variously understood according to the weight given by the interpreter to scientific investigations of the world.
+
+The notion of unity in diversity of Scripture claims that the Bible presents a noncontradictory and consistent message concerning God and redemptive history. The fact of diversity is observed in comparing the diversity of time, culture, authors' perspectives, literary genre, and the theological themes.[151]
+
+Studies from many theologians considering the "unity in diversity" to be found in the New Testament (and the Bible as a whole) have been collected and summarized by New Testament theologian Frank Stagg. He describes them as some basic presuppositions, tenets, and concerns common among the New Testament writers, giving to the New Testament its "unity in diversity":
+
+For the Roman Catholic Church, there are two modes of Revelation: Scripture and Tradition. Both of them are interpreted by the teachings of the Church. The Roman Catholic view is expressed clearly in the Catechism of the Catholic Church (1997):
+
+§ 82: As a result the Church, to whom the transmission and interpretation of Revelation is entrusted, does not derive her certainty about all revealed truths from the holy Scriptures alone. Both Scripture and Tradition must be accepted and honoured with equal sentiments of devotion and reverence.
+
+§ 107: The inspired books teach the truth. Since therefore all that the inspired authors or sacred writers affirm should be regarded as affirmed by the Holy Spirit, we must acknowledge that the books of Scripture firmly, faithfully, and without error teach that truth which God, for the sake of our salvation, wished to see confided to the Sacred Scriptures.
+
+In Catholic terminology the teaching office is called the Magisterium.  The Catholic view should not be confused with the two-source theory.  As the Catechism states in §§ 80 and 81, Revelation has "one common source ... two distinct modes of transmission."[153]
+
+While many Eastern Orthodox writers distinguish between Scripture and Tradition, Bishop Kallistos Ware says that for the Orthodox there is only one source of the Christian faith, Holy Tradition, within which Scripture exists.[154]
+
+Traditional Anglicans believe that "Holy Scripture containeth all things necessary to salvation", (Article VI), but also that the Catholic Creeds "ought thoroughly to be received and believed" (Article VIII), and that the Church "hath authority in Controversies of Faith" and is "a witness and keeper of Holy Writ" (Article XX).[155] Classical Anglicanism, therefore, like Orthodoxy, holds that Holy Tradition is the only safe guardian against perversion and innovation in the interpretation of Scripture.
+
+In the famous words of Thomas Ken, Bishop of Bath and Wells: "As for my religion, I dye in the holy catholic and apostolic faith professed by the whole Church before the disunion of East and West, more particularly in the communion of the Church of England, as it stands distinguished from all Papal and Puritan innovations, and as it adheres to the doctrine of the Cross."
+
+Following the doctrine of sola scriptura, Protestants believe that their traditions of faith, practice and interpretations carry forward what the scriptures teach, and so tradition is not a source of authority in itself. Their traditions derive authority from the Bible, and are therefore always open to reevaluation. This openness to doctrinal revision has extended in Liberal Protestant traditions even to the reevaluation of the doctrine of Scripture upon which the Reformation was founded, and members of these traditions may even question whether the Bible is infallible in doctrine, inerrant in historical and other factual statements, and whether it has uniquely divine authority. However, the adjustments made by modern Protestants to their doctrine of scripture vary widely.
+
+Within the US, the Chicago Statement on Biblical Inerrancy (1978) is a statement, articulating evangelical views on this issue. Paragraph four of its summary states: "Being wholly and verbally God-given, Scripture is without error or fault in all its teaching, no less in what it states about God's acts in creation, about the events of world history, and about its own literary origins under God, than in its witness to God's saving grace in individual lives."[156]
+
+Mainline American Protestant denominations, including the United Methodist Church, Presbyterian Church USA, The Episcopal Church, and Evangelical Lutheran Church in America, do not teach the doctrine of inerrancy as set forth in the Chicago Statement. All of these churches have more ancient doctrinal statements asserting the authority of scripture, but may interpret these statements in such a way as to allow for a very broad range of teaching—from evangelicalism to skepticism. It is not an impediment to ordination in these denominations to teach that the scriptures contain errors, or that the authors follow a more or less unenlightened ethics that, however appropriate it may have seemed in the authors' time, moderns would be very wrong to follow blindly.
+
+For example, ordination of women is universally accepted in the mainline churches, abortion is condemned as a grievous social tragedy but not always a personal sin or a crime against an unborn person, and homosexuality is sometimes recognized as a genetic propensity or morally neutral preference that should be neither encouraged nor condemned. In North America, the most contentious of these issues among these churches at the present time is how far the ordination of gay men and lesbians should be accepted.
+
+Officials of the Presbyterian Church USA report: "We acknowledge the role of scriptural authority in the Presbyterian Church, but Presbyterians generally do not believe in biblical inerrancy. Presbyterians do not insist that every detail of chronology or sequence or prescientific description in scripture be true in literal form. Our confessions do teach biblical infallibility. Infallibility affirms the entire truthfulness of scripture without depending on every exact detail."[157]
+
+Those who hold a more liberal view of the Bible as a human witness to the glory of God, the work of fallible humans who wrote from a limited experience unusual only for the insight they have gained through their inspired struggle to know God in the midst of a troubled world. Therefore, they tend not to accept such doctrines as inerrancy. These churches also tend to retain the social activism of their evangelical forebears of the 19th century, placing particular emphasis on those teachings of scripture that teach compassion for the poor and concern for social justice.
+
+The message of personal salvation is, generally speaking, of the good that comes to oneself and the world through following the New Testament's Golden Rule admonition to love others without hypocrisy or prejudice. Toward these ends, the "spirit" of the New Testament, more than the letter, is infallible and authoritative.
+
+There are some movements that believe the Bible contains the teachings of Jesus but who reject the churches that were formed following its publication. These people believe all individuals can communicate directly with God and therefore do not need guidance or doctrines from a church. These people are known as Christian anarchists.
+
+Messianic Judaism generally holds the same view of New Testament authority as evangelical Protestants.[158] According to the view of some Messianic Jewish congregations, Jesus did not annul the Torah, but that its interpretation is revised and ultimately explained through the Apostolic Scriptures.[159]
+
+Jehovah's Witnesses accept the New Testament as divinely inspired Scripture, and as infallible in every detail, with equal authority as the Hebrew Scriptures. They view it as the written revelation and good news of the Messiah, the ransom sacrifice of Jesus, and the Kingdom of God, explaining and expounding the Hebrew Bible, not replacing but vitally supplementing it. They also view the New Testament as the primary instruction guide for Christian living, and church discipline. They generally call the New Testament the "Christian Greek Scriptures", and see only the "covenants" as "old" or "new", but not any part of the actual Scriptures themselves.[160]
+
+Oneness Pentecostalism subscribes to the common Protestant doctrine of sola scriptura. They view the Bible as the inspired Word of God, and as absolutely inerrant in its contents (though not necessarily in every translation).[161][162] They regard the New Testament as perfect and inerrant in every way, revealing the Lord Jesus Christ in the Flesh, and his Atonement, and which also explains and illuminates the Old Testament perfectly, and is part of the Bible canon, not because church councils or decrees claimed it so, but by witness of the Holy Spirit.[163][164]
+
+The Seventh-day Adventist Church holds the New Testament as the inspired Word of God, with God influencing the "thoughts" of the Apostles in the writing, not necessarily every word though.  The first fundamental belief of the Seventh-Day Adventist church stated that "The Holy Scriptures are the infallible revelation of [God's] will." Adventist theologians generally reject the "verbal inspiration" position on Scripture held by many conservative evangelical Christians. They believe instead that God inspired the thoughts of the biblical authors and apostles, and that the writers then expressed these thoughts in their own words.[165] This view is popularly known as "thought inspiration", and most Adventist members hold to that view. According to Ed Christian, former JATS editor, "few if any ATS members believe in verbal inerrancy".[166]
+
+Regarding the teachings of the New Testament compared to the Old, and the application in the New Covenant, Adventists have traditionally taught that the Decalogue is part of the moral law of God, which was not abrogated by the ministry and death of Jesus Christ. Therefore, the fourth commandment concerning the Sabbath is as applicable to Christian believers as the other nine. Adventists have often taught a distinction between "moral law" and "ceremonial law". According to Adventist beliefs, the moral law continues into the "New Testament era", but the ceremonial law was done away with by Jesus.
+
+How the Mosaic law should be applied came up at Adventist conferences in the past, and Adventist theologians such as A. T. Jones and E. J. Waggoner looked at the problem addressed by Paul in Galatians as not the ceremonial law, but rather the wrong use of the law (legalism). They were opposed by Uriah Smith and George Butler at the 1888 Conference. Smith in particular thought the Galatians issue had been settled by Ellen White already, yet in 1890 she claimed justification by faith is "the third angel's message in verity."[citation needed]
+
+Ellen White interpreted Colossians 2:14 as saying that the ceremonial law was nailed to the cross.[167]
+
+Members of The Church of Jesus Christ of Latter-day Saints (LDS Church) believe that the New Testament, as part of the Christian biblical canon, is accurate "as far as it is translated correctly".[168] They believe the Bible as originally revealed is the word of God, but that the processes of transcription and translation have introduced errors into the texts as currently available, and therefore they cannot be regarded as completely inerrant.[169][170] In addition to the Old and New Testaments, the Book of Mormon, the Doctrine and Covenants and the Pearl of Great Price are considered part of their scriptural canon.[171][172]
+
+Despite the wide variety among Christian liturgies, texts from the New Testament play a role in almost all forms of Christian worship. In addition to some language derived from the New Testament in the liturgy itself (e.g., the Trisagion may be based on Apocalypse 4:8, and the beginning of the "Hymn of Praise" draws upon Luke 2:14), the reading of extended passages from the New Testament is a practice common to almost all Christian worship, liturgical or not.
+
+These readings are most often part of an established lectionary (i.e., selected texts to be read at church services on specific days), and (together with an Old Testament reading and a Psalm) include a non-gospel reading from the New Testament and culminate with a Gospel reading. No readings from the Book of Revelation, however, are included in the standard lectionary of the Eastern Orthodox churches.
+
+Central to the Christian liturgy is the celebration of the Eucharist or "Holy Communion". The Words of Institution that begin this rite are drawn directly from 1 Corinthians 11:23–26. In addition, the communal recitation of the Lord's Prayer (in the form found in the Gospel of Matthew 6:9–13) is also a standard feature of Christian worship.
+
+Most of the influence of the New Testament upon the arts has come from the Gospels and the Book of Revelation.[citation needed] Literary expansion of the Nativity of Jesus found in the Gospels of Matthew and Luke began already in the 2nd century, and the portrayal of the Nativity has continued in various art forms to this day. The earliest Christian art would often depict scenes from the New Testament such as the raising of Lazarus, the baptism of Jesus or the motif of the Good Shepherd.
+
+Biblical paraphrases and poetic renditions of stories from the life of Christ (e.g., the Heliand) became popular in the Middle Ages, as did the portrayal of the arrest, trial and execution of Jesus in Passion plays. Indeed, the Passion became a central theme in Christian art and music. The ministry and Passion of Jesus, as portrayed in one or more of the New Testament Gospels, has also been a theme in film, almost since the inception of the medium (e.g., La Passion, France, 1903).

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+
+
+A pet, or companion animal, is an animal kept primarily for a person's company or entertainment rather than as a working animal, livestock or a laboratory animal. Popular pets are often considered to have attractive appearances, intelligence and relatable personalities, but some pets may be taken in on an altruistic basis (such as a stray animal) and accepted by the owner regardless of these characteristics.
+
+Two of the most popular pets are dogs and cats; the technical term for a cat lover is an ailurophile and a dog lover a cynophile. Other animals commonly kept include: rabbits; ferrets; pigs; rodents, such as gerbils, hamsters, chinchillas, rats, mice, and guinea pigs; avian pets, such as parrots, passerines and fowls; reptile pets, such as turtles, alligators, crocodiles, lizards, and snakes; aquatic pets, such as fish, freshwater and saltwater snails, amphibians like frogs and salamanders; and arthropod pets, such as tarantulas and hermit crabs. Small pets may be grouped together as pocket pets, while the equine and bovine group include the largest companion animals.
+
+Pets provide their owners (or "guardians")[1] both physical and emotional benefits. Walking a dog can provide both the human and the dog with exercise, fresh air and social interaction. Pets can give companionship to people who are living alone or elderly adults who do not have adequate social interaction with other people. There is a medically approved class of therapy animals, mostly dogs or cats, that are brought to visit confined humans, such as children in hospitals or elders in nursing homes. Pet therapy utilizes trained animals and handlers to achieve specific physical, social, cognitive or emotional goals with patients.
+
+People most commonly get pets for companionship, to protect a home or property or because of the perceived beauty or attractiveness of the animals.[2] A 1994 Canadian study found that the most common reasons for not owning a pet were lack of ability to care for the pet when traveling (34.6%), lack of time (28.6%) and lack of suitable housing (28.3%), with dislike of pets being less common (19.6%).[2] Some scholars, ethicists and animal rights organizations have raised concerns over keeping pets because of the lack of autonomy and the objectification of non-human animals.[3]
+
+In China, spending on domestic animals has grown from an estimated $3.12 billion in 2010 to $25 billion in 2018. The Chinese people own 51 million dogs and 41 million cats, with pet owners often preferring to source pet food internationally.[4] There are a total of 755 million pets, increased from 389 million in 2013.[5]
+
+According to a survey promoted by Italian family associations in 2009, it is estimated that there are approximately 45 million pets in Italy. This includes 7 million dogs, 7.5 million cats, 16 million fish, 12 million birds, and 10 million snakes.[6]
+
+A 2007 survey by the University of Bristol found that 26% of UK households owned cats and 31% owned dogs, estimating total domestic populations of approximately 10.3 million cats and 10.5 million dogs in 2006.[7] The survey also found that 47.2% of households with a cat had at least one person educated to degree level, compared with 38.4% of homes with dogs.[8]
+
+Sixty-eight percent of U.S. households, or about 85 million families, own a pet, according to the 2017-2018 National Pet Owners Survey conducted by the American Pet Products Association (APPA). This is up from 56 percent of U.S. households in 1988, the first year the survey was conducted.[9]There are approximately 86.4 million pet cats and approximately 78.2 million pet dogs in the United States,[10][11] and a United States 2007–2008 survey showed that dog-owning households outnumbered those owning cats, but that the total number of pet cats was higher than that of dogs. The same was true for 2011.[12] In 2013, pets outnumbered children four to one in the United States.[13]
+
+Keeping animals as pets may be detrimental to their health if certain requirements are not met. An important issue is inappropriate feeding, which may produce clinical effects. The consumption of chocolate or grapes by dogs, for example, may prove fatal.
+
+Certain species of houseplants can also prove toxic if consumed by pets. Examples include philodendrons and Easter lilies (which can cause severe kidney damage to cats)[16][17] and poinsettias, begonia, and aloe vera (which are mildly toxic to dogs).[18][19]
+
+Housepets, particularly dogs and cats in industrialized societies, are also highly susceptible to obesity. Overweight pets have been shown to be at a higher risk of developing diabetes, liver problems, joint pain, kidney failure, and cancer. Lack of exercise and high-caloric diets are considered to be the primary contributors to pet obesity.[20][21][22]
+
+It is widely believed among the public, and among many scientists, that pets probably bring mental and physical health benefits to their owners;[23] a 1987 NIH statement cautiously argued that existing data was "suggestive" of a significant benefit.[24] A recent dissent comes from a 2017 RAND study, which found that at least in the case of children, having a pet per se failed to improve physical or mental health by a statistically significant amount; instead, the study found children who were already prone to being healthy were more likely to get pets in the first place.[23][25][26] Unfortunately, conducting long-term randomized trials to settle the issue would be costly or infeasible.[24][26]
+
+Pets might have the ability to stimulate their caregivers, in particular the elderly, giving people someone to take care of, someone to exercise with, and someone to help them heal from a physically or psychologically troubled past.[24][27][28] Animal company can also help people to preserve acceptable levels of happiness despite the presence of mood symptoms like anxiety or depression.[29] Having a pet may also help people achieve health goals, such as lowered blood pressure, or mental goals, such as decreased stress.[30][31][32][33][34][35] There is evidence that having a pet can help a person lead a longer, healthier life. In a 1986 study of 92 people hospitalized for coronary ailments, within a year, 11 of the 29 patients without pets had died, compared to only 3 of the 52 patients who had pets.[28] Having pet(s) was shown to significantly reduce triglycerides, and thus heart disease risk, in the elderly.[36] A study by the National Institute of Health found that people who owned dogs were less likely to die as a result of a heart attack than those who did not own one.[37] There is some evidence that pets may have a therapeutic effect in dementia cases.[38] Other studies have shown that for the elderly, good health may be a requirement for having a pet, and not a result.[39] Dogs trained to be guide dogs can help people with vision impairment. Dogs trained in the field of Animal-Assisted Therapy (AAT) can also benefit people with other disabilities.[24][40]
+
+People residing in a long-term care facility, such as a hospice or nursing home, may experience health benefits from pets. Pets help them to cope with the emotional issues related to their illness. They also offer physical contact with another living creature, something that is often missing in an elder's life.[10][41] Pets for nursing homes are chosen based on the size of the pet, the amount of care that the breed needs, and the population and size of the care institution.[28] Appropriate pets go through a screening process and, if it is a dog, additional training programs to become a therapy dog.[42] There are three types of therapy dogs: facility therapy dogs, animal-assisted therapy dogs, and therapeutic visitation dogs. The most common therapy dogs are therapeutic visitation dogs. These dogs are household pets whose handlers take time to visit hospitals, nursing homes, detention facilities, and rehabilitation facilities.[27] Different pets require varying amounts of attention and care; for example, cats may have lower maintenance requirements than dogs.[43]
+
+In addition to providing health benefits for their owners, pets also impact the social lives of their owners and their connection to their community. There is some evidence that pets can facilitate social interaction.[44] Assistant Professor of Sociology at the University of Colorado at Boulder, Leslie Irvine has focused her attention on pets of the homeless population. Her studies of pet ownership among the homeless found that many modify their life activities for fear of losing their pets. Pet ownership prompts them to act responsibly, with many making a deliberate choice not to drink or use drugs, and to avoid contact with substance abusers or those involved in any criminal activity for fear of being separated from their pet. Additionally, many refuse to house in shelters if their pet is not allowed to stay with them.[45]
+
+Health risks that are associated with pets include:
+
+The European Convention for the Protection of Pet Animals is a 1987 treaty of the Council of Europe – but accession to the treaty is open to all states in the world – to promote the welfare of pet animals and ensure minimum standards for their treatment and protection. It went into effect on 1 May 1992, and as of June 2020, it has been ratified by 24 states.[47]
+
+States, cities, and towns in Western nations commonly enact local ordinances to limit the number or kind of pets a person may keep personally or for business purposes. Prohibited pets may be specific to certain breeds (such as pit bulls or Rottweilers), they may apply to general categories of animals (such as livestock, exotic animals, wild animals, and canid or felid hybrids), or they may simply be based on the animal's size. Additional or different maintenance rules and regulations may also apply. Condominium associations and owners of rental properties also commonly limit or forbid tenants' keeping of pets.[citation needed]
+
+The keeping of animals as pets can cause concerns with regard to animal rights and welfare.[48][49][50] Pets have commonly been considered private property, owned by individual persons. However, many legal protections have existed (historically and today) with the intention of safeguarding pets' (and other animals') well-being.[51][52][53][54] Since the year 2000, a small but increasing number of jurisdictions in North America have enacted laws redefining pet's owners as guardians. Intentions have been characterized as simply changing attitudes and perceptions (but not legal consequences) to working toward legal personhood for pets themselves. Some veterinarians and breeders have opposed these moves. The question of pets' legal status can arise with concern to purchase or adoption, custody, divorce, estate and inheritance, injury, damage, and veterinary malpractice.[55][56][57][58]
+
+In Belgium and the Netherlands, the government publishes white lists and black lists (called 'positive' and 'negative lists') with animal species that are designated to be appropriate to be kept as pets (positive) or not (negative). The Dutch Ministry of Economic Affairs and Climate Policy originally established its first positive list (positieflijst) per 1 February 2015 for a set of 100 mammals (including cats, dogs and production animals) deemed appropriate as pets on the recommendations of Wageningen University.[59] Parliamentary debates about such a pet list date back to the 1980s, with continuous disagreements about which species should be included and how the law should be enforced.[60] In January 2017, the white list was expanded to 123 species, while the black list that had been set up was expanded (with animals like the brown bear and two great kangaroo species) to contain 153 species unfit for petting, such as the armadillo, the sloth, the European hare and the wild boar.[61]
+
+Pets have a considerable environmental impact, especially in countries where they are common or held in high densities. For instance, the 163 million dogs and cats kept in the United States consume about 20% of the amount of dietary energy that humans do and an estimated 33% of the animal-derived energy.[62] They produce about 30% ± 13%, by mass, as much feces as Americans, and through their diet, constitute about 25–30% of the environmental impacts from animal production in terms of the use of land, water, fossil fuel, phosphate, and biocides. Dog and cat animal product consumption is responsible for the release of up to 64 ± 16 million tons CO2-equivalent methane and nitrous oxide, two powerful greenhouse gasses. Americans are the largest pet owners in the world, but pet ownership in the US has considerable environmental costs.[62]
+
+While many people have kept many different species of animals in captivity over the course of human history, only a relative few have been kept long enough to be considered domesticated. Other types of animals, notably monkeys, have never been domesticated but are still sold and kept as pets. There are also inanimate objects that have been kept as "pets", either as a form of a game or humorously (e.g. the Pet Rock or Chia Pet). Some wild animals are kept as pets, such as tigers, even though this is illegal. There is a market for illegal pets.
+
+Domesticated pets are most common. A domesticated animal is a species that has been made fit for a human environment[63] by being consistently kept in captivity and selectively bred over a long enough period of time that it exhibits marked differences in behavior and appearance from its wild relatives. Domestication contrasts with taming, which is simply when an un-domesticated, wild animal has become tolerant of human presence, and perhaps, even enjoys it.
+
+Wild animals are kept as pets. The term “wild” in this context specifically applies to any species of animal which has not undergone a fundamental change in behavior to facilitate a close co-existence with humans. Some species may have been bred in captivity for a considerable length of time, but are still not recognized as domesticated.
+
+Generally, wild animals are recognized as not suitable to keep as pets, and this practice is completely banned in many places. In other areas, certain species are allowed to be kept, and it is usually required for the owner to obtain a permit. It is considered animal cruelty by some, as most often, wild animals require precise and constant care that is very difficult to meet in captive conditions. Many large and instinctively aggressive animals are extremely dangerous, and numerous times have they killed their handlers.
+
+Archaeology suggests that human ownership of dogs as pets may date back to at least 12,000 years ago.[64]
+
+Ancient Greeks and Romans would openly grieve for the loss of a dog, evidenced by inscriptions left on tombstones commemorating their loss.[65] The surviving epitaphs dedicated to horses are more likely to reference a gratitude for the companionship that had come from war horses rather than race horses. The latter may have chiefly been commemorated as a way to further the owner's fame and glory.[66] In Ancient Egypt, dogs and baboons were kept as pets and buried with their owners. Dogs were given names, which is significant as Egyptians considered names to have magical properties. [67]
+
+Throughout the seventeenth and eighteenth-century pet keeping in the modern sense gradually became accepted throughout Britain. Initially, aristocrats kept dogs for both companionship and hunting. Thus, pet keeping was a sign of elitism within society. By the nineteenth century, the rise of the middle class stimulated the development of pet keeping and it became inscribed within the bourgeois culture.[68]
+
+As the popularity of pet-keeping in the modern sense rose during the Victorian era, animals became a fixture within urban culture as commodities and decorative objects.[69] Pet keeping generated a commercial opportunity for entrepreneurs. By the mid-nineteenth century, nearly twenty thousand street vendors in London dealt with live animals.[70] Also, the popularity of animals developed a demand for animal goods such as accessories and guides for pet keeping. Pet care developed into a big business by the end of the nineteenth century.[71]
+
+Profiteers also sought out pet stealing as a means for economic gain. Utilizing the affection that owners had for their pets, professional dog stealers would capture animals and hold them for ransom.[72] The development of dog stealing reflects the increased value of pets. Pets gradually became defined as the property of their owners. Laws were created that punished offenders for their burglary.[73]
+
+Pets and animals also had social and cultural implications throughout the nineteenth century. The categorization of dogs by their breeds reflected the hierarchical, social order of the Victorian era. The pedigree of a dog represented the high status and lineage of their owners and reinforced social stratification.[74] Middle-class owners, however, valued the ability to associate with the upper-class through ownership of their pets. The ability to care for a pet signified respectability and the capability to be self-sufficient.[75] According to Harriet Ritvo, the identification of “elite animal and elite owner was not a confirmation of the owner’s status but a way of redefining it.”[76]
+
+The popularity of dog and pet keeping generated animal fancy. Dog fanciers showed enthusiasm for owning pets, breeding dogs, and showing dogs in various shows. The first dog show took place on 28 June 1859 in Newcastle and focused mostly on sporting and hunting dogs.[77] However, pet owners produced an eagerness to demonstrate their pets as well as have an outlet to compete.[78] Thus, pet animals gradually were included within dog shows. The first large show, which would host one thousand entries, took place in Chelsea in 1863.[79] The Kennel Club was created in 1873 to ensure fairness and organization within dog shows. The development of the Stud Book by the Kennel Club defined policies, presented a national registry system of purebred dogs, and essentially institutionalized dog shows.[80]
+
+Pet ownership by animals in the wild, as an analogue to the human phenomenon, has not been observed and is likely non-existent in nature.[81][82] One group of capuchin monkeys was observed appearing to care for a marmoset, a fellow New World monkey species, however observations of chimpanzees apparently "playing" with small animals like hyraxes have ended with the chimpanzees killing the animals and tossing the corpses around.[83]
+
+A 2010 study states that human relationships with animals have an exclusive human cognitive component and that pet-keeping is a fundamental and ancient attribute of the human species. Anthropomorphism, or the projection of human feelings, thoughts and attributes on to animals, is a defining feature of human pet-keeping. The study identifies it as the same trait in evolution responsible for domestication and concern for animal welfare. It is estimated to have arisen at least 100,000 years before present (ybp) in Homo sapiens sapiens.[82]
+
+It is debated whether this redirection of human nurturing behaviour towards non-human animals, in the form of pet-keeping, was maladaptive, due to being biologically costly, or whether it was positively selected for.[84][85][82] Two studies suggest that the human ability to domesticate and keep pets came from the same fundamental evolutionary trait and that this trait provided a material benefit in the form of domestication that was sufficiently adaptive to be positively selected for.[82][85]:300 A 2011 study suggests that the practical functions that some pets provide, such as assisting hunting or removing pests, could've resulted in enough evolutionary advantage to allow for the persistence of this behaviour in humans and outweigh the economic burden held by pets kept as playthings for immediate emotional rewards.[86] Two other studies suggest that the behaviour constitutes an error, side effect or misapplication of the evolved mechanisms responsible for human empathy and theory of mind to cover non-human animals which has not sufficiently impacted its evolutionary advantage in the long run.[85]:300
+
+Animals in captivity, with the help of caretakers, have been considered to have owned "pets". Examples of this include Koko the gorilla and several pet cats, Tonda the orangutan and a pet cat and Tarra the elephant and a dog named Bella.[83]
+
+Katharine of Aragon with a monkey
+
+The Girl with the Marmot by Jean-Honoré Fragonard
+
+- Young Lady with parrot by Édouard Manet 1866
+
+Antoinette Metayer (1732–88) and her pet dog
+
+The Lady with an Ermine
+
+Sir Henry Raeburn - Boy and Rabbit
+
+Eos, A Favorite Greyhound of Prince Albert
+
+A Neapolitan Woman
+
+Signal, a Grey Arab, with a Groom in the Desert
+
+Eduardo Leon Garrido. An Elegant Lady with her Dog
+
+The Fireplace depicting a Pug, James Tissot
+
+Rosa Bonheur - Portrait of William F. Cody
+
+Hunt
+
+
+
+
+
+
+

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+New Year's Day, also simply called New Year, is observed on 1 January, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.
+
+In pre-Christian Rome under the Julian calendar, the day was dedicated to Janus, god of gateways and beginnings, for whom January is also named. As a date in the Gregorian calendar of Christendom, New Year's Day liturgically marked the Feast of the Naming and Circumcision of Jesus, which is still observed as such in the Anglican Church and Lutheran Church.[2][3]  The Roman Catholic Church celebrates on this day the Solemnity of Mary, Mother of God.
+
+In present day, with most countries now using the Gregorian calendar as their de facto calendar, New Year's Day is among the most celebrated public holidays in the world, often observed with fireworks at the stroke of midnight as the new year starts in each time zone. Other global New Year's Day traditions include making New Year's resolutions and calling one's friends and family.[1]
+
+
+
+Mesopotamia (modern-day Iraq) instituted the concept of celebrating the new year in 2000 BC and celebrated new year around the time of the vernal equinox, in mid-March.[4][5] The early Roman calendar designated 1 March as the first day of the year. The calendar had just 10 months, beginning with March. That the new year once began with the month of March is still reflected in some of the names of the months. September through to December, the ninth through to the twelfth months of the Gregorian calendar, were originally positioned as the seventh through to the tenth months. (Septem is Latin for "seven"; octo, "eight"; novem, "nine"; and decem, "ten".) Roman legend usually credited their second king Numa with the establishment of the two new months of Ianuarius and Februarius. These were first placed at the end of the year, but at some point came to be considered the first two months instead.[6]
+
+The January kalend (Latin: Kalendae Ianuariae), the start of the month of January, came to be celebrated as the new year at some point after it became the day for the inaugurating new consuls in 153 BC. Romans had long dated their years by these consulships, rather than sequentially, and making the kalends of January start the new year aligned this dating. Still, private and religious celebrations around the March new year continued for some time and there is no consensus on the question of the timing for 1 January's new status.[7] Once it became the new year, however, it became a time for family gatherings and celebrations. A series of disasters, notably including the failed rebellion of M. Aemilius Lepidus in 78 BC, established a superstition against allowing Rome's market days to fall on the kalends of January and the pontiffs employed intercalation to avoid its occurrence.[8][9]
+
+In 567 AD, the Council of Tours formally abolished 1 January as the beginning of the year.[citation needed] At various times and in various places throughout mediaeval Christian Europe, the new year was celebrated on 25 December in honour of the birth of Jesus; 1 March in the old Roman style; 25 March in honour of Lady Day and the Feast of the Annunciation; and on the movable feast of Easter. These days were also astronomically and astrologically significant since, at the time of the Julian reform, 25 March had been understood as the spring equinox and 25 December as the winter solstice. (The Julian calendar's small disagreement with the solar year, however, shifted these days earlier before the Council of Nicaea which formed the basis of the calculations used during the Gregorian reform of the calendar.[citation needed]) Mediaeval calendars nonetheless often continued to display the months running from January to December, despite their readers reckoning the transition from one year to the next on a different day.[citation needed]
+
+Among the 7th-century pagans of Flanders and the Netherlands, it was the custom to exchange gifts on the first day of the new year. This custom was deplored by Saint Eligius (died 659 or 660), who warned the Flemish and Dutch: "(Do not) make vetulas, [little figures of the Old Woman], little deer or iotticos or set tables [for the house-elf, compare Puck] at night or exchange New Year gifts or supply superfluous drinks [another Yule custom]."[10] However, on the date that European Christians celebrated the New Year, they exchanged Christmas presents because New Year's Day fell within the 12 days of the Christmas season in the Western Christian liturgical calendar;[11] the custom of exchanging Christmas gifts in a Christian context is traced back to the Biblical Magi who gave gifts to the Child Jesus.[12][13]
+
+Because of the leap year error in the Julian calendar, the date of Easter had drifted backward since the First Council of Nicaea decided the computation of the date of Easter in 325. By the sixteenth century, the drift from the observed equinox had become unacceptable. In 1582, Pope Gregory XIII declared the Gregorian calendar widely used today, correcting the error by a deletion of 10 days. The Gregorian calendar reform also (in effect) restored 1 January as New Year's Day. Although most Catholic countries adopted the Gregorian calendar almost immediately, it was only gradually adopted among Protestant countries. The British, for example, did not adopt the reformed calendar until 1752. Until then, the British Empire  –  and its American colonies  –  still celebrated the new year on 25 March.
+
+Most nations of Western Europe officially adopted 1 January as New Year's Day somewhat before they adopted the Gregorian Calendar. In Tudor England, New Year's Day, along with Christmas Day and Twelfth Night, was celebrated as one of three main festivities among the twelve days of Christmastide.[14] There, until the adoption of the Gregorian Calendar in 1752, the first day of the new year was the Western Christian Feast of the Annunciation, on 25 March, also called "Lady Day". Dates predicated on the year beginning on 25 March became known as Annunciation Style dates, while dates of the Gregorian Calendar commencing on 1 January were distinguished as Circumcision Style dates,[15] because this was the date of the Feast of the Circumcision, the observed memorial of the eighth day of Jesus Christ's life after his birth, counted from the latter's observation on Christmas, 25 December. Pope Gregory acknowledged 1 January as the beginning of the new year according to his reform of the Catholic Liturgical Calendar.[16]
+
+In cultures that traditionally or currently use calendars other than the Gregorian, New Year's Day is often also an important celebration. Some countries concurrently use Gregorian and another calendar. New Year's Day in the alternative calendar attracts alternative celebrations of that new year:
+
+The first of January represents the fresh start of a new year after a period of remembrance of the passing year, including on radio, television, and in newspapers, which starts in early December in countries around the world. Publications have year-end articles that review the changes during the previous year. In some cases, publications may set their entire year work alight in the hope that the smoke emitted from the flame brings new life to the company.  There are also articles on planned or expected changes in the coming year.
+
+This day is traditionally a religious feast, but since the 1900s has also become an occasion to celebrate the night of 31 December—New Year's Eve—with parties, public celebrations (often involving fireworks shows) and other traditions focused on the impending arrival of midnight and the new year. Watchnight services are also still observed by many.[26]
+
+The celebrations and activities held worldwide on 1 January as part of New Year's Day commonly include the following:
+
+Music associated with New Year's Day comes in both classical and popular genres, and there is also Christmas song focus on the arrival of a new year during the Christmas and holiday season.
+
+A common image used, often as an editorial cartoon, is that of an incarnation of Father Time (or the "Old Year") wearing a sash across his chest with the previous year printed on it passing on his duties to the Baby New Year (or the "New Year"), an infant wearing a sash with the new year printed on it.[35]
+
+Babies born on New Year's Day are commonly called New Year babies. Hospitals, such as the Dyersburg Regional Medical Center[36] in the US, give out prizes to the first baby born in that hospital in the new year. These prizes are often donated by local businesses.  Prizes may include various baby-related items such as baby formula, baby blankets, diapers, and gift certificates to stores which specialise in baby-related merchandise.
+
+The Anglican Church and the Lutheran Church celebrate the Feast of the Circumcision of Christ on 1 January, based on the belief that if Jesus was born on 25 December, then according to Hebrew tradition, his circumcision would have taken place on the eighth day of his life (1 January). The Roman Catholic Church celebrates on this day the Solemnity of Mary, Mother of God, which is also a Holy Day of Obligation. In the United States, New Year's Day is a postal holiday.[37]
+
+Johann Sebastian Bach composed several church cantatas for the double occasion:
+
+(federal) = federal holidays, (abbreviation) = state/territorial holidays, (religious) = religious holidays, (cultural) = holiday related to a specific racial/ethnic group or sexual minority, (week) = week-long holidays, (month) = month-long holidays, (36) = Title 36 Observances and Ceremonies
+Bold indicates major holidays commonly celebrated in the United States, which often represent the major celebrations of the month.

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+
+
+A pet, or companion animal, is an animal kept primarily for a person's company or entertainment rather than as a working animal, livestock or a laboratory animal. Popular pets are often considered to have attractive appearances, intelligence and relatable personalities, but some pets may be taken in on an altruistic basis (such as a stray animal) and accepted by the owner regardless of these characteristics.
+
+Two of the most popular pets are dogs and cats; the technical term for a cat lover is an ailurophile and a dog lover a cynophile. Other animals commonly kept include: rabbits; ferrets; pigs; rodents, such as gerbils, hamsters, chinchillas, rats, mice, and guinea pigs; avian pets, such as parrots, passerines and fowls; reptile pets, such as turtles, alligators, crocodiles, lizards, and snakes; aquatic pets, such as fish, freshwater and saltwater snails, amphibians like frogs and salamanders; and arthropod pets, such as tarantulas and hermit crabs. Small pets may be grouped together as pocket pets, while the equine and bovine group include the largest companion animals.
+
+Pets provide their owners (or "guardians")[1] both physical and emotional benefits. Walking a dog can provide both the human and the dog with exercise, fresh air and social interaction. Pets can give companionship to people who are living alone or elderly adults who do not have adequate social interaction with other people. There is a medically approved class of therapy animals, mostly dogs or cats, that are brought to visit confined humans, such as children in hospitals or elders in nursing homes. Pet therapy utilizes trained animals and handlers to achieve specific physical, social, cognitive or emotional goals with patients.
+
+People most commonly get pets for companionship, to protect a home or property or because of the perceived beauty or attractiveness of the animals.[2] A 1994 Canadian study found that the most common reasons for not owning a pet were lack of ability to care for the pet when traveling (34.6%), lack of time (28.6%) and lack of suitable housing (28.3%), with dislike of pets being less common (19.6%).[2] Some scholars, ethicists and animal rights organizations have raised concerns over keeping pets because of the lack of autonomy and the objectification of non-human animals.[3]
+
+In China, spending on domestic animals has grown from an estimated $3.12 billion in 2010 to $25 billion in 2018. The Chinese people own 51 million dogs and 41 million cats, with pet owners often preferring to source pet food internationally.[4] There are a total of 755 million pets, increased from 389 million in 2013.[5]
+
+According to a survey promoted by Italian family associations in 2009, it is estimated that there are approximately 45 million pets in Italy. This includes 7 million dogs, 7.5 million cats, 16 million fish, 12 million birds, and 10 million snakes.[6]
+
+A 2007 survey by the University of Bristol found that 26% of UK households owned cats and 31% owned dogs, estimating total domestic populations of approximately 10.3 million cats and 10.5 million dogs in 2006.[7] The survey also found that 47.2% of households with a cat had at least one person educated to degree level, compared with 38.4% of homes with dogs.[8]
+
+Sixty-eight percent of U.S. households, or about 85 million families, own a pet, according to the 2017-2018 National Pet Owners Survey conducted by the American Pet Products Association (APPA). This is up from 56 percent of U.S. households in 1988, the first year the survey was conducted.[9]There are approximately 86.4 million pet cats and approximately 78.2 million pet dogs in the United States,[10][11] and a United States 2007–2008 survey showed that dog-owning households outnumbered those owning cats, but that the total number of pet cats was higher than that of dogs. The same was true for 2011.[12] In 2013, pets outnumbered children four to one in the United States.[13]
+
+Keeping animals as pets may be detrimental to their health if certain requirements are not met. An important issue is inappropriate feeding, which may produce clinical effects. The consumption of chocolate or grapes by dogs, for example, may prove fatal.
+
+Certain species of houseplants can also prove toxic if consumed by pets. Examples include philodendrons and Easter lilies (which can cause severe kidney damage to cats)[16][17] and poinsettias, begonia, and aloe vera (which are mildly toxic to dogs).[18][19]
+
+Housepets, particularly dogs and cats in industrialized societies, are also highly susceptible to obesity. Overweight pets have been shown to be at a higher risk of developing diabetes, liver problems, joint pain, kidney failure, and cancer. Lack of exercise and high-caloric diets are considered to be the primary contributors to pet obesity.[20][21][22]
+
+It is widely believed among the public, and among many scientists, that pets probably bring mental and physical health benefits to their owners;[23] a 1987 NIH statement cautiously argued that existing data was "suggestive" of a significant benefit.[24] A recent dissent comes from a 2017 RAND study, which found that at least in the case of children, having a pet per se failed to improve physical or mental health by a statistically significant amount; instead, the study found children who were already prone to being healthy were more likely to get pets in the first place.[23][25][26] Unfortunately, conducting long-term randomized trials to settle the issue would be costly or infeasible.[24][26]
+
+Pets might have the ability to stimulate their caregivers, in particular the elderly, giving people someone to take care of, someone to exercise with, and someone to help them heal from a physically or psychologically troubled past.[24][27][28] Animal company can also help people to preserve acceptable levels of happiness despite the presence of mood symptoms like anxiety or depression.[29] Having a pet may also help people achieve health goals, such as lowered blood pressure, or mental goals, such as decreased stress.[30][31][32][33][34][35] There is evidence that having a pet can help a person lead a longer, healthier life. In a 1986 study of 92 people hospitalized for coronary ailments, within a year, 11 of the 29 patients without pets had died, compared to only 3 of the 52 patients who had pets.[28] Having pet(s) was shown to significantly reduce triglycerides, and thus heart disease risk, in the elderly.[36] A study by the National Institute of Health found that people who owned dogs were less likely to die as a result of a heart attack than those who did not own one.[37] There is some evidence that pets may have a therapeutic effect in dementia cases.[38] Other studies have shown that for the elderly, good health may be a requirement for having a pet, and not a result.[39] Dogs trained to be guide dogs can help people with vision impairment. Dogs trained in the field of Animal-Assisted Therapy (AAT) can also benefit people with other disabilities.[24][40]
+
+People residing in a long-term care facility, such as a hospice or nursing home, may experience health benefits from pets. Pets help them to cope with the emotional issues related to their illness. They also offer physical contact with another living creature, something that is often missing in an elder's life.[10][41] Pets for nursing homes are chosen based on the size of the pet, the amount of care that the breed needs, and the population and size of the care institution.[28] Appropriate pets go through a screening process and, if it is a dog, additional training programs to become a therapy dog.[42] There are three types of therapy dogs: facility therapy dogs, animal-assisted therapy dogs, and therapeutic visitation dogs. The most common therapy dogs are therapeutic visitation dogs. These dogs are household pets whose handlers take time to visit hospitals, nursing homes, detention facilities, and rehabilitation facilities.[27] Different pets require varying amounts of attention and care; for example, cats may have lower maintenance requirements than dogs.[43]
+
+In addition to providing health benefits for their owners, pets also impact the social lives of their owners and their connection to their community. There is some evidence that pets can facilitate social interaction.[44] Assistant Professor of Sociology at the University of Colorado at Boulder, Leslie Irvine has focused her attention on pets of the homeless population. Her studies of pet ownership among the homeless found that many modify their life activities for fear of losing their pets. Pet ownership prompts them to act responsibly, with many making a deliberate choice not to drink or use drugs, and to avoid contact with substance abusers or those involved in any criminal activity for fear of being separated from their pet. Additionally, many refuse to house in shelters if their pet is not allowed to stay with them.[45]
+
+Health risks that are associated with pets include:
+
+The European Convention for the Protection of Pet Animals is a 1987 treaty of the Council of Europe – but accession to the treaty is open to all states in the world – to promote the welfare of pet animals and ensure minimum standards for their treatment and protection. It went into effect on 1 May 1992, and as of June 2020, it has been ratified by 24 states.[47]
+
+States, cities, and towns in Western nations commonly enact local ordinances to limit the number or kind of pets a person may keep personally or for business purposes. Prohibited pets may be specific to certain breeds (such as pit bulls or Rottweilers), they may apply to general categories of animals (such as livestock, exotic animals, wild animals, and canid or felid hybrids), or they may simply be based on the animal's size. Additional or different maintenance rules and regulations may also apply. Condominium associations and owners of rental properties also commonly limit or forbid tenants' keeping of pets.[citation needed]
+
+The keeping of animals as pets can cause concerns with regard to animal rights and welfare.[48][49][50] Pets have commonly been considered private property, owned by individual persons. However, many legal protections have existed (historically and today) with the intention of safeguarding pets' (and other animals') well-being.[51][52][53][54] Since the year 2000, a small but increasing number of jurisdictions in North America have enacted laws redefining pet's owners as guardians. Intentions have been characterized as simply changing attitudes and perceptions (but not legal consequences) to working toward legal personhood for pets themselves. Some veterinarians and breeders have opposed these moves. The question of pets' legal status can arise with concern to purchase or adoption, custody, divorce, estate and inheritance, injury, damage, and veterinary malpractice.[55][56][57][58]
+
+In Belgium and the Netherlands, the government publishes white lists and black lists (called 'positive' and 'negative lists') with animal species that are designated to be appropriate to be kept as pets (positive) or not (negative). The Dutch Ministry of Economic Affairs and Climate Policy originally established its first positive list (positieflijst) per 1 February 2015 for a set of 100 mammals (including cats, dogs and production animals) deemed appropriate as pets on the recommendations of Wageningen University.[59] Parliamentary debates about such a pet list date back to the 1980s, with continuous disagreements about which species should be included and how the law should be enforced.[60] In January 2017, the white list was expanded to 123 species, while the black list that had been set up was expanded (with animals like the brown bear and two great kangaroo species) to contain 153 species unfit for petting, such as the armadillo, the sloth, the European hare and the wild boar.[61]
+
+Pets have a considerable environmental impact, especially in countries where they are common or held in high densities. For instance, the 163 million dogs and cats kept in the United States consume about 20% of the amount of dietary energy that humans do and an estimated 33% of the animal-derived energy.[62] They produce about 30% ± 13%, by mass, as much feces as Americans, and through their diet, constitute about 25–30% of the environmental impacts from animal production in terms of the use of land, water, fossil fuel, phosphate, and biocides. Dog and cat animal product consumption is responsible for the release of up to 64 ± 16 million tons CO2-equivalent methane and nitrous oxide, two powerful greenhouse gasses. Americans are the largest pet owners in the world, but pet ownership in the US has considerable environmental costs.[62]
+
+While many people have kept many different species of animals in captivity over the course of human history, only a relative few have been kept long enough to be considered domesticated. Other types of animals, notably monkeys, have never been domesticated but are still sold and kept as pets. There are also inanimate objects that have been kept as "pets", either as a form of a game or humorously (e.g. the Pet Rock or Chia Pet). Some wild animals are kept as pets, such as tigers, even though this is illegal. There is a market for illegal pets.
+
+Domesticated pets are most common. A domesticated animal is a species that has been made fit for a human environment[63] by being consistently kept in captivity and selectively bred over a long enough period of time that it exhibits marked differences in behavior and appearance from its wild relatives. Domestication contrasts with taming, which is simply when an un-domesticated, wild animal has become tolerant of human presence, and perhaps, even enjoys it.
+
+Wild animals are kept as pets. The term “wild” in this context specifically applies to any species of animal which has not undergone a fundamental change in behavior to facilitate a close co-existence with humans. Some species may have been bred in captivity for a considerable length of time, but are still not recognized as domesticated.
+
+Generally, wild animals are recognized as not suitable to keep as pets, and this practice is completely banned in many places. In other areas, certain species are allowed to be kept, and it is usually required for the owner to obtain a permit. It is considered animal cruelty by some, as most often, wild animals require precise and constant care that is very difficult to meet in captive conditions. Many large and instinctively aggressive animals are extremely dangerous, and numerous times have they killed their handlers.
+
+Archaeology suggests that human ownership of dogs as pets may date back to at least 12,000 years ago.[64]
+
+Ancient Greeks and Romans would openly grieve for the loss of a dog, evidenced by inscriptions left on tombstones commemorating their loss.[65] The surviving epitaphs dedicated to horses are more likely to reference a gratitude for the companionship that had come from war horses rather than race horses. The latter may have chiefly been commemorated as a way to further the owner's fame and glory.[66] In Ancient Egypt, dogs and baboons were kept as pets and buried with their owners. Dogs were given names, which is significant as Egyptians considered names to have magical properties. [67]
+
+Throughout the seventeenth and eighteenth-century pet keeping in the modern sense gradually became accepted throughout Britain. Initially, aristocrats kept dogs for both companionship and hunting. Thus, pet keeping was a sign of elitism within society. By the nineteenth century, the rise of the middle class stimulated the development of pet keeping and it became inscribed within the bourgeois culture.[68]
+
+As the popularity of pet-keeping in the modern sense rose during the Victorian era, animals became a fixture within urban culture as commodities and decorative objects.[69] Pet keeping generated a commercial opportunity for entrepreneurs. By the mid-nineteenth century, nearly twenty thousand street vendors in London dealt with live animals.[70] Also, the popularity of animals developed a demand for animal goods such as accessories and guides for pet keeping. Pet care developed into a big business by the end of the nineteenth century.[71]
+
+Profiteers also sought out pet stealing as a means for economic gain. Utilizing the affection that owners had for their pets, professional dog stealers would capture animals and hold them for ransom.[72] The development of dog stealing reflects the increased value of pets. Pets gradually became defined as the property of their owners. Laws were created that punished offenders for their burglary.[73]
+
+Pets and animals also had social and cultural implications throughout the nineteenth century. The categorization of dogs by their breeds reflected the hierarchical, social order of the Victorian era. The pedigree of a dog represented the high status and lineage of their owners and reinforced social stratification.[74] Middle-class owners, however, valued the ability to associate with the upper-class through ownership of their pets. The ability to care for a pet signified respectability and the capability to be self-sufficient.[75] According to Harriet Ritvo, the identification of “elite animal and elite owner was not a confirmation of the owner’s status but a way of redefining it.”[76]
+
+The popularity of dog and pet keeping generated animal fancy. Dog fanciers showed enthusiasm for owning pets, breeding dogs, and showing dogs in various shows. The first dog show took place on 28 June 1859 in Newcastle and focused mostly on sporting and hunting dogs.[77] However, pet owners produced an eagerness to demonstrate their pets as well as have an outlet to compete.[78] Thus, pet animals gradually were included within dog shows. The first large show, which would host one thousand entries, took place in Chelsea in 1863.[79] The Kennel Club was created in 1873 to ensure fairness and organization within dog shows. The development of the Stud Book by the Kennel Club defined policies, presented a national registry system of purebred dogs, and essentially institutionalized dog shows.[80]
+
+Pet ownership by animals in the wild, as an analogue to the human phenomenon, has not been observed and is likely non-existent in nature.[81][82] One group of capuchin monkeys was observed appearing to care for a marmoset, a fellow New World monkey species, however observations of chimpanzees apparently "playing" with small animals like hyraxes have ended with the chimpanzees killing the animals and tossing the corpses around.[83]
+
+A 2010 study states that human relationships with animals have an exclusive human cognitive component and that pet-keeping is a fundamental and ancient attribute of the human species. Anthropomorphism, or the projection of human feelings, thoughts and attributes on to animals, is a defining feature of human pet-keeping. The study identifies it as the same trait in evolution responsible for domestication and concern for animal welfare. It is estimated to have arisen at least 100,000 years before present (ybp) in Homo sapiens sapiens.[82]
+
+It is debated whether this redirection of human nurturing behaviour towards non-human animals, in the form of pet-keeping, was maladaptive, due to being biologically costly, or whether it was positively selected for.[84][85][82] Two studies suggest that the human ability to domesticate and keep pets came from the same fundamental evolutionary trait and that this trait provided a material benefit in the form of domestication that was sufficiently adaptive to be positively selected for.[82][85]:300 A 2011 study suggests that the practical functions that some pets provide, such as assisting hunting or removing pests, could've resulted in enough evolutionary advantage to allow for the persistence of this behaviour in humans and outweigh the economic burden held by pets kept as playthings for immediate emotional rewards.[86] Two other studies suggest that the behaviour constitutes an error, side effect or misapplication of the evolved mechanisms responsible for human empathy and theory of mind to cover non-human animals which has not sufficiently impacted its evolutionary advantage in the long run.[85]:300
+
+Animals in captivity, with the help of caretakers, have been considered to have owned "pets". Examples of this include Koko the gorilla and several pet cats, Tonda the orangutan and a pet cat and Tarra the elephant and a dog named Bella.[83]
+
+Katharine of Aragon with a monkey
+
+The Girl with the Marmot by Jean-Honoré Fragonard
+
+- Young Lady with parrot by Édouard Manet 1866
+
+Antoinette Metayer (1732–88) and her pet dog
+
+The Lady with an Ermine
+
+Sir Henry Raeburn - Boy and Rabbit
+
+Eos, A Favorite Greyhound of Prince Albert
+
+A Neapolitan Woman
+
+Signal, a Grey Arab, with a Groom in the Desert
+
+Eduardo Leon Garrido. An Elegant Lady with her Dog
+
+The Fireplace depicting a Pug, James Tissot
+
+Rosa Bonheur - Portrait of William F. Cody
+
+Hunt
+
+
+
+
+
+
+

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+Coordinates: 42°S 173°E / 42°S 173°E / -42; 173
+
+New Zealand (Māori: Aotearoa [aɔˈtɛaɾɔa]) is an island country in the southwestern Pacific Ocean. It comprises two main landmasses—the North Island (Te Ika-a-Māui) and the South Island (Te Waipounamu)—and around 600 smaller islands, covering a total area of 268,021 square kilometres (103,500 sq mi). New Zealand is about 2,000 kilometres (1,200 mi) east of Australia across the Tasman Sea and 1,000 kilometres (600 mi) south of the islands of New Caledonia, Fiji, and Tonga. The country's varied topography and sharp mountain peaks, including the Southern Alps, owe much to tectonic uplift and volcanic eruptions. New Zealand's capital city is Wellington, and its most populous city is Auckland.
+
+Owing to their remoteness, the islands of New Zealand were the last large habitable lands to be settled by humans. Between about 1280 and 1350, Polynesians began to settle in the islands, and then developed a distinctive Māori culture. In 1642, Dutch explorer Abel Tasman became the first European to sight New Zealand. In 1840, representatives of the United Kingdom and Māori chiefs signed the Treaty of Waitangi, which declared British sovereignty over the islands. In 1841, New Zealand became a colony within the British Empire and in 1907 it became a dominion; it gained full statutory independence in 1947 and the British monarch remained the head of state. Today, the majority of New Zealand's population of 5 million is of European descent; the indigenous Māori are the largest minority, followed by Asians and Pacific Islanders. Reflecting this, New Zealand's culture is mainly derived from Māori and early British settlers, with recent broadening arising from increased immigration. The official languages are English, Māori, and New Zealand Sign Language, with English being very dominant.
+
+A developed country, New Zealand ranks highly in international comparisons of national performance, such as quality of life, education, protection of civil liberties, government transparency, and economic freedom. New Zealand underwent major economic changes during the 1980s, which transformed it from a protectionist to a liberalised free-trade economy. The service sector dominates the national economy, followed by the industrial sector, and agriculture; international tourism is a significant source of revenue. Nationally, legislative authority is vested in an elected, unicameral Parliament, while executive political power is exercised by the Cabinet, led by the prime minister, currently Jacinda Ardern. Queen Elizabeth II is the country's monarch and is represented by a governor-general, currently Dame Patsy Reddy. In addition, New Zealand is organised into 11 regional councils and 67 territorial authorities for local government purposes. The Realm of New Zealand also includes Tokelau (a dependent territory); the Cook Islands and Niue (self-governing states in free association with New Zealand); and the Ross Dependency, which is New Zealand's territorial claim in Antarctica.
+
+New Zealand is a member of the United Nations, Commonwealth of Nations, ANZUS, Organisation for Economic Co-operation and Development, ASEAN Plus Six, Asia-Pacific Economic Cooperation, the Pacific Community and the Pacific Islands Forum.
+
+The first European visitor to New Zealand, Dutch explorer Abel Tasman, named the islands Staten Land, believing they were part of the Staten Landt that Jacob Le Maire had sighted off the southern end of South America.[11][12] Hendrik Brouwer proved that the South American land was a small island in 1643, and Dutch cartographers subsequently renamed Tasman's discovery Nova Zeelandia, from Latin, after the Dutch province of Zeeland.[11][13] This name was later anglicised to "New Zealand".[14][15]
+
+Aotearoa (pronounced [aɔˈtɛaɾɔa] in Māori and /ˌaʊtɛəˈroʊ.ə/ in English; often translated as "land of the long white cloud")[16] is the current Māori name for New Zealand. It is unknown whether Māori had a name for the whole country before the arrival of Europeans, with Aotearoa originally referring to just the North Island.[17] Māori had several traditional names for the two main islands, including Te Ika-a-Māui (the fish of Māui) for the North Island and Te Waipounamu (the waters of greenstone) or Te Waka o Aoraki (the canoe of Aoraki) for the South Island.[18] Early European maps labelled the islands North (North Island), Middle (South Island) and South (Stewart Island / Rakiura).[19] In 1830, mapmakers began to use "North" and "South" on their maps to distinguish the two largest islands and by 1907 this was the accepted norm.[15] The New Zealand Geographic Board discovered in 2009 that the names of the North Island and South Island had never been formalised, and names and alternative names were formalised in 2013. This set the names as North Island or Te Ika-a-Māui, and South Island or Te Waipounamu.[20] For each island, either its English or Māori name can be used, or both can be used together.[20]
+
+New Zealand is one of the last major landmasses settled by humans. Radiocarbon dating, evidence of deforestation[22] and mitochondrial DNA variability within Māori populations[23] suggest that Eastern Polynesians first settled the New Zealand archipelago between 1250 and 1300,[18][24] although newer  archaeological and genetic research points to a date no earlier than about 1280, with at least the main settlement period between about 1320 and 1350,[25][26] consistent with evidence based on genealogical traditions.[27][28] This represented a culmination in a long series of voyages through the Pacific islands.[29] Over the centuries that followed, the Polynesian settlers developed a distinct culture now known as Māori. The population formed different iwi (tribes) and hapū (subtribes) which would sometimes cooperate, sometimes compete and sometimes fight against each other.[30] At some point a group of Māori migrated to Rēkohu, now known as the Chatham Islands, where they developed their distinct Moriori culture.[31][32] The Moriori population was all but wiped out between 1835 and 1862, largely because of Taranaki Māori invasion and enslavement in the 1830s, although European diseases also contributed. In 1862 only 101 survived, and the last known full-blooded Moriori died in 1933.[33]
+
+The first Europeans known to have reached New Zealand were the Dutch explorer Abel Tasman and his crew in 1642.[34] In a hostile encounter, four crew members were killed and at least one Māori was hit by canister shot.[35] Europeans did not revisit New Zealand until 1769 when British explorer James Cook mapped almost the entire coastline.[34] Following Cook, New Zealand was visited by numerous European and North American whaling, sealing and trading ships. They traded European food, metal tools, weapons and other goods for timber, Māori food, artefacts and water.[36] The introduction of the potato and the musket transformed Māori agriculture and warfare. Potatoes provided a reliable food surplus, which enabled longer and more sustained military campaigns.[37] The resulting intertribal Musket Wars encompassed over 600 battles between 1801 and 1840, killing 30,000–40,000 Māori.[38] From the early 19th century, Christian missionaries began to settle New Zealand, eventually converting most of the Māori population.[39] The Māori population declined to around 40% of its pre-contact level during the 19th century; introduced diseases were the major factor.[40]
+
+In 1788 Captain Arthur Phillip assumed the position of Governor of the new British colony of New South Wales which according to his commission included New Zealand.[41] The British Government appointed James Busby as British Resident to New Zealand in 1832 following a petition from northern Māori.[42] In 1835, following an announcement of impending French settlement by Charles de Thierry, the nebulous United Tribes of New Zealand sent a Declaration of Independence to King William IV of the United Kingdom asking for protection.[42] Ongoing unrest, the proposed settlement of New Zealand by the New Zealand Company (which had already sent its first ship of surveyors to buy land from Māori) and the dubious legal standing of the Declaration of Independence prompted the Colonial Office to send Captain William Hobson to claim sovereignty for the United Kingdom and negotiate a treaty with the Māori.[43] The Treaty of Waitangi was first signed in the Bay of Islands on 6 February 1840.[44] In response to the New Zealand Company's attempts to establish an independent settlement in Wellington[45] and French settlers purchasing land in Akaroa,[46] Hobson declared British sovereignty over all of New Zealand on 21 May 1840, even though copies of the Treaty were still circulating throughout the country for Māori to sign.[47] With the signing of the Treaty and declaration of sovereignty the number of immigrants, particularly from the United Kingdom, began to increase.[48]
+
+New Zealand, still part of the colony of New South Wales, became a separate Colony of New Zealand on 1 July 1841.[49] Armed conflict began between the Colonial government and
+Māori in 1843 with the Wairau Affray over land and disagreements over sovereignty. These conflicts, mainly in the North Island, saw thousands of imperial troops and the Royal Navy come to New Zealand and became known as the New Zealand Wars. Following these armed conflicts, large amounts of Māori land was confiscated by the government to meet settler demands.[50]
+
+The colony gained a representative government in 1852 and the first Parliament met in 1854.[51] In 1856 the colony effectively became self-governing, gaining responsibility over all domestic matters other than native policy.[51] (Control over native policy was granted in the mid-1860s.[51]) Following concerns that the South Island might form a separate colony, premier Alfred Domett moved a resolution to transfer the capital from Auckland to a locality near Cook Strait.[52] Wellington was chosen for its central location, with Parliament officially sitting there for the first time in 1865.[53]
+
+In 1891 the Liberal Party came to power as the first organised political party.[54] The Liberal Government, led by Richard Seddon for most of its period in office,[55] passed many important social and economic measures. In 1893 New Zealand was the first nation in the world to grant all women the right to vote[54] and in 1894 pioneered the adoption of compulsory arbitration between employers and unions.[56]
+
+In 1907, at the request of the New Zealand Parliament, King Edward VII proclaimed New Zealand a Dominion within the British Empire,[57] reflecting its self-governing status.[58] In 1947 the country adopted the Statute of Westminster, confirming that the British Parliament could no longer legislate for New Zealand without the consent of New Zealand.[51]
+
+Early in the 20th century, New Zealand was involved in world affairs, fighting in the First and Second World Wars[59] and suffering through the Great Depression.[60] The depression led to the election of the First Labour Government and the establishment of a comprehensive welfare state and a protectionist economy.[61] New Zealand experienced increasing prosperity following the Second World War[62] and Māori began to leave their traditional rural life and move to the cities in search of work.[63] A Māori protest movement developed, which criticised Eurocentrism and worked for greater recognition of Māori culture and of the Treaty of Waitangi.[64] In 1975, a Waitangi Tribunal was set up to investigate alleged breaches of the Treaty, and it was enabled to investigate historic grievances in 1985.[44] The government has negotiated settlements of these grievances with many iwi,[65] although Māori claims to the foreshore and seabed proved controversial in the 2000s.[66][67]
+
+New Zealand is a constitutional monarchy with a parliamentary democracy,[68] although its constitution is not codified.[69] Elizabeth II is the queen of New Zealand[70] and thus the head of state.[71] The queen is represented by the governor-general, whom she appoints on the advice of the prime minister.[72] The governor-general can exercise the Crown's prerogative powers, such as reviewing cases of injustice and making appointments of ministers, ambassadors and other key public officials,[73] and in rare situations, the reserve powers (e.g. the power to dissolve parliament or refuse the royal assent of a bill into law).[74] The powers of the monarch and the governor-general are limited by constitutional constraints and they cannot normally be exercised without the advice of ministers.[74]
+
+The New Zealand Parliament holds legislative power and consists of the queen and the House of Representatives.[75] It also included an upper house, the Legislative Council, until this was abolished in 1950.[75] The supremacy of parliament over the Crown and other government institutions was established in England by the Bill of Rights 1689 and has been ratified as law in New Zealand.[75] The House of Representatives is democratically elected and a government is formed from the party or coalition with the majority of seats. If no majority is formed, a minority government can be formed if support from other parties during confidence and supply votes is assured.[75] The governor-general appoints ministers under advice from the prime minister, who is by convention the parliamentary leader of the governing party or coalition.[76] Cabinet, formed by ministers and led by the prime minister, is the highest policy-making body in government and responsible for deciding significant government actions.[77] Members of Cabinet make major decisions collectively, and are therefore collectively responsible for the consequences of these decisions.[78]
+
+A parliamentary general election must be called no later than three years after the previous election.[79] Almost all general elections between 1853 and 1993 were held under the first-past-the-post voting system.[80] Since the 1996 election, a form of proportional representation called mixed-member proportional (MMP) has been used.[69] Under the MMP system, each person has two votes; one is for a candidate standing in the voter's electorate and the other is for a party. Since the 2014 election, there have been 71 electorates (which include seven Māori electorates in which only Māori can optionally vote),[81] and the remaining 49 of the 120 seats are assigned so that representation in parliament reflects the party vote, with the threshold that a party must win at least one electorate or 5% of the total party vote before it is eligible for a seat.[82]
+
+Elections since the 1930s have been dominated by two political parties, National and Labour.[80] Between March 2005 and August 2006, New Zealand became the first country in the world in which all the highest offices in the land—head of state, governor-general, prime minister, speaker and chief justice—were occupied simultaneously by women.[83] The current prime minister is Jacinda Ardern, who has been in office since 26 October 2017.[84] She is the country's third female prime minister.[85]
+
+New Zealand's judiciary, headed by the chief justice,[86] includes the Supreme Court, Court of Appeal, the High Court, and subordinate courts.[87] Judges and judicial officers are appointed non-politically and under strict rules regarding tenure to help maintain judicial independence.[69] This theoretically allows the judiciary to interpret the law based solely on the legislation enacted by Parliament without other influences on their decisions.[88]
+
+New Zealand is identified as one of the world's most stable and well-governed states.[89] As at 2017[update], the country was ranked fourth in the strength of its democratic institutions,[90] and first in government transparency and lack of corruption.[91] A 2017 Human Rights Report by the U.S. Department of State noted that the government generally respected the rights of individuals, but voiced concerns regarding the social status of the Māori population.[92] New Zealand ranks highly for civic participation in the political process, with 80% voter turnout during recent elections, compared to an OECD average of 68%.[93]
+
+Early colonial New Zealand allowed the British Government to determine external trade and be responsible for foreign policy.[94] The 1923 and 1926 Imperial Conferences decided that New Zealand should be allowed to negotiate its own political treaties and the first commercial treaty was ratified in 1928 with Japan. On 3 September 1939 New Zealand allied itself with Britain and declared war on Germany with Prime Minister Michael Joseph Savage proclaiming, "Where she goes, we go; where she stands, we stand."[95]
+
+In 1951 the United Kingdom became increasingly focused on its European interests,[96] while New Zealand joined Australia and the United States in the ANZUS security treaty.[97] The influence of the United States on New Zealand weakened following protests over the Vietnam War,[98] the refusal of the United States to admonish France after the sinking of the Rainbow Warrior,[99] disagreements over environmental and agricultural trade issues and New Zealand's nuclear-free policy.[100][101] Despite the United States' suspension of ANZUS obligations the treaty remained in effect between New Zealand and Australia, whose foreign policy has followed a similar historical trend.[102] Close political contact is maintained between the two countries, with free trade agreements and travel arrangements that allow citizens to visit, live and work in both countries without restrictions.[103] In 2013[update] there were about 650,000 New Zealand citizens living in Australia, which is equivalent to 15% of the resident population of New Zealand.[104]
+
+New Zealand has a strong presence among the Pacific Island countries. A large proportion of New Zealand's aid goes to these countries and many Pacific people migrate to New Zealand for employment.[105] Permanent migration is regulated under the 1970 Samoan Quota Scheme and the 2002 Pacific Access Category, which allow up to 1,100 Samoan nationals and up to 750 other Pacific Islanders respectively to become permanent New Zealand residents each year. A seasonal workers scheme for temporary migration was introduced in 2007 and in 2009 about 8,000 Pacific Islanders were employed under it.[106] New Zealand is involved in the Pacific Islands Forum, the Pacific Community, Asia-Pacific Economic Cooperation and the Association of Southeast Asian Nations Regional Forum (including the East Asia Summit).[103] New Zealand has been described as an emerging power.[107][108] The country is a member of the United Nations,[109] the Commonwealth of Nations[110] and the Organisation for Economic Co-operation and Development (OECD),[111] and participates in the Five Power Defence Arrangements.[112]
+
+New Zealand's military services—the Defence Force—comprise the New Zealand Army, the Royal New Zealand Air Force and the Royal New Zealand Navy.[113] New Zealand's national defence needs are modest, since a direct attack is unlikely.[114] However, its military has had a global presence. The country fought in both world wars, with notable campaigns in Gallipoli, Crete,[115] El Alamein[116] and Cassino.[117] The Gallipoli campaign played an important part in fostering New Zealand's national identity[118][119] and strengthened the ANZAC tradition it shares with Australia.[120]
+
+In addition to Vietnam and the two world wars, New Zealand fought in the Second Boer War,[121] the Korean War,[122] the Malayan Emergency,[123] the Gulf War and the Afghanistan War. It has contributed forces to several regional and global peacekeeping missions, such as those in Cyprus, Somalia, Bosnia and Herzegovina, the Sinai, Angola, Cambodia, the Iran–Iraq border, Bougainville, East Timor, and the Solomon Islands.[124]
+
+The early European settlers divided New Zealand into provinces, which had a degree of autonomy.[125] Because of financial pressures and the desire to consolidate railways, education, land sales and other policies, government was centralised and the provinces were abolished in 1876.[126] The provinces are remembered in regional public holidays[127] and sporting rivalries.[128]
+
+Since 1876, various councils have administered local areas under legislation determined by the central government.[125][129] In 1989, the government reorganised local government into the current two-tier structure of regional councils and territorial authorities.[130] The 249 municipalities[130] that existed in 1975 have now been consolidated into 67 territorial authorities and 11 regional councils.[131] The regional councils' role is to regulate "the natural environment with particular emphasis on resource management",[130] while territorial authorities are responsible for sewage, water, local roads, building consents and other local matters.[132][133] Five of the territorial councils are unitary authorities and also act as regional councils.[133] The territorial authorities consist of 13 city councils, 53 district councils, and the Chatham Islands Council. While officially the Chatham Islands Council is not a unitary authority, it undertakes many functions of a regional council.[134]
+
+The Realm of New Zealand, one of 16 Commonwealth realms,[135] is the entire area over which the queen of New Zealand is sovereign, and comprises New Zealand, Tokelau, the Ross Dependency, the Cook Islands and Niue.[68] The Cook Islands and Niue are self-governing states in free association with New Zealand.[136][137] The New Zealand Parliament cannot pass legislation for these countries, but with their consent can act on behalf of them in foreign affairs and defence. Tokelau is classified as a non-self-governing territory, but is administered by a council of three elders (one from each Tokelauan atoll).[138] The Ross Dependency is New Zealand's territorial claim in Antarctica, where it operates the Scott Base research facility.[139] New Zealand nationality law treats all parts of the realm equally, so most people born in New Zealand, the Cook Islands, Niue, Tokelau and the Ross Dependency are New Zealand citizens.[140][n 7]
+
+New Zealand is located near the centre of the water hemisphere and is made up of two main islands and a number of smaller islands. The two main islands (the North Island, or Te Ika-a-Māui, and the South Island, or Te Waipounamu) are separated by Cook Strait, 22 kilometres (14 mi) wide at its narrowest point.[142] Besides the North and South Islands, the five largest inhabited islands are Stewart Island (across the Foveaux Strait), Chatham Island, Great Barrier Island (in the Hauraki Gulf),[143] D'Urville Island (in the Marlborough Sounds)[144] and Waiheke Island (about 22 km (14 mi) from central Auckland).[145]
+
+New Zealand is long and narrow—over 1,600 kilometres (990 mi) along its north-north-east axis with a maximum width of 400 kilometres (250 mi)[146]—with about 15,000 km (9,300 mi) of coastline[147] and a total land area of 268,000 square kilometres (103,500 sq mi).[148] Because of its far-flung outlying islands and long coastline, the country has extensive marine resources. Its exclusive economic zone is one of the largest in the world, covering more than 15 times its land area.[149]
+
+The South Island is the largest landmass of New Zealand. It is divided along its length by the Southern Alps.[150] There are 18 peaks over 3,000 metres (9,800 ft), the highest of which is Aoraki / Mount Cook at 3,724 metres (12,218 ft).[151] Fiordland's steep mountains and deep fiords record the extensive ice age glaciation of this southwestern corner of the South Island.[152] The North Island is less mountainous but is marked by volcanism.[153] The highly active Taupo Volcanic Zone has formed a large volcanic plateau, punctuated by the North Island's highest mountain, Mount Ruapehu (2,797 metres (9,177 ft)). The plateau also hosts the country's largest lake, Lake Taupo,[154] nestled in the caldera of one of the world's most active supervolcanoes.[155]
+
+The country owes its varied topography, and perhaps even its emergence above the waves, to the dynamic boundary it straddles between the Pacific and Indo-Australian Plates.[156] New Zealand is part of Zealandia, a microcontinent nearly half the size of Australia that gradually submerged after breaking away from the Gondwanan supercontinent.[157][158] About 25 million years ago, a shift in plate tectonic movements began to contort and crumple the region. This is now most evident in the Southern Alps, formed by compression of the crust beside the Alpine Fault. Elsewhere the plate boundary involves the subduction of one plate under the other, producing the Puysegur Trench to the south, the Hikurangi Trench east of the North Island, and the Kermadec and Tonga Trenches[159] further north.[156]
+
+New Zealand is part of a region known as Australasia, together with Australia.[160] It also forms the southwestern extremity of the geographic and ethnographic region called Polynesia.[161] The term Oceania is often used to denote the wider region encompassing the Australian continent, New Zealand and various islands in the Pacific Ocean that are not included in the seven-continent model.[162]
+
+Rural scene near Queenstown
+
+The Emerald Lakes, Mt Tongariro
+
+Lake Gunn
+
+Pencarrow Head, Wellington
+
+New Zealand's climate is predominantly temperate maritime (Köppen: Cfb), with mean annual temperatures ranging from 10 °C (50 °F) in the south to 16 °C (61 °F) in the north.[163] Historical maxima and minima are 42.4 °C (108.32 °F) in Rangiora, Canterbury and −25.6 °C (−14.08 °F) in Ranfurly, Otago.[164] Conditions vary sharply across regions from extremely wet on the West Coast of the South Island to almost semi-arid in Central Otago and the Mackenzie Basin of inland Canterbury, and subtropical in Northland.[165][166] Of the seven largest cities, Christchurch is the driest, receiving on average only 640 millimetres (25 in) of rain per year and Wellington the wettest, receiving almost twice that amount.[167] Auckland, Wellington and Christchurch all receive a yearly average of more than 2,000 hours of sunshine. The southern and southwestern parts of the South Island have a cooler and cloudier climate, with around 1,400–1,600 hours; the northern and northeastern parts of the South Island are the sunniest areas of the country and receive about 2,400–2,500 hours.[168] The general snow season is early June until early October, though cold snaps can occur outside this season.[169] Snowfall is common in the eastern and southern parts of the South Island and mountain areas across the country.[163]
+
+The table below lists climate normals for the warmest and coldest months in New Zealand's six largest cities. North Island cities are generally warmest in February. South Island cities are warmest in January.
+
+New Zealand's geographic isolation for 80 million years[171] and island biogeography has influenced evolution of the country's species of animals, fungi and plants. Physical isolation has caused biological isolation, resulting in a dynamic evolutionary ecology with examples of very distinctive plants and animals as well as populations of widespread species.[172][173] About 82% of New Zealand's indigenous vascular plants are endemic, covering 1,944 species across 65 genera.[174][175] The number of fungi recorded from New Zealand, including lichen-forming species, is not known, nor is the proportion of those fungi which are endemic, but one estimate suggests there are about 2,300 species of lichen-forming fungi in New Zealand[174] and 40% of these are endemic.[176] The two main types of forest are those dominated by broadleaf trees with emergent podocarps, or by southern beech in cooler climates.[177] The remaining vegetation types consist of grasslands, the majority of which are tussock.[178]
+
+Before the arrival of humans, an estimated 80% of the land was covered in forest, with only high alpine, wet, infertile and volcanic areas without trees.[179] Massive deforestation occurred after humans arrived, with around half the forest cover lost to fire after Polynesian settlement.[180] Much of the remaining forest fell after European settlement, being logged or cleared to make room for pastoral farming, leaving forest occupying only 23% of the land.[181]
+
+The forests were dominated by birds, and the lack of mammalian predators led to some like the kiwi, kakapo, weka and takahē evolving flightlessness.[182] The arrival of humans, associated changes to habitat, and the introduction of rats, ferrets and other mammals led to the extinction of many bird species, including large birds like the moa and Haast's eagle.[183][184]
+
+Other indigenous animals are represented by reptiles (tuatara, skinks and geckos), frogs,[185] spiders,[186] insects (wētā)[187] and snails.[188] Some, such as the tuatara, are so unique that they have been called living fossils.[189] Three species of bats (one since extinct) were the only sign of native land mammals in New Zealand until the 2006 discovery of bones from a unique, mouse-sized land mammal at least 16 million years old.[190][191] Marine mammals however are abundant, with almost half the world's cetaceans (whales, dolphins, and porpoises) and large numbers of fur seals reported in New Zealand waters.[192] Many seabirds breed in New Zealand, a third of them unique to the country.[193] More penguin species are found in New Zealand than in any other country.[194]
+
+Since human arrival, almost half of the country's vertebrate species have become extinct, including at least fifty-one birds, three frogs, three lizards, one freshwater fish, and one bat. Others are endangered or have had their range severely reduced.[183] However, New Zealand conservationists have pioneered several methods to help threatened wildlife recover, including island sanctuaries, pest control, wildlife translocation, fostering and ecological restoration of islands and other protected areas.[195][196][197][198]
+
+New Zealand has an advanced market economy,[199] ranked 16th in the 2018[update] Human Development Index[8] and third in the 2018[update] Index of Economic Freedom.[200] It is a high-income economy with a nominal gross domestic product (GDP) per capita of US$36,254.[6] The currency is the New Zealand dollar, informally known as the "Kiwi dollar"; it also circulates in the Cook Islands (see Cook Islands dollar), Niue, Tokelau, and the Pitcairn Islands.[201]
+
+Historically, extractive industries have contributed strongly to New Zealand's economy, focussing at different times on sealing, whaling, flax, gold, kauri gum, and native timber.[202] The first shipment of refrigerated meat on the Dunedin in 1882 led to the establishment of meat and dairy exports to Britain, a trade which provided the basis for strong economic growth in New Zealand.[203] High demand for agricultural products from the United Kingdom and the United States helped New Zealanders achieve higher living standards than both Australia and Western Europe in the 1950s and 1960s.[204] In 1973, New Zealand's export market was reduced when the United Kingdom joined the European Economic Community[205] and other compounding factors, such as the 1973 oil and 1979 energy crises, led to a severe economic depression.[206] Living standards in New Zealand fell behind those of Australia and Western Europe, and by 1982 New Zealand had the lowest per-capita income of all the developed nations surveyed by the World Bank.[207] In the mid-1980s New Zealand deregulated its agricultural sector by phasing out subsidies over a three-year period.[208][209] Since 1984, successive governments engaged in major macroeconomic restructuring (known first as Rogernomics and then Ruthanasia), rapidly transforming New Zealand from a protected and highly regulated economy to a liberalised free-trade economy.[210][211]
+
+Unemployment peaked above 10% in 1991 and 1992,[213] following the 1987 share market crash, but eventually fell to a record low (since 1986) of 3.7% in 2007 (ranking third from twenty-seven comparable OECD nations).[213] However, the global financial crisis that followed had a major impact on New Zealand, with the GDP shrinking for five consecutive quarters, the longest recession in over thirty years,[214][215] and unemployment rising back to 7% in late 2009.[216] Unemployment rates for different age groups follow similar trends, but are consistently higher among youth. In the December 2014 quarter, the general unemployment rate was around 5.8%, while the unemployment rate for youth aged 15 to 21 was 15.6%.[213] New Zealand has experienced a series of "brain drains" since the 1970s[217] that still continue today.[218] Nearly one quarter of highly skilled workers live overseas, mostly in Australia and Britain, which is the largest proportion from any developed nation.[219] In recent decades, however, a "brain gain" has brought in educated professionals from Europe and less developed countries.[220][221] Today New Zealand's economy benefits from a high level of innovation.[222]
+
+New Zealand is heavily dependent on international trade,[223] particularly in agricultural products.[224] Exports account for 24% of its output,[147] making New Zealand vulnerable to international commodity prices and global economic slowdowns. Food products made up 55% of the value of all the country's exports in 2014; wood was the second largest earner (7%).[225] New Zealand's main trading partners, as at June 2018[update], are China (NZ$27.8b), Australia ($26.2b), the European Union ($22.9b), the United States ($17.6b), and Japan ($8.4b).[226] On 7 April 2008, New Zealand and China signed the New Zealand–China Free Trade Agreement, the first such agreement China has signed with a developed country.[227] The service sector is the largest sector in the economy, followed by manufacturing and construction and then farming and raw material extraction.[147] Tourism plays a significant role in the economy, contributing $12.9 billion (or 5.6%) to New Zealand's total GDP and supporting 7.5% of the total workforce in 2016.[228] International visitor arrivals are expected to increase at a rate of 5.4% annually up to 2022.[228]
+
+Wool was New Zealand's major agricultural export during the late 19th century.[202] Even as late as the 1960s it made up over a third of all export revenues,[202] but since then its price has steadily dropped relative to other commodities[229] and wool is no longer profitable for many farmers.[230] In contrast dairy farming increased, with the number of dairy cows doubling between 1990 and 2007,[231] to become New Zealand's largest export earner.[232] In the year to June 2018, dairy products accounted for 17.7% ($14.1 billion) of total exports,[226] and the country's largest company, Fonterra, controls almost one-third of the international dairy trade.[233] Other exports in 2017-18 were meat (8.8%), wood and wood products (6.2%), fruit (3.6%), machinery (2.2%) and wine (2.1%).[226] New Zealand's wine industry has followed a similar trend to dairy, the number of vineyards doubling over the same period,[234] overtaking wool exports for the first time in 2007.[235][236]
+
+In 2015, renewable energy generated 40.1% of New Zealand's gross energy supply.[237]  The majority of the country's electricity supply is generated from hydroelectric power, with major schemes on the Waikato, Waitaki and Clutha rivers, as well as at Manapouri. Geothermal power is also a significant generator of electricity, with several large stations located across the Taupo Volcanic Zone in the North Island. The five main companies in the generation and retail market are Contact Energy, Genesis Energy, Mercury Energy, Meridian Energy, and TrustPower. State-owned Transpower operates the high-voltage transmission grids in the North and South Islands, as well as the Inter-Island HVDC link connecting the two together.[237]
+
+The provision of water supply and sanitation is generally of good quality. Regional authorities provide water abstraction, treatment and distribution infrastructure to most developed areas.[238][239]
+
+New Zealand's transport network comprises 94,000 kilometres (58,410 mi) of roads, including 199 kilometres (124 mi) of motorways,[240] and 4,128 kilometres (2,565 mi) of railway lines.[147] Most major cities and towns are linked by bus services, although the private car is the predominant mode of transport.[241] The railways were privatised in 1993, but were re-nationalised by the government in stages between 2004 and 2008. The state-owned enterprise KiwiRail now operates the railways, with the exception of commuter services in Auckland and Wellington which are operated by Transdev[242] and Metlink,[243] respectively. Railways run the length of the country, although most lines now carry freight rather than passengers.[244] The road and rail networks in the two main islands are linked by roll-on/roll-off ferries between Wellington and Picton, operated by Interislander (part of KiwiRail) and Bluebridge. Most international visitors arrive via air[245] and New Zealand has six international airports, but currently[update] only the Auckland and Christchurch airports connect directly with countries other than Australia or Fiji.[246]
+
+The New Zealand Post Office had a monopoly over telecommunications in New Zealand until 1987 when Telecom New Zealand was formed, initially as a state-owned enterprise and then privatised in 1990.[247] Chorus, which was split from Telecom (now Spark) in 2011,[248] still owns the majority of the telecommunications infrastructure, but competition from other providers has increased.[247] A large-scale rollout of gigabit-capable fibre to the premises, branded as Ultra-Fast Broadband, began in 2009 with a target of being available to 87% of the population by 2022.[249] As of 2017[update], the United Nations International Telecommunication Union ranks New Zealand 13th in the development of information and communications infrastructure.[250]
+
+Early indigenous contribution to science in New Zealand was by Māori tohunga accumulating knowledge of agricultural practice and the effects of herbal remedies in the treatment of illness and disease. Cook's voyages in the 1700s and Darwin's in 1835 had important scientific botanical and zoological objectives.[251] The establishment of universities in the 19th century fostered scientific discoveries by notable New Zealanders including Ernest Rutherford for splitting the atom, William Pickering for rocket science, Maurice Wilkins for helping discover DNA, Beatrice Tinsley for galaxy formation, and Alan MacDiarmid for conducting polymers.[252]
+
+Crown Research Institutes (CRIs) were formed in 1992 from existing government-owned research organisations. Their role is to research and develop new science, knowledge, products and services across the economic, environmental, social and cultural spectrum for the benefit of New Zealand.[253] The total gross expenditure on research and development (R&D) as a proportion of GDP rose to 1.37% in 2018, up from 1.23% in 2015. New Zealand ranks 21st in the OECD for its gross R&D spending as a percentage of GDP.[254]
+
+The 2018 New Zealand census enumerated a resident population of 4,699,755, an increase of 10.8% over the 2013 figure.[3] As of July 2020, the total population has risen to an estimated 5,010,290.[n 8][5] In May 2020 Statistics New Zealand reported that New Zealand's population had climbed above 5 million people in March 2020.[256]
+
+New Zealand is a predominantly urban country, with 83.6% of the population living in urban areas, and 52.3% of the population living in the seven cities with populations exceeding 100,000.[257] Auckland, with over 1 million residents, is by far the largest city.[257] New Zealand cities generally rank highly on international livability measures. For instance, in 2016 Auckland was ranked the world's third most liveable city and Wellington the twelfth by the Mercer Quality of Living Survey.[258]
+
+Life expectancy for New Zealanders in 2012 was 84 years for females, and 80.2 years for males.[259] Life expectancy at birth is forecast to increase from 80 years to 85 years in 2050 and infant mortality is expected to decline.[260] New Zealand's fertility rate of 2.1 is relatively high for a developed country, and natural births account for a significant proportion of population growth. Consequently, the country has a young population compared to most industrialised nations, with 20% of New Zealanders being 14 years old or younger.[147] In 2018 the median age of the New Zealand population was 38.1 years.[261] By 2050 the median age is projected to rise to 43 years and the percentage of people 60 years of age and older to rise from 18% to 29%.[260] In 2008 the leading cause of premature death was cancer, at 29.8%, followed by ischaemic heart disease, 19.7%, and then cerebrovascular disease, 9.2%.[262] As of 2016[update], total expenditure on health care (including private sector spending) is 9.2% of GDP.[263]
+
+
+
+In the 2018 census, 71.8% of New Zealand residents identified ethnically as European, and 16.5% as Māori. Other major ethnic groups include Asian (15.3%) and Pacific peoples (9.0%), two-thirds of whom live in the Auckland Region.[n 3][3] The population has become more diverse in recent decades: in 1961, the census reported that the population of New Zealand was 92% European and 7% Māori, with Asian and Pacific minorities sharing the remaining 1%.[264]
+
+While the demonym for a New Zealand citizen is New Zealander, the informal "Kiwi" is commonly used both internationally[265] and by locals.[266] The Māori loanword Pākehā has been used to refer to New Zealanders of European descent, although some reject this name. The word Pākehā today is increasingly used to refer to all non-Polynesian New Zealanders.[267]
+
+The Māori were the first people to reach New Zealand, followed by the early European settlers. Following colonisation, immigrants were predominantly from Britain, Ireland and Australia because of restrictive policies similar to the White Australia policy.[268] There was also significant Dutch, Dalmatian,[269] German, and Italian immigration, together with indirect European immigration through Australia, North America, South America and South Africa.[270][271] Net migration increased after the Second World War; in the 1970s and 1980s policies were relaxed and immigration from Asia was promoted.[271][272] In 2009–10, an annual target of 45,000–50,000 permanent residence approvals was set by the New Zealand Immigration Service—more than one new migrant for every 100 New Zealand residents.[273] In the 2018 census, 27.4% of people counted were not born in New Zealand, up from 25.2% in the 2013 census. Over half (52.4%) of New Zealand's overseas-born population lives in the Auckland Region.[274] The United Kingdom remains the largest source of New Zealand's immigrant population, with around a quarter of all overseas-born New Zealanders born there; other major sources of New Zealand's overseas-born population are China, India, Australia, South Africa, Fiji and Samoa.[275] The number of fee-paying international students increased sharply in the late 1990s, with more than 20,000 studying in public tertiary institutions in 2002.[276]
+
+English is the predominant language in New Zealand, spoken by 95.4% of the population.[3] New Zealand English is similar to Australian English and many speakers from the Northern Hemisphere are unable to tell the accents apart.[278] The most prominent differences between the New Zealand English dialect and other English dialects are the shifts in the short front vowels: the short-"i" sound (as in "kit") has centralised towards the schwa sound (the "a" in "comma" and "about"); the short-"e" sound (as in "dress") has moved towards the short-"i" sound; and the short-"a" sound (as in "trap") has moved to the short-"e" sound.[279]
+
+After the Second World War, Māori were discouraged from speaking their own language (te reo Māori) in schools and workplaces and it existed as a community language only in a few remote areas.[280] It has recently undergone a process of revitalisation,[281] being declared one of New Zealand's official languages in 1987,[282] and is spoken by 4.0% of the population.[3][n 9] There are now Māori language immersion schools and two television channels that broadcast predominantly in Māori.[284] Many places have both their Māori and English names officially recognised.[285]
+
+As recorded in the 2018 census,[3] Samoan is the most widely spoken non-official language (2.2%), followed by "Northern Chinese" (including Mandarin, 2.0%), Hindi (1.5%), and French (1.2%). 22,986 people (0.5%) reported the ability to use New Zealand Sign Language, which became one of New Zealand's official languages in 2006.[286]
+
+Christianity is the predominant religion in New Zealand, although its society is among the most secular in the world.[288][289] In the 2018 census, 44.7% of respondents identified with one or more religions, including 37.0% identifying as Christians. Another 48.5% indicated that they had no religion.[n 10][3] Of those who affiliate with a particular Christian denomination, the main responses are Anglicanism (6.7%), Roman Catholicism (6.3%), and Presbyterianism (4.7%).[3] The Māori-based Ringatū and Rātana religions (1.2%) are also Christian in origin.[3][287] Immigration and demographic change in recent decades has contributed to the growth of minority religions, such as Hinduism (2.6%), Islam (1.3%), Buddhism (1.1%), and Sikhism (0.9%).[3] The Auckland Region exhibited the greatest religious diversity.[290]
+
+Primary and secondary schooling is compulsory for children aged 6 to 16, with the majority attending from the age of 5.[291] There are 13 school years and attending state (public) schools is free to New Zealand citizens and permanent residents from a person's 5th birthday to the end of the calendar year following their 19th birthday.[292] New Zealand has an adult literacy rate of 99%,[147] and over half of the population aged 15 to 29 hold a tertiary qualification.[291] There are five types of government-owned tertiary institutions: universities, colleges of education, polytechnics, specialist colleges, and wānanga,[293] in addition to private training establishments.[294] In the adult population 14.2% have a bachelor's degree or higher, 30.4% have some form of secondary qualification as their highest qualification and 22.4% have no formal qualification.[295] The OECD's Programme for International Student Assessment ranks New Zealand's education system as the seventh best in the world, with students performing exceptionally well in reading, mathematics and science.[296]
+
+Early Māori adapted the tropically based east Polynesian culture in line with the challenges associated with a larger and more diverse environment, eventually developing their own distinctive culture. Social organisation was largely communal with families (whānau), subtribes (hapū) and tribes (iwi) ruled by a chief (rangatira), whose position was subject to the community's approval.[297] The British and Irish immigrants brought aspects of their own culture to New Zealand and also influenced Māori culture,[298][299] particularly with the introduction of Christianity.[300] However, Māori still regard their allegiance to tribal groups as a vital part of their identity, and Māori kinship roles resemble those of other Polynesian peoples.[301] More recently American, Australian, Asian and other European cultures have exerted influence on New Zealand. Non-Māori Polynesian cultures are also apparent, with Pasifika, the world's largest Polynesian festival, now an annual event in Auckland.[302]
+
+The largely rural life in early New Zealand led to the image of New Zealanders being rugged, industrious problem solvers.[303] Modesty was expected and enforced through the "tall poppy syndrome", where high achievers received harsh criticism.[304] At the time New Zealand was not known as an intellectual country.[305] From the early 20th century until the late 1960s, Māori culture was suppressed by the attempted assimilation of Māori into British New Zealanders.[280] In the 1960s, as tertiary education became more available and cities expanded[306] urban culture began to dominate.[307] However, rural imagery and themes are common in New Zealand's art, literature and media.[308]
+
+New Zealand's national symbols are influenced by natural, historical, and Māori sources. The silver fern is an emblem appearing on army insignia and sporting team uniforms.[309] Certain items of popular culture thought to be unique to New Zealand are called "Kiwiana".[309]
+
+As part of the resurgence of Māori culture, the traditional crafts of carving and weaving are now more widely practised and Māori artists are increasing in number and influence.[310] Most Māori carvings feature human figures, generally with three fingers and either a natural-looking, detailed head or a grotesque head.[311] Surface patterns consisting of spirals, ridges, notches and fish scales decorate most carvings.[312] The pre-eminent Māori architecture consisted of carved meeting houses (wharenui) decorated with symbolic carvings and illustrations. These buildings were originally designed to be constantly rebuilt, changing and adapting to different whims or needs.[313]
+
+Māori decorated the white wood of buildings, canoes and cenotaphs using red (a mixture of red ochre and shark fat) and black (made from soot) paint and painted pictures of birds, reptiles and other designs on cave walls.[314] Māori tattoos (moko) consisting of coloured soot mixed with gum were cut into the flesh with a bone chisel.[315] Since European arrival paintings and photographs have been dominated by landscapes, originally not as works of art but as factual portrayals of New Zealand.[316] Portraits of Māori were also common, with early painters often portraying them as "noble savages", exotic beauties or friendly natives.[316] The country's isolation delayed the influence of European artistic trends allowing local artists to develop their own distinctive style of regionalism.[317] During the 1960s and 1970s many artists combined traditional Māori and Western techniques, creating unique art forms.[318] New Zealand art and craft has gradually achieved an international audience, with exhibitions in the Venice Biennale in 2001 and the "Paradise Now" exhibition in New York in 2004.[310][319]
+
+Māori cloaks are made of fine flax fibre and patterned with black, red and white triangles, diamonds and other geometric shapes.[320] Greenstone was fashioned into earrings and necklaces, with the most well-known design being the hei-tiki, a distorted human figure sitting cross-legged with its head tilted to the side.[321] Europeans brought English fashion etiquette to New Zealand, and until the 1950s most people dressed up for social occasions.[322] Standards have since relaxed and New Zealand fashion has received a reputation for being casual, practical and lacklustre.[323][324] However, the local fashion industry has grown significantly since 2000, doubling exports and increasing from a handful to about 50 established labels, with some labels gaining international recognition.[324]
+
+Māori quickly adopted writing as a means of sharing ideas, and many of their oral stories and poems were converted to the written form.[325] Most early English literature was obtained from Britain and it was not until the 1950s when local publishing outlets increased that New Zealand literature started to become widely known.[326] Although still largely influenced by global trends (modernism) and events (the Great Depression), writers in the 1930s began to develop stories increasingly focused on their experiences in New Zealand. During this period literature changed from a journalistic activity to a more academic pursuit.[327] Participation in the world wars gave some New Zealand writers a new perspective on New Zealand culture and with the post-war expansion of universities local literature flourished.[328] Dunedin is a UNESCO City of Literature.[329]
+
+New Zealand music has been influenced by blues, jazz, country, rock and roll and hip hop, with many of these genres given a unique New Zealand interpretation.[330] Māori developed traditional chants and songs from their ancient Southeast Asian origins, and after centuries of isolation created a unique "monotonous" and "doleful" sound.[331] Flutes and trumpets were used as musical instruments[332] or as signalling devices during war or special occasions.[333] Early settlers brought over their ethnic music, with brass bands and choral music being popular, and musicians began touring New Zealand in the 1860s.[334][335] Pipe bands became widespread during the early 20th century.[336] The New Zealand recording industry began to develop from 1940 onwards and many New Zealand musicians have obtained success in Britain and the United States.[330] Some artists release Māori language songs and the Māori tradition-based art of kapa haka (song and dance) has made a resurgence.[337] The New Zealand Music Awards are held annually by Recorded Music NZ; the awards were first held in 1965 by Reckitt & Colman as the Loxene Golden Disc awards.[338] Recorded Music NZ also publishes the country's official weekly record charts.[339]
+
+Public radio was introduced in New Zealand in 1922.[341] A state-owned television service began in 1960.[342] Deregulation in the 1980s saw a sudden increase in the numbers of radio and television stations.[343] New Zealand television primarily broadcasts American and British programming, along with many Australian and local shows.[344] The number of New Zealand films significantly increased during the 1970s. In 1978 the New Zealand Film Commission started assisting local film-makers and many films attained a world audience, some receiving international acknowledgement.[343] The highest-grossing New Zealand films are Hunt for the Wilderpeople, Boy, The World's Fastest Indian, Whale Rider, Once Were Warriors and The Piano.[345] The country's diverse scenery and compact size, plus government incentives,[346] have encouraged some producers to shoot big-budget productions in New Zealand, including The Lord of the Rings and The Hobbit film trilogies, Avatar, The Chronicles of Narnia, King Kong, Wolverine and The Last Samurai.[347] The New Zealand media industry is dominated by a small number of companies, most of which are foreign-owned, although the state retains ownership of some television and radio stations.[348] Since 1994, Freedom House has consistently ranked New Zealand's press freedom in the top twenty, with the 19th freest media in 2015[update].[349]
+
+Most of the major sporting codes played in New Zealand have British origins.[350] Rugby union is considered the national sport[351] and attracts the most spectators.[352] Golf, netball, tennis and cricket have the highest rates of adult participation, while netball, rugby union and football (soccer) are particularly popular among young people.[352][353] Around 54% of New Zealand adolescents participate in sports for their school.[353] Victorious rugby tours to Australia and the United Kingdom in the late 1880s and the early 1900s played an early role in instilling a national identity.[354] Horseracing was also a popular spectator sport and became part of the "Rugby, Racing and Beer" culture during the 1960s.[355] Māori participation in European sports was particularly evident in rugby and the country's team performs a haka, a traditional Māori challenge, before international matches.[356] New Zealand is known for its extreme sports, adventure tourism[357] and strong mountaineering tradition, as seen in the success of notable New Zealander Sir Edmund Hillary.[358][359] Other outdoor pursuits such as cycling, fishing, swimming, running, tramping, canoeing, hunting, snowsports, surfing and sailing are also popular.[360] New Zealand has seen regular sailing success in the America's Cup regatta since 1995.[361] The Polynesian sport of waka ama racing has experienced a resurgence of interest in New Zealand since the 1980s.[362]
+
+New Zealand has competitive international teams in rugby union, rugby league, netball, cricket, softball, and sailing. New Zealand participated at the Summer Olympics in 1908 and 1912 as a joint team with Australia, before first participating on its own in 1920.[363] The country has ranked highly on a medals-to-population ratio at recent Games.[364][365] The "All Blacks", the national rugby union team, are the most successful in the history of international rugby[366] and have won the World Cup three times.[367]
+
+The national cuisine has been described as Pacific Rim, incorporating the native Māori cuisine and diverse culinary traditions introduced by settlers and immigrants from Europe, Polynesia and Asia.[368] New Zealand yields produce from land and sea—most crops and livestock, such as maize, potatoes and pigs, were gradually introduced by the early European settlers.[369] Distinctive ingredients or dishes include lamb, salmon, kōura (crayfish),[370] dredge oysters, whitebait, pāua (abalone), mussels, scallops, pipis and tuatua (both are types of New Zealand shellfish),[371] kūmara (sweet potato), kiwifruit, tamarillo and pavlova (considered a national dish).[372][368] A hāngi is a traditional Māori method of cooking food using heated rocks buried in a pit oven. After European colonisation, Māori began cooking with pots and ovens and the hāngi was used less frequently, although it is still used for formal occasions such as tangihanga.[373]
+
+Click on a coloured area to see an article about English in that country or region

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+Coordinates: 42°S 173°E / 42°S 173°E / -42; 173
+
+New Zealand (Māori: Aotearoa [aɔˈtɛaɾɔa]) is an island country in the southwestern Pacific Ocean. It comprises two main landmasses—the North Island (Te Ika-a-Māui) and the South Island (Te Waipounamu)—and around 600 smaller islands, covering a total area of 268,021 square kilometres (103,500 sq mi). New Zealand is about 2,000 kilometres (1,200 mi) east of Australia across the Tasman Sea and 1,000 kilometres (600 mi) south of the islands of New Caledonia, Fiji, and Tonga. The country's varied topography and sharp mountain peaks, including the Southern Alps, owe much to tectonic uplift and volcanic eruptions. New Zealand's capital city is Wellington, and its most populous city is Auckland.
+
+Owing to their remoteness, the islands of New Zealand were the last large habitable lands to be settled by humans. Between about 1280 and 1350, Polynesians began to settle in the islands, and then developed a distinctive Māori culture. In 1642, Dutch explorer Abel Tasman became the first European to sight New Zealand. In 1840, representatives of the United Kingdom and Māori chiefs signed the Treaty of Waitangi, which declared British sovereignty over the islands. In 1841, New Zealand became a colony within the British Empire and in 1907 it became a dominion; it gained full statutory independence in 1947 and the British monarch remained the head of state. Today, the majority of New Zealand's population of 5 million is of European descent; the indigenous Māori are the largest minority, followed by Asians and Pacific Islanders. Reflecting this, New Zealand's culture is mainly derived from Māori and early British settlers, with recent broadening arising from increased immigration. The official languages are English, Māori, and New Zealand Sign Language, with English being very dominant.
+
+A developed country, New Zealand ranks highly in international comparisons of national performance, such as quality of life, education, protection of civil liberties, government transparency, and economic freedom. New Zealand underwent major economic changes during the 1980s, which transformed it from a protectionist to a liberalised free-trade economy. The service sector dominates the national economy, followed by the industrial sector, and agriculture; international tourism is a significant source of revenue. Nationally, legislative authority is vested in an elected, unicameral Parliament, while executive political power is exercised by the Cabinet, led by the prime minister, currently Jacinda Ardern. Queen Elizabeth II is the country's monarch and is represented by a governor-general, currently Dame Patsy Reddy. In addition, New Zealand is organised into 11 regional councils and 67 territorial authorities for local government purposes. The Realm of New Zealand also includes Tokelau (a dependent territory); the Cook Islands and Niue (self-governing states in free association with New Zealand); and the Ross Dependency, which is New Zealand's territorial claim in Antarctica.
+
+New Zealand is a member of the United Nations, Commonwealth of Nations, ANZUS, Organisation for Economic Co-operation and Development, ASEAN Plus Six, Asia-Pacific Economic Cooperation, the Pacific Community and the Pacific Islands Forum.
+
+The first European visitor to New Zealand, Dutch explorer Abel Tasman, named the islands Staten Land, believing they were part of the Staten Landt that Jacob Le Maire had sighted off the southern end of South America.[11][12] Hendrik Brouwer proved that the South American land was a small island in 1643, and Dutch cartographers subsequently renamed Tasman's discovery Nova Zeelandia, from Latin, after the Dutch province of Zeeland.[11][13] This name was later anglicised to "New Zealand".[14][15]
+
+Aotearoa (pronounced [aɔˈtɛaɾɔa] in Māori and /ˌaʊtɛəˈroʊ.ə/ in English; often translated as "land of the long white cloud")[16] is the current Māori name for New Zealand. It is unknown whether Māori had a name for the whole country before the arrival of Europeans, with Aotearoa originally referring to just the North Island.[17] Māori had several traditional names for the two main islands, including Te Ika-a-Māui (the fish of Māui) for the North Island and Te Waipounamu (the waters of greenstone) or Te Waka o Aoraki (the canoe of Aoraki) for the South Island.[18] Early European maps labelled the islands North (North Island), Middle (South Island) and South (Stewart Island / Rakiura).[19] In 1830, mapmakers began to use "North" and "South" on their maps to distinguish the two largest islands and by 1907 this was the accepted norm.[15] The New Zealand Geographic Board discovered in 2009 that the names of the North Island and South Island had never been formalised, and names and alternative names were formalised in 2013. This set the names as North Island or Te Ika-a-Māui, and South Island or Te Waipounamu.[20] For each island, either its English or Māori name can be used, or both can be used together.[20]
+
+New Zealand is one of the last major landmasses settled by humans. Radiocarbon dating, evidence of deforestation[22] and mitochondrial DNA variability within Māori populations[23] suggest that Eastern Polynesians first settled the New Zealand archipelago between 1250 and 1300,[18][24] although newer  archaeological and genetic research points to a date no earlier than about 1280, with at least the main settlement period between about 1320 and 1350,[25][26] consistent with evidence based on genealogical traditions.[27][28] This represented a culmination in a long series of voyages through the Pacific islands.[29] Over the centuries that followed, the Polynesian settlers developed a distinct culture now known as Māori. The population formed different iwi (tribes) and hapū (subtribes) which would sometimes cooperate, sometimes compete and sometimes fight against each other.[30] At some point a group of Māori migrated to Rēkohu, now known as the Chatham Islands, where they developed their distinct Moriori culture.[31][32] The Moriori population was all but wiped out between 1835 and 1862, largely because of Taranaki Māori invasion and enslavement in the 1830s, although European diseases also contributed. In 1862 only 101 survived, and the last known full-blooded Moriori died in 1933.[33]
+
+The first Europeans known to have reached New Zealand were the Dutch explorer Abel Tasman and his crew in 1642.[34] In a hostile encounter, four crew members were killed and at least one Māori was hit by canister shot.[35] Europeans did not revisit New Zealand until 1769 when British explorer James Cook mapped almost the entire coastline.[34] Following Cook, New Zealand was visited by numerous European and North American whaling, sealing and trading ships. They traded European food, metal tools, weapons and other goods for timber, Māori food, artefacts and water.[36] The introduction of the potato and the musket transformed Māori agriculture and warfare. Potatoes provided a reliable food surplus, which enabled longer and more sustained military campaigns.[37] The resulting intertribal Musket Wars encompassed over 600 battles between 1801 and 1840, killing 30,000–40,000 Māori.[38] From the early 19th century, Christian missionaries began to settle New Zealand, eventually converting most of the Māori population.[39] The Māori population declined to around 40% of its pre-contact level during the 19th century; introduced diseases were the major factor.[40]
+
+In 1788 Captain Arthur Phillip assumed the position of Governor of the new British colony of New South Wales which according to his commission included New Zealand.[41] The British Government appointed James Busby as British Resident to New Zealand in 1832 following a petition from northern Māori.[42] In 1835, following an announcement of impending French settlement by Charles de Thierry, the nebulous United Tribes of New Zealand sent a Declaration of Independence to King William IV of the United Kingdom asking for protection.[42] Ongoing unrest, the proposed settlement of New Zealand by the New Zealand Company (which had already sent its first ship of surveyors to buy land from Māori) and the dubious legal standing of the Declaration of Independence prompted the Colonial Office to send Captain William Hobson to claim sovereignty for the United Kingdom and negotiate a treaty with the Māori.[43] The Treaty of Waitangi was first signed in the Bay of Islands on 6 February 1840.[44] In response to the New Zealand Company's attempts to establish an independent settlement in Wellington[45] and French settlers purchasing land in Akaroa,[46] Hobson declared British sovereignty over all of New Zealand on 21 May 1840, even though copies of the Treaty were still circulating throughout the country for Māori to sign.[47] With the signing of the Treaty and declaration of sovereignty the number of immigrants, particularly from the United Kingdom, began to increase.[48]
+
+New Zealand, still part of the colony of New South Wales, became a separate Colony of New Zealand on 1 July 1841.[49] Armed conflict began between the Colonial government and
+Māori in 1843 with the Wairau Affray over land and disagreements over sovereignty. These conflicts, mainly in the North Island, saw thousands of imperial troops and the Royal Navy come to New Zealand and became known as the New Zealand Wars. Following these armed conflicts, large amounts of Māori land was confiscated by the government to meet settler demands.[50]
+
+The colony gained a representative government in 1852 and the first Parliament met in 1854.[51] In 1856 the colony effectively became self-governing, gaining responsibility over all domestic matters other than native policy.[51] (Control over native policy was granted in the mid-1860s.[51]) Following concerns that the South Island might form a separate colony, premier Alfred Domett moved a resolution to transfer the capital from Auckland to a locality near Cook Strait.[52] Wellington was chosen for its central location, with Parliament officially sitting there for the first time in 1865.[53]
+
+In 1891 the Liberal Party came to power as the first organised political party.[54] The Liberal Government, led by Richard Seddon for most of its period in office,[55] passed many important social and economic measures. In 1893 New Zealand was the first nation in the world to grant all women the right to vote[54] and in 1894 pioneered the adoption of compulsory arbitration between employers and unions.[56]
+
+In 1907, at the request of the New Zealand Parliament, King Edward VII proclaimed New Zealand a Dominion within the British Empire,[57] reflecting its self-governing status.[58] In 1947 the country adopted the Statute of Westminster, confirming that the British Parliament could no longer legislate for New Zealand without the consent of New Zealand.[51]
+
+Early in the 20th century, New Zealand was involved in world affairs, fighting in the First and Second World Wars[59] and suffering through the Great Depression.[60] The depression led to the election of the First Labour Government and the establishment of a comprehensive welfare state and a protectionist economy.[61] New Zealand experienced increasing prosperity following the Second World War[62] and Māori began to leave their traditional rural life and move to the cities in search of work.[63] A Māori protest movement developed, which criticised Eurocentrism and worked for greater recognition of Māori culture and of the Treaty of Waitangi.[64] In 1975, a Waitangi Tribunal was set up to investigate alleged breaches of the Treaty, and it was enabled to investigate historic grievances in 1985.[44] The government has negotiated settlements of these grievances with many iwi,[65] although Māori claims to the foreshore and seabed proved controversial in the 2000s.[66][67]
+
+New Zealand is a constitutional monarchy with a parliamentary democracy,[68] although its constitution is not codified.[69] Elizabeth II is the queen of New Zealand[70] and thus the head of state.[71] The queen is represented by the governor-general, whom she appoints on the advice of the prime minister.[72] The governor-general can exercise the Crown's prerogative powers, such as reviewing cases of injustice and making appointments of ministers, ambassadors and other key public officials,[73] and in rare situations, the reserve powers (e.g. the power to dissolve parliament or refuse the royal assent of a bill into law).[74] The powers of the monarch and the governor-general are limited by constitutional constraints and they cannot normally be exercised without the advice of ministers.[74]
+
+The New Zealand Parliament holds legislative power and consists of the queen and the House of Representatives.[75] It also included an upper house, the Legislative Council, until this was abolished in 1950.[75] The supremacy of parliament over the Crown and other government institutions was established in England by the Bill of Rights 1689 and has been ratified as law in New Zealand.[75] The House of Representatives is democratically elected and a government is formed from the party or coalition with the majority of seats. If no majority is formed, a minority government can be formed if support from other parties during confidence and supply votes is assured.[75] The governor-general appoints ministers under advice from the prime minister, who is by convention the parliamentary leader of the governing party or coalition.[76] Cabinet, formed by ministers and led by the prime minister, is the highest policy-making body in government and responsible for deciding significant government actions.[77] Members of Cabinet make major decisions collectively, and are therefore collectively responsible for the consequences of these decisions.[78]
+
+A parliamentary general election must be called no later than three years after the previous election.[79] Almost all general elections between 1853 and 1993 were held under the first-past-the-post voting system.[80] Since the 1996 election, a form of proportional representation called mixed-member proportional (MMP) has been used.[69] Under the MMP system, each person has two votes; one is for a candidate standing in the voter's electorate and the other is for a party. Since the 2014 election, there have been 71 electorates (which include seven Māori electorates in which only Māori can optionally vote),[81] and the remaining 49 of the 120 seats are assigned so that representation in parliament reflects the party vote, with the threshold that a party must win at least one electorate or 5% of the total party vote before it is eligible for a seat.[82]
+
+Elections since the 1930s have been dominated by two political parties, National and Labour.[80] Between March 2005 and August 2006, New Zealand became the first country in the world in which all the highest offices in the land—head of state, governor-general, prime minister, speaker and chief justice—were occupied simultaneously by women.[83] The current prime minister is Jacinda Ardern, who has been in office since 26 October 2017.[84] She is the country's third female prime minister.[85]
+
+New Zealand's judiciary, headed by the chief justice,[86] includes the Supreme Court, Court of Appeal, the High Court, and subordinate courts.[87] Judges and judicial officers are appointed non-politically and under strict rules regarding tenure to help maintain judicial independence.[69] This theoretically allows the judiciary to interpret the law based solely on the legislation enacted by Parliament without other influences on their decisions.[88]
+
+New Zealand is identified as one of the world's most stable and well-governed states.[89] As at 2017[update], the country was ranked fourth in the strength of its democratic institutions,[90] and first in government transparency and lack of corruption.[91] A 2017 Human Rights Report by the U.S. Department of State noted that the government generally respected the rights of individuals, but voiced concerns regarding the social status of the Māori population.[92] New Zealand ranks highly for civic participation in the political process, with 80% voter turnout during recent elections, compared to an OECD average of 68%.[93]
+
+Early colonial New Zealand allowed the British Government to determine external trade and be responsible for foreign policy.[94] The 1923 and 1926 Imperial Conferences decided that New Zealand should be allowed to negotiate its own political treaties and the first commercial treaty was ratified in 1928 with Japan. On 3 September 1939 New Zealand allied itself with Britain and declared war on Germany with Prime Minister Michael Joseph Savage proclaiming, "Where she goes, we go; where she stands, we stand."[95]
+
+In 1951 the United Kingdom became increasingly focused on its European interests,[96] while New Zealand joined Australia and the United States in the ANZUS security treaty.[97] The influence of the United States on New Zealand weakened following protests over the Vietnam War,[98] the refusal of the United States to admonish France after the sinking of the Rainbow Warrior,[99] disagreements over environmental and agricultural trade issues and New Zealand's nuclear-free policy.[100][101] Despite the United States' suspension of ANZUS obligations the treaty remained in effect between New Zealand and Australia, whose foreign policy has followed a similar historical trend.[102] Close political contact is maintained between the two countries, with free trade agreements and travel arrangements that allow citizens to visit, live and work in both countries without restrictions.[103] In 2013[update] there were about 650,000 New Zealand citizens living in Australia, which is equivalent to 15% of the resident population of New Zealand.[104]
+
+New Zealand has a strong presence among the Pacific Island countries. A large proportion of New Zealand's aid goes to these countries and many Pacific people migrate to New Zealand for employment.[105] Permanent migration is regulated under the 1970 Samoan Quota Scheme and the 2002 Pacific Access Category, which allow up to 1,100 Samoan nationals and up to 750 other Pacific Islanders respectively to become permanent New Zealand residents each year. A seasonal workers scheme for temporary migration was introduced in 2007 and in 2009 about 8,000 Pacific Islanders were employed under it.[106] New Zealand is involved in the Pacific Islands Forum, the Pacific Community, Asia-Pacific Economic Cooperation and the Association of Southeast Asian Nations Regional Forum (including the East Asia Summit).[103] New Zealand has been described as an emerging power.[107][108] The country is a member of the United Nations,[109] the Commonwealth of Nations[110] and the Organisation for Economic Co-operation and Development (OECD),[111] and participates in the Five Power Defence Arrangements.[112]
+
+New Zealand's military services—the Defence Force—comprise the New Zealand Army, the Royal New Zealand Air Force and the Royal New Zealand Navy.[113] New Zealand's national defence needs are modest, since a direct attack is unlikely.[114] However, its military has had a global presence. The country fought in both world wars, with notable campaigns in Gallipoli, Crete,[115] El Alamein[116] and Cassino.[117] The Gallipoli campaign played an important part in fostering New Zealand's national identity[118][119] and strengthened the ANZAC tradition it shares with Australia.[120]
+
+In addition to Vietnam and the two world wars, New Zealand fought in the Second Boer War,[121] the Korean War,[122] the Malayan Emergency,[123] the Gulf War and the Afghanistan War. It has contributed forces to several regional and global peacekeeping missions, such as those in Cyprus, Somalia, Bosnia and Herzegovina, the Sinai, Angola, Cambodia, the Iran–Iraq border, Bougainville, East Timor, and the Solomon Islands.[124]
+
+The early European settlers divided New Zealand into provinces, which had a degree of autonomy.[125] Because of financial pressures and the desire to consolidate railways, education, land sales and other policies, government was centralised and the provinces were abolished in 1876.[126] The provinces are remembered in regional public holidays[127] and sporting rivalries.[128]
+
+Since 1876, various councils have administered local areas under legislation determined by the central government.[125][129] In 1989, the government reorganised local government into the current two-tier structure of regional councils and territorial authorities.[130] The 249 municipalities[130] that existed in 1975 have now been consolidated into 67 territorial authorities and 11 regional councils.[131] The regional councils' role is to regulate "the natural environment with particular emphasis on resource management",[130] while territorial authorities are responsible for sewage, water, local roads, building consents and other local matters.[132][133] Five of the territorial councils are unitary authorities and also act as regional councils.[133] The territorial authorities consist of 13 city councils, 53 district councils, and the Chatham Islands Council. While officially the Chatham Islands Council is not a unitary authority, it undertakes many functions of a regional council.[134]
+
+The Realm of New Zealand, one of 16 Commonwealth realms,[135] is the entire area over which the queen of New Zealand is sovereign, and comprises New Zealand, Tokelau, the Ross Dependency, the Cook Islands and Niue.[68] The Cook Islands and Niue are self-governing states in free association with New Zealand.[136][137] The New Zealand Parliament cannot pass legislation for these countries, but with their consent can act on behalf of them in foreign affairs and defence. Tokelau is classified as a non-self-governing territory, but is administered by a council of three elders (one from each Tokelauan atoll).[138] The Ross Dependency is New Zealand's territorial claim in Antarctica, where it operates the Scott Base research facility.[139] New Zealand nationality law treats all parts of the realm equally, so most people born in New Zealand, the Cook Islands, Niue, Tokelau and the Ross Dependency are New Zealand citizens.[140][n 7]
+
+New Zealand is located near the centre of the water hemisphere and is made up of two main islands and a number of smaller islands. The two main islands (the North Island, or Te Ika-a-Māui, and the South Island, or Te Waipounamu) are separated by Cook Strait, 22 kilometres (14 mi) wide at its narrowest point.[142] Besides the North and South Islands, the five largest inhabited islands are Stewart Island (across the Foveaux Strait), Chatham Island, Great Barrier Island (in the Hauraki Gulf),[143] D'Urville Island (in the Marlborough Sounds)[144] and Waiheke Island (about 22 km (14 mi) from central Auckland).[145]
+
+New Zealand is long and narrow—over 1,600 kilometres (990 mi) along its north-north-east axis with a maximum width of 400 kilometres (250 mi)[146]—with about 15,000 km (9,300 mi) of coastline[147] and a total land area of 268,000 square kilometres (103,500 sq mi).[148] Because of its far-flung outlying islands and long coastline, the country has extensive marine resources. Its exclusive economic zone is one of the largest in the world, covering more than 15 times its land area.[149]
+
+The South Island is the largest landmass of New Zealand. It is divided along its length by the Southern Alps.[150] There are 18 peaks over 3,000 metres (9,800 ft), the highest of which is Aoraki / Mount Cook at 3,724 metres (12,218 ft).[151] Fiordland's steep mountains and deep fiords record the extensive ice age glaciation of this southwestern corner of the South Island.[152] The North Island is less mountainous but is marked by volcanism.[153] The highly active Taupo Volcanic Zone has formed a large volcanic plateau, punctuated by the North Island's highest mountain, Mount Ruapehu (2,797 metres (9,177 ft)). The plateau also hosts the country's largest lake, Lake Taupo,[154] nestled in the caldera of one of the world's most active supervolcanoes.[155]
+
+The country owes its varied topography, and perhaps even its emergence above the waves, to the dynamic boundary it straddles between the Pacific and Indo-Australian Plates.[156] New Zealand is part of Zealandia, a microcontinent nearly half the size of Australia that gradually submerged after breaking away from the Gondwanan supercontinent.[157][158] About 25 million years ago, a shift in plate tectonic movements began to contort and crumple the region. This is now most evident in the Southern Alps, formed by compression of the crust beside the Alpine Fault. Elsewhere the plate boundary involves the subduction of one plate under the other, producing the Puysegur Trench to the south, the Hikurangi Trench east of the North Island, and the Kermadec and Tonga Trenches[159] further north.[156]
+
+New Zealand is part of a region known as Australasia, together with Australia.[160] It also forms the southwestern extremity of the geographic and ethnographic region called Polynesia.[161] The term Oceania is often used to denote the wider region encompassing the Australian continent, New Zealand and various islands in the Pacific Ocean that are not included in the seven-continent model.[162]
+
+Rural scene near Queenstown
+
+The Emerald Lakes, Mt Tongariro
+
+Lake Gunn
+
+Pencarrow Head, Wellington
+
+New Zealand's climate is predominantly temperate maritime (Köppen: Cfb), with mean annual temperatures ranging from 10 °C (50 °F) in the south to 16 °C (61 °F) in the north.[163] Historical maxima and minima are 42.4 °C (108.32 °F) in Rangiora, Canterbury and −25.6 °C (−14.08 °F) in Ranfurly, Otago.[164] Conditions vary sharply across regions from extremely wet on the West Coast of the South Island to almost semi-arid in Central Otago and the Mackenzie Basin of inland Canterbury, and subtropical in Northland.[165][166] Of the seven largest cities, Christchurch is the driest, receiving on average only 640 millimetres (25 in) of rain per year and Wellington the wettest, receiving almost twice that amount.[167] Auckland, Wellington and Christchurch all receive a yearly average of more than 2,000 hours of sunshine. The southern and southwestern parts of the South Island have a cooler and cloudier climate, with around 1,400–1,600 hours; the northern and northeastern parts of the South Island are the sunniest areas of the country and receive about 2,400–2,500 hours.[168] The general snow season is early June until early October, though cold snaps can occur outside this season.[169] Snowfall is common in the eastern and southern parts of the South Island and mountain areas across the country.[163]
+
+The table below lists climate normals for the warmest and coldest months in New Zealand's six largest cities. North Island cities are generally warmest in February. South Island cities are warmest in January.
+
+New Zealand's geographic isolation for 80 million years[171] and island biogeography has influenced evolution of the country's species of animals, fungi and plants. Physical isolation has caused biological isolation, resulting in a dynamic evolutionary ecology with examples of very distinctive plants and animals as well as populations of widespread species.[172][173] About 82% of New Zealand's indigenous vascular plants are endemic, covering 1,944 species across 65 genera.[174][175] The number of fungi recorded from New Zealand, including lichen-forming species, is not known, nor is the proportion of those fungi which are endemic, but one estimate suggests there are about 2,300 species of lichen-forming fungi in New Zealand[174] and 40% of these are endemic.[176] The two main types of forest are those dominated by broadleaf trees with emergent podocarps, or by southern beech in cooler climates.[177] The remaining vegetation types consist of grasslands, the majority of which are tussock.[178]
+
+Before the arrival of humans, an estimated 80% of the land was covered in forest, with only high alpine, wet, infertile and volcanic areas without trees.[179] Massive deforestation occurred after humans arrived, with around half the forest cover lost to fire after Polynesian settlement.[180] Much of the remaining forest fell after European settlement, being logged or cleared to make room for pastoral farming, leaving forest occupying only 23% of the land.[181]
+
+The forests were dominated by birds, and the lack of mammalian predators led to some like the kiwi, kakapo, weka and takahē evolving flightlessness.[182] The arrival of humans, associated changes to habitat, and the introduction of rats, ferrets and other mammals led to the extinction of many bird species, including large birds like the moa and Haast's eagle.[183][184]
+
+Other indigenous animals are represented by reptiles (tuatara, skinks and geckos), frogs,[185] spiders,[186] insects (wētā)[187] and snails.[188] Some, such as the tuatara, are so unique that they have been called living fossils.[189] Three species of bats (one since extinct) were the only sign of native land mammals in New Zealand until the 2006 discovery of bones from a unique, mouse-sized land mammal at least 16 million years old.[190][191] Marine mammals however are abundant, with almost half the world's cetaceans (whales, dolphins, and porpoises) and large numbers of fur seals reported in New Zealand waters.[192] Many seabirds breed in New Zealand, a third of them unique to the country.[193] More penguin species are found in New Zealand than in any other country.[194]
+
+Since human arrival, almost half of the country's vertebrate species have become extinct, including at least fifty-one birds, three frogs, three lizards, one freshwater fish, and one bat. Others are endangered or have had their range severely reduced.[183] However, New Zealand conservationists have pioneered several methods to help threatened wildlife recover, including island sanctuaries, pest control, wildlife translocation, fostering and ecological restoration of islands and other protected areas.[195][196][197][198]
+
+New Zealand has an advanced market economy,[199] ranked 16th in the 2018[update] Human Development Index[8] and third in the 2018[update] Index of Economic Freedom.[200] It is a high-income economy with a nominal gross domestic product (GDP) per capita of US$36,254.[6] The currency is the New Zealand dollar, informally known as the "Kiwi dollar"; it also circulates in the Cook Islands (see Cook Islands dollar), Niue, Tokelau, and the Pitcairn Islands.[201]
+
+Historically, extractive industries have contributed strongly to New Zealand's economy, focussing at different times on sealing, whaling, flax, gold, kauri gum, and native timber.[202] The first shipment of refrigerated meat on the Dunedin in 1882 led to the establishment of meat and dairy exports to Britain, a trade which provided the basis for strong economic growth in New Zealand.[203] High demand for agricultural products from the United Kingdom and the United States helped New Zealanders achieve higher living standards than both Australia and Western Europe in the 1950s and 1960s.[204] In 1973, New Zealand's export market was reduced when the United Kingdom joined the European Economic Community[205] and other compounding factors, such as the 1973 oil and 1979 energy crises, led to a severe economic depression.[206] Living standards in New Zealand fell behind those of Australia and Western Europe, and by 1982 New Zealand had the lowest per-capita income of all the developed nations surveyed by the World Bank.[207] In the mid-1980s New Zealand deregulated its agricultural sector by phasing out subsidies over a three-year period.[208][209] Since 1984, successive governments engaged in major macroeconomic restructuring (known first as Rogernomics and then Ruthanasia), rapidly transforming New Zealand from a protected and highly regulated economy to a liberalised free-trade economy.[210][211]
+
+Unemployment peaked above 10% in 1991 and 1992,[213] following the 1987 share market crash, but eventually fell to a record low (since 1986) of 3.7% in 2007 (ranking third from twenty-seven comparable OECD nations).[213] However, the global financial crisis that followed had a major impact on New Zealand, with the GDP shrinking for five consecutive quarters, the longest recession in over thirty years,[214][215] and unemployment rising back to 7% in late 2009.[216] Unemployment rates for different age groups follow similar trends, but are consistently higher among youth. In the December 2014 quarter, the general unemployment rate was around 5.8%, while the unemployment rate for youth aged 15 to 21 was 15.6%.[213] New Zealand has experienced a series of "brain drains" since the 1970s[217] that still continue today.[218] Nearly one quarter of highly skilled workers live overseas, mostly in Australia and Britain, which is the largest proportion from any developed nation.[219] In recent decades, however, a "brain gain" has brought in educated professionals from Europe and less developed countries.[220][221] Today New Zealand's economy benefits from a high level of innovation.[222]
+
+New Zealand is heavily dependent on international trade,[223] particularly in agricultural products.[224] Exports account for 24% of its output,[147] making New Zealand vulnerable to international commodity prices and global economic slowdowns. Food products made up 55% of the value of all the country's exports in 2014; wood was the second largest earner (7%).[225] New Zealand's main trading partners, as at June 2018[update], are China (NZ$27.8b), Australia ($26.2b), the European Union ($22.9b), the United States ($17.6b), and Japan ($8.4b).[226] On 7 April 2008, New Zealand and China signed the New Zealand–China Free Trade Agreement, the first such agreement China has signed with a developed country.[227] The service sector is the largest sector in the economy, followed by manufacturing and construction and then farming and raw material extraction.[147] Tourism plays a significant role in the economy, contributing $12.9 billion (or 5.6%) to New Zealand's total GDP and supporting 7.5% of the total workforce in 2016.[228] International visitor arrivals are expected to increase at a rate of 5.4% annually up to 2022.[228]
+
+Wool was New Zealand's major agricultural export during the late 19th century.[202] Even as late as the 1960s it made up over a third of all export revenues,[202] but since then its price has steadily dropped relative to other commodities[229] and wool is no longer profitable for many farmers.[230] In contrast dairy farming increased, with the number of dairy cows doubling between 1990 and 2007,[231] to become New Zealand's largest export earner.[232] In the year to June 2018, dairy products accounted for 17.7% ($14.1 billion) of total exports,[226] and the country's largest company, Fonterra, controls almost one-third of the international dairy trade.[233] Other exports in 2017-18 were meat (8.8%), wood and wood products (6.2%), fruit (3.6%), machinery (2.2%) and wine (2.1%).[226] New Zealand's wine industry has followed a similar trend to dairy, the number of vineyards doubling over the same period,[234] overtaking wool exports for the first time in 2007.[235][236]
+
+In 2015, renewable energy generated 40.1% of New Zealand's gross energy supply.[237]  The majority of the country's electricity supply is generated from hydroelectric power, with major schemes on the Waikato, Waitaki and Clutha rivers, as well as at Manapouri. Geothermal power is also a significant generator of electricity, with several large stations located across the Taupo Volcanic Zone in the North Island. The five main companies in the generation and retail market are Contact Energy, Genesis Energy, Mercury Energy, Meridian Energy, and TrustPower. State-owned Transpower operates the high-voltage transmission grids in the North and South Islands, as well as the Inter-Island HVDC link connecting the two together.[237]
+
+The provision of water supply and sanitation is generally of good quality. Regional authorities provide water abstraction, treatment and distribution infrastructure to most developed areas.[238][239]
+
+New Zealand's transport network comprises 94,000 kilometres (58,410 mi) of roads, including 199 kilometres (124 mi) of motorways,[240] and 4,128 kilometres (2,565 mi) of railway lines.[147] Most major cities and towns are linked by bus services, although the private car is the predominant mode of transport.[241] The railways were privatised in 1993, but were re-nationalised by the government in stages between 2004 and 2008. The state-owned enterprise KiwiRail now operates the railways, with the exception of commuter services in Auckland and Wellington which are operated by Transdev[242] and Metlink,[243] respectively. Railways run the length of the country, although most lines now carry freight rather than passengers.[244] The road and rail networks in the two main islands are linked by roll-on/roll-off ferries between Wellington and Picton, operated by Interislander (part of KiwiRail) and Bluebridge. Most international visitors arrive via air[245] and New Zealand has six international airports, but currently[update] only the Auckland and Christchurch airports connect directly with countries other than Australia or Fiji.[246]
+
+The New Zealand Post Office had a monopoly over telecommunications in New Zealand until 1987 when Telecom New Zealand was formed, initially as a state-owned enterprise and then privatised in 1990.[247] Chorus, which was split from Telecom (now Spark) in 2011,[248] still owns the majority of the telecommunications infrastructure, but competition from other providers has increased.[247] A large-scale rollout of gigabit-capable fibre to the premises, branded as Ultra-Fast Broadband, began in 2009 with a target of being available to 87% of the population by 2022.[249] As of 2017[update], the United Nations International Telecommunication Union ranks New Zealand 13th in the development of information and communications infrastructure.[250]
+
+Early indigenous contribution to science in New Zealand was by Māori tohunga accumulating knowledge of agricultural practice and the effects of herbal remedies in the treatment of illness and disease. Cook's voyages in the 1700s and Darwin's in 1835 had important scientific botanical and zoological objectives.[251] The establishment of universities in the 19th century fostered scientific discoveries by notable New Zealanders including Ernest Rutherford for splitting the atom, William Pickering for rocket science, Maurice Wilkins for helping discover DNA, Beatrice Tinsley for galaxy formation, and Alan MacDiarmid for conducting polymers.[252]
+
+Crown Research Institutes (CRIs) were formed in 1992 from existing government-owned research organisations. Their role is to research and develop new science, knowledge, products and services across the economic, environmental, social and cultural spectrum for the benefit of New Zealand.[253] The total gross expenditure on research and development (R&D) as a proportion of GDP rose to 1.37% in 2018, up from 1.23% in 2015. New Zealand ranks 21st in the OECD for its gross R&D spending as a percentage of GDP.[254]
+
+The 2018 New Zealand census enumerated a resident population of 4,699,755, an increase of 10.8% over the 2013 figure.[3] As of July 2020, the total population has risen to an estimated 5,010,290.[n 8][5] In May 2020 Statistics New Zealand reported that New Zealand's population had climbed above 5 million people in March 2020.[256]
+
+New Zealand is a predominantly urban country, with 83.6% of the population living in urban areas, and 52.3% of the population living in the seven cities with populations exceeding 100,000.[257] Auckland, with over 1 million residents, is by far the largest city.[257] New Zealand cities generally rank highly on international livability measures. For instance, in 2016 Auckland was ranked the world's third most liveable city and Wellington the twelfth by the Mercer Quality of Living Survey.[258]
+
+Life expectancy for New Zealanders in 2012 was 84 years for females, and 80.2 years for males.[259] Life expectancy at birth is forecast to increase from 80 years to 85 years in 2050 and infant mortality is expected to decline.[260] New Zealand's fertility rate of 2.1 is relatively high for a developed country, and natural births account for a significant proportion of population growth. Consequently, the country has a young population compared to most industrialised nations, with 20% of New Zealanders being 14 years old or younger.[147] In 2018 the median age of the New Zealand population was 38.1 years.[261] By 2050 the median age is projected to rise to 43 years and the percentage of people 60 years of age and older to rise from 18% to 29%.[260] In 2008 the leading cause of premature death was cancer, at 29.8%, followed by ischaemic heart disease, 19.7%, and then cerebrovascular disease, 9.2%.[262] As of 2016[update], total expenditure on health care (including private sector spending) is 9.2% of GDP.[263]
+
+
+
+In the 2018 census, 71.8% of New Zealand residents identified ethnically as European, and 16.5% as Māori. Other major ethnic groups include Asian (15.3%) and Pacific peoples (9.0%), two-thirds of whom live in the Auckland Region.[n 3][3] The population has become more diverse in recent decades: in 1961, the census reported that the population of New Zealand was 92% European and 7% Māori, with Asian and Pacific minorities sharing the remaining 1%.[264]
+
+While the demonym for a New Zealand citizen is New Zealander, the informal "Kiwi" is commonly used both internationally[265] and by locals.[266] The Māori loanword Pākehā has been used to refer to New Zealanders of European descent, although some reject this name. The word Pākehā today is increasingly used to refer to all non-Polynesian New Zealanders.[267]
+
+The Māori were the first people to reach New Zealand, followed by the early European settlers. Following colonisation, immigrants were predominantly from Britain, Ireland and Australia because of restrictive policies similar to the White Australia policy.[268] There was also significant Dutch, Dalmatian,[269] German, and Italian immigration, together with indirect European immigration through Australia, North America, South America and South Africa.[270][271] Net migration increased after the Second World War; in the 1970s and 1980s policies were relaxed and immigration from Asia was promoted.[271][272] In 2009–10, an annual target of 45,000–50,000 permanent residence approvals was set by the New Zealand Immigration Service—more than one new migrant for every 100 New Zealand residents.[273] In the 2018 census, 27.4% of people counted were not born in New Zealand, up from 25.2% in the 2013 census. Over half (52.4%) of New Zealand's overseas-born population lives in the Auckland Region.[274] The United Kingdom remains the largest source of New Zealand's immigrant population, with around a quarter of all overseas-born New Zealanders born there; other major sources of New Zealand's overseas-born population are China, India, Australia, South Africa, Fiji and Samoa.[275] The number of fee-paying international students increased sharply in the late 1990s, with more than 20,000 studying in public tertiary institutions in 2002.[276]
+
+English is the predominant language in New Zealand, spoken by 95.4% of the population.[3] New Zealand English is similar to Australian English and many speakers from the Northern Hemisphere are unable to tell the accents apart.[278] The most prominent differences between the New Zealand English dialect and other English dialects are the shifts in the short front vowels: the short-"i" sound (as in "kit") has centralised towards the schwa sound (the "a" in "comma" and "about"); the short-"e" sound (as in "dress") has moved towards the short-"i" sound; and the short-"a" sound (as in "trap") has moved to the short-"e" sound.[279]
+
+After the Second World War, Māori were discouraged from speaking their own language (te reo Māori) in schools and workplaces and it existed as a community language only in a few remote areas.[280] It has recently undergone a process of revitalisation,[281] being declared one of New Zealand's official languages in 1987,[282] and is spoken by 4.0% of the population.[3][n 9] There are now Māori language immersion schools and two television channels that broadcast predominantly in Māori.[284] Many places have both their Māori and English names officially recognised.[285]
+
+As recorded in the 2018 census,[3] Samoan is the most widely spoken non-official language (2.2%), followed by "Northern Chinese" (including Mandarin, 2.0%), Hindi (1.5%), and French (1.2%). 22,986 people (0.5%) reported the ability to use New Zealand Sign Language, which became one of New Zealand's official languages in 2006.[286]
+
+Christianity is the predominant religion in New Zealand, although its society is among the most secular in the world.[288][289] In the 2018 census, 44.7% of respondents identified with one or more religions, including 37.0% identifying as Christians. Another 48.5% indicated that they had no religion.[n 10][3] Of those who affiliate with a particular Christian denomination, the main responses are Anglicanism (6.7%), Roman Catholicism (6.3%), and Presbyterianism (4.7%).[3] The Māori-based Ringatū and Rātana religions (1.2%) are also Christian in origin.[3][287] Immigration and demographic change in recent decades has contributed to the growth of minority religions, such as Hinduism (2.6%), Islam (1.3%), Buddhism (1.1%), and Sikhism (0.9%).[3] The Auckland Region exhibited the greatest religious diversity.[290]
+
+Primary and secondary schooling is compulsory for children aged 6 to 16, with the majority attending from the age of 5.[291] There are 13 school years and attending state (public) schools is free to New Zealand citizens and permanent residents from a person's 5th birthday to the end of the calendar year following their 19th birthday.[292] New Zealand has an adult literacy rate of 99%,[147] and over half of the population aged 15 to 29 hold a tertiary qualification.[291] There are five types of government-owned tertiary institutions: universities, colleges of education, polytechnics, specialist colleges, and wānanga,[293] in addition to private training establishments.[294] In the adult population 14.2% have a bachelor's degree or higher, 30.4% have some form of secondary qualification as their highest qualification and 22.4% have no formal qualification.[295] The OECD's Programme for International Student Assessment ranks New Zealand's education system as the seventh best in the world, with students performing exceptionally well in reading, mathematics and science.[296]
+
+Early Māori adapted the tropically based east Polynesian culture in line with the challenges associated with a larger and more diverse environment, eventually developing their own distinctive culture. Social organisation was largely communal with families (whānau), subtribes (hapū) and tribes (iwi) ruled by a chief (rangatira), whose position was subject to the community's approval.[297] The British and Irish immigrants brought aspects of their own culture to New Zealand and also influenced Māori culture,[298][299] particularly with the introduction of Christianity.[300] However, Māori still regard their allegiance to tribal groups as a vital part of their identity, and Māori kinship roles resemble those of other Polynesian peoples.[301] More recently American, Australian, Asian and other European cultures have exerted influence on New Zealand. Non-Māori Polynesian cultures are also apparent, with Pasifika, the world's largest Polynesian festival, now an annual event in Auckland.[302]
+
+The largely rural life in early New Zealand led to the image of New Zealanders being rugged, industrious problem solvers.[303] Modesty was expected and enforced through the "tall poppy syndrome", where high achievers received harsh criticism.[304] At the time New Zealand was not known as an intellectual country.[305] From the early 20th century until the late 1960s, Māori culture was suppressed by the attempted assimilation of Māori into British New Zealanders.[280] In the 1960s, as tertiary education became more available and cities expanded[306] urban culture began to dominate.[307] However, rural imagery and themes are common in New Zealand's art, literature and media.[308]
+
+New Zealand's national symbols are influenced by natural, historical, and Māori sources. The silver fern is an emblem appearing on army insignia and sporting team uniforms.[309] Certain items of popular culture thought to be unique to New Zealand are called "Kiwiana".[309]
+
+As part of the resurgence of Māori culture, the traditional crafts of carving and weaving are now more widely practised and Māori artists are increasing in number and influence.[310] Most Māori carvings feature human figures, generally with three fingers and either a natural-looking, detailed head or a grotesque head.[311] Surface patterns consisting of spirals, ridges, notches and fish scales decorate most carvings.[312] The pre-eminent Māori architecture consisted of carved meeting houses (wharenui) decorated with symbolic carvings and illustrations. These buildings were originally designed to be constantly rebuilt, changing and adapting to different whims or needs.[313]
+
+Māori decorated the white wood of buildings, canoes and cenotaphs using red (a mixture of red ochre and shark fat) and black (made from soot) paint and painted pictures of birds, reptiles and other designs on cave walls.[314] Māori tattoos (moko) consisting of coloured soot mixed with gum were cut into the flesh with a bone chisel.[315] Since European arrival paintings and photographs have been dominated by landscapes, originally not as works of art but as factual portrayals of New Zealand.[316] Portraits of Māori were also common, with early painters often portraying them as "noble savages", exotic beauties or friendly natives.[316] The country's isolation delayed the influence of European artistic trends allowing local artists to develop their own distinctive style of regionalism.[317] During the 1960s and 1970s many artists combined traditional Māori and Western techniques, creating unique art forms.[318] New Zealand art and craft has gradually achieved an international audience, with exhibitions in the Venice Biennale in 2001 and the "Paradise Now" exhibition in New York in 2004.[310][319]
+
+Māori cloaks are made of fine flax fibre and patterned with black, red and white triangles, diamonds and other geometric shapes.[320] Greenstone was fashioned into earrings and necklaces, with the most well-known design being the hei-tiki, a distorted human figure sitting cross-legged with its head tilted to the side.[321] Europeans brought English fashion etiquette to New Zealand, and until the 1950s most people dressed up for social occasions.[322] Standards have since relaxed and New Zealand fashion has received a reputation for being casual, practical and lacklustre.[323][324] However, the local fashion industry has grown significantly since 2000, doubling exports and increasing from a handful to about 50 established labels, with some labels gaining international recognition.[324]
+
+Māori quickly adopted writing as a means of sharing ideas, and many of their oral stories and poems were converted to the written form.[325] Most early English literature was obtained from Britain and it was not until the 1950s when local publishing outlets increased that New Zealand literature started to become widely known.[326] Although still largely influenced by global trends (modernism) and events (the Great Depression), writers in the 1930s began to develop stories increasingly focused on their experiences in New Zealand. During this period literature changed from a journalistic activity to a more academic pursuit.[327] Participation in the world wars gave some New Zealand writers a new perspective on New Zealand culture and with the post-war expansion of universities local literature flourished.[328] Dunedin is a UNESCO City of Literature.[329]
+
+New Zealand music has been influenced by blues, jazz, country, rock and roll and hip hop, with many of these genres given a unique New Zealand interpretation.[330] Māori developed traditional chants and songs from their ancient Southeast Asian origins, and after centuries of isolation created a unique "monotonous" and "doleful" sound.[331] Flutes and trumpets were used as musical instruments[332] or as signalling devices during war or special occasions.[333] Early settlers brought over their ethnic music, with brass bands and choral music being popular, and musicians began touring New Zealand in the 1860s.[334][335] Pipe bands became widespread during the early 20th century.[336] The New Zealand recording industry began to develop from 1940 onwards and many New Zealand musicians have obtained success in Britain and the United States.[330] Some artists release Māori language songs and the Māori tradition-based art of kapa haka (song and dance) has made a resurgence.[337] The New Zealand Music Awards are held annually by Recorded Music NZ; the awards were first held in 1965 by Reckitt & Colman as the Loxene Golden Disc awards.[338] Recorded Music NZ also publishes the country's official weekly record charts.[339]
+
+Public radio was introduced in New Zealand in 1922.[341] A state-owned television service began in 1960.[342] Deregulation in the 1980s saw a sudden increase in the numbers of radio and television stations.[343] New Zealand television primarily broadcasts American and British programming, along with many Australian and local shows.[344] The number of New Zealand films significantly increased during the 1970s. In 1978 the New Zealand Film Commission started assisting local film-makers and many films attained a world audience, some receiving international acknowledgement.[343] The highest-grossing New Zealand films are Hunt for the Wilderpeople, Boy, The World's Fastest Indian, Whale Rider, Once Were Warriors and The Piano.[345] The country's diverse scenery and compact size, plus government incentives,[346] have encouraged some producers to shoot big-budget productions in New Zealand, including The Lord of the Rings and The Hobbit film trilogies, Avatar, The Chronicles of Narnia, King Kong, Wolverine and The Last Samurai.[347] The New Zealand media industry is dominated by a small number of companies, most of which are foreign-owned, although the state retains ownership of some television and radio stations.[348] Since 1994, Freedom House has consistently ranked New Zealand's press freedom in the top twenty, with the 19th freest media in 2015[update].[349]
+
+Most of the major sporting codes played in New Zealand have British origins.[350] Rugby union is considered the national sport[351] and attracts the most spectators.[352] Golf, netball, tennis and cricket have the highest rates of adult participation, while netball, rugby union and football (soccer) are particularly popular among young people.[352][353] Around 54% of New Zealand adolescents participate in sports for their school.[353] Victorious rugby tours to Australia and the United Kingdom in the late 1880s and the early 1900s played an early role in instilling a national identity.[354] Horseracing was also a popular spectator sport and became part of the "Rugby, Racing and Beer" culture during the 1960s.[355] Māori participation in European sports was particularly evident in rugby and the country's team performs a haka, a traditional Māori challenge, before international matches.[356] New Zealand is known for its extreme sports, adventure tourism[357] and strong mountaineering tradition, as seen in the success of notable New Zealander Sir Edmund Hillary.[358][359] Other outdoor pursuits such as cycling, fishing, swimming, running, tramping, canoeing, hunting, snowsports, surfing and sailing are also popular.[360] New Zealand has seen regular sailing success in the America's Cup regatta since 1995.[361] The Polynesian sport of waka ama racing has experienced a resurgence of interest in New Zealand since the 1980s.[362]
+
+New Zealand has competitive international teams in rugby union, rugby league, netball, cricket, softball, and sailing. New Zealand participated at the Summer Olympics in 1908 and 1912 as a joint team with Australia, before first participating on its own in 1920.[363] The country has ranked highly on a medals-to-population ratio at recent Games.[364][365] The "All Blacks", the national rugby union team, are the most successful in the history of international rugby[366] and have won the World Cup three times.[367]
+
+The national cuisine has been described as Pacific Rim, incorporating the native Māori cuisine and diverse culinary traditions introduced by settlers and immigrants from Europe, Polynesia and Asia.[368] New Zealand yields produce from land and sea—most crops and livestock, such as maize, potatoes and pigs, were gradually introduced by the early European settlers.[369] Distinctive ingredients or dishes include lamb, salmon, kōura (crayfish),[370] dredge oysters, whitebait, pāua (abalone), mussels, scallops, pipis and tuatua (both are types of New Zealand shellfish),[371] kūmara (sweet potato), kiwifruit, tamarillo and pavlova (considered a national dish).[372][368] A hāngi is a traditional Māori method of cooking food using heated rocks buried in a pit oven. After European colonisation, Māori began cooking with pots and ovens and the hāngi was used less frequently, although it is still used for formal occasions such as tangihanga.[373]
+
+Click on a coloured area to see an article about English in that country or region

en/4188.html.txt

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+
+
+Coordinates: 42°S 173°E / 42°S 173°E / -42; 173
+
+New Zealand (Māori: Aotearoa [aɔˈtɛaɾɔa]) is an island country in the southwestern Pacific Ocean. It comprises two main landmasses—the North Island (Te Ika-a-Māui) and the South Island (Te Waipounamu)—and around 600 smaller islands, covering a total area of 268,021 square kilometres (103,500 sq mi). New Zealand is about 2,000 kilometres (1,200 mi) east of Australia across the Tasman Sea and 1,000 kilometres (600 mi) south of the islands of New Caledonia, Fiji, and Tonga. The country's varied topography and sharp mountain peaks, including the Southern Alps, owe much to tectonic uplift and volcanic eruptions. New Zealand's capital city is Wellington, and its most populous city is Auckland.
+
+Owing to their remoteness, the islands of New Zealand were the last large habitable lands to be settled by humans. Between about 1280 and 1350, Polynesians began to settle in the islands, and then developed a distinctive Māori culture. In 1642, Dutch explorer Abel Tasman became the first European to sight New Zealand. In 1840, representatives of the United Kingdom and Māori chiefs signed the Treaty of Waitangi, which declared British sovereignty over the islands. In 1841, New Zealand became a colony within the British Empire and in 1907 it became a dominion; it gained full statutory independence in 1947 and the British monarch remained the head of state. Today, the majority of New Zealand's population of 5 million is of European descent; the indigenous Māori are the largest minority, followed by Asians and Pacific Islanders. Reflecting this, New Zealand's culture is mainly derived from Māori and early British settlers, with recent broadening arising from increased immigration. The official languages are English, Māori, and New Zealand Sign Language, with English being very dominant.
+
+A developed country, New Zealand ranks highly in international comparisons of national performance, such as quality of life, education, protection of civil liberties, government transparency, and economic freedom. New Zealand underwent major economic changes during the 1980s, which transformed it from a protectionist to a liberalised free-trade economy. The service sector dominates the national economy, followed by the industrial sector, and agriculture; international tourism is a significant source of revenue. Nationally, legislative authority is vested in an elected, unicameral Parliament, while executive political power is exercised by the Cabinet, led by the prime minister, currently Jacinda Ardern. Queen Elizabeth II is the country's monarch and is represented by a governor-general, currently Dame Patsy Reddy. In addition, New Zealand is organised into 11 regional councils and 67 territorial authorities for local government purposes. The Realm of New Zealand also includes Tokelau (a dependent territory); the Cook Islands and Niue (self-governing states in free association with New Zealand); and the Ross Dependency, which is New Zealand's territorial claim in Antarctica.
+
+New Zealand is a member of the United Nations, Commonwealth of Nations, ANZUS, Organisation for Economic Co-operation and Development, ASEAN Plus Six, Asia-Pacific Economic Cooperation, the Pacific Community and the Pacific Islands Forum.
+
+The first European visitor to New Zealand, Dutch explorer Abel Tasman, named the islands Staten Land, believing they were part of the Staten Landt that Jacob Le Maire had sighted off the southern end of South America.[11][12] Hendrik Brouwer proved that the South American land was a small island in 1643, and Dutch cartographers subsequently renamed Tasman's discovery Nova Zeelandia, from Latin, after the Dutch province of Zeeland.[11][13] This name was later anglicised to "New Zealand".[14][15]
+
+Aotearoa (pronounced [aɔˈtɛaɾɔa] in Māori and /ˌaʊtɛəˈroʊ.ə/ in English; often translated as "land of the long white cloud")[16] is the current Māori name for New Zealand. It is unknown whether Māori had a name for the whole country before the arrival of Europeans, with Aotearoa originally referring to just the North Island.[17] Māori had several traditional names for the two main islands, including Te Ika-a-Māui (the fish of Māui) for the North Island and Te Waipounamu (the waters of greenstone) or Te Waka o Aoraki (the canoe of Aoraki) for the South Island.[18] Early European maps labelled the islands North (North Island), Middle (South Island) and South (Stewart Island / Rakiura).[19] In 1830, mapmakers began to use "North" and "South" on their maps to distinguish the two largest islands and by 1907 this was the accepted norm.[15] The New Zealand Geographic Board discovered in 2009 that the names of the North Island and South Island had never been formalised, and names and alternative names were formalised in 2013. This set the names as North Island or Te Ika-a-Māui, and South Island or Te Waipounamu.[20] For each island, either its English or Māori name can be used, or both can be used together.[20]
+
+New Zealand is one of the last major landmasses settled by humans. Radiocarbon dating, evidence of deforestation[22] and mitochondrial DNA variability within Māori populations[23] suggest that Eastern Polynesians first settled the New Zealand archipelago between 1250 and 1300,[18][24] although newer  archaeological and genetic research points to a date no earlier than about 1280, with at least the main settlement period between about 1320 and 1350,[25][26] consistent with evidence based on genealogical traditions.[27][28] This represented a culmination in a long series of voyages through the Pacific islands.[29] Over the centuries that followed, the Polynesian settlers developed a distinct culture now known as Māori. The population formed different iwi (tribes) and hapū (subtribes) which would sometimes cooperate, sometimes compete and sometimes fight against each other.[30] At some point a group of Māori migrated to Rēkohu, now known as the Chatham Islands, where they developed their distinct Moriori culture.[31][32] The Moriori population was all but wiped out between 1835 and 1862, largely because of Taranaki Māori invasion and enslavement in the 1830s, although European diseases also contributed. In 1862 only 101 survived, and the last known full-blooded Moriori died in 1933.[33]
+
+The first Europeans known to have reached New Zealand were the Dutch explorer Abel Tasman and his crew in 1642.[34] In a hostile encounter, four crew members were killed and at least one Māori was hit by canister shot.[35] Europeans did not revisit New Zealand until 1769 when British explorer James Cook mapped almost the entire coastline.[34] Following Cook, New Zealand was visited by numerous European and North American whaling, sealing and trading ships. They traded European food, metal tools, weapons and other goods for timber, Māori food, artefacts and water.[36] The introduction of the potato and the musket transformed Māori agriculture and warfare. Potatoes provided a reliable food surplus, which enabled longer and more sustained military campaigns.[37] The resulting intertribal Musket Wars encompassed over 600 battles between 1801 and 1840, killing 30,000–40,000 Māori.[38] From the early 19th century, Christian missionaries began to settle New Zealand, eventually converting most of the Māori population.[39] The Māori population declined to around 40% of its pre-contact level during the 19th century; introduced diseases were the major factor.[40]
+
+In 1788 Captain Arthur Phillip assumed the position of Governor of the new British colony of New South Wales which according to his commission included New Zealand.[41] The British Government appointed James Busby as British Resident to New Zealand in 1832 following a petition from northern Māori.[42] In 1835, following an announcement of impending French settlement by Charles de Thierry, the nebulous United Tribes of New Zealand sent a Declaration of Independence to King William IV of the United Kingdom asking for protection.[42] Ongoing unrest, the proposed settlement of New Zealand by the New Zealand Company (which had already sent its first ship of surveyors to buy land from Māori) and the dubious legal standing of the Declaration of Independence prompted the Colonial Office to send Captain William Hobson to claim sovereignty for the United Kingdom and negotiate a treaty with the Māori.[43] The Treaty of Waitangi was first signed in the Bay of Islands on 6 February 1840.[44] In response to the New Zealand Company's attempts to establish an independent settlement in Wellington[45] and French settlers purchasing land in Akaroa,[46] Hobson declared British sovereignty over all of New Zealand on 21 May 1840, even though copies of the Treaty were still circulating throughout the country for Māori to sign.[47] With the signing of the Treaty and declaration of sovereignty the number of immigrants, particularly from the United Kingdom, began to increase.[48]
+
+New Zealand, still part of the colony of New South Wales, became a separate Colony of New Zealand on 1 July 1841.[49] Armed conflict began between the Colonial government and
+Māori in 1843 with the Wairau Affray over land and disagreements over sovereignty. These conflicts, mainly in the North Island, saw thousands of imperial troops and the Royal Navy come to New Zealand and became known as the New Zealand Wars. Following these armed conflicts, large amounts of Māori land was confiscated by the government to meet settler demands.[50]
+
+The colony gained a representative government in 1852 and the first Parliament met in 1854.[51] In 1856 the colony effectively became self-governing, gaining responsibility over all domestic matters other than native policy.[51] (Control over native policy was granted in the mid-1860s.[51]) Following concerns that the South Island might form a separate colony, premier Alfred Domett moved a resolution to transfer the capital from Auckland to a locality near Cook Strait.[52] Wellington was chosen for its central location, with Parliament officially sitting there for the first time in 1865.[53]
+
+In 1891 the Liberal Party came to power as the first organised political party.[54] The Liberal Government, led by Richard Seddon for most of its period in office,[55] passed many important social and economic measures. In 1893 New Zealand was the first nation in the world to grant all women the right to vote[54] and in 1894 pioneered the adoption of compulsory arbitration between employers and unions.[56]
+
+In 1907, at the request of the New Zealand Parliament, King Edward VII proclaimed New Zealand a Dominion within the British Empire,[57] reflecting its self-governing status.[58] In 1947 the country adopted the Statute of Westminster, confirming that the British Parliament could no longer legislate for New Zealand without the consent of New Zealand.[51]
+
+Early in the 20th century, New Zealand was involved in world affairs, fighting in the First and Second World Wars[59] and suffering through the Great Depression.[60] The depression led to the election of the First Labour Government and the establishment of a comprehensive welfare state and a protectionist economy.[61] New Zealand experienced increasing prosperity following the Second World War[62] and Māori began to leave their traditional rural life and move to the cities in search of work.[63] A Māori protest movement developed, which criticised Eurocentrism and worked for greater recognition of Māori culture and of the Treaty of Waitangi.[64] In 1975, a Waitangi Tribunal was set up to investigate alleged breaches of the Treaty, and it was enabled to investigate historic grievances in 1985.[44] The government has negotiated settlements of these grievances with many iwi,[65] although Māori claims to the foreshore and seabed proved controversial in the 2000s.[66][67]
+
+New Zealand is a constitutional monarchy with a parliamentary democracy,[68] although its constitution is not codified.[69] Elizabeth II is the queen of New Zealand[70] and thus the head of state.[71] The queen is represented by the governor-general, whom she appoints on the advice of the prime minister.[72] The governor-general can exercise the Crown's prerogative powers, such as reviewing cases of injustice and making appointments of ministers, ambassadors and other key public officials,[73] and in rare situations, the reserve powers (e.g. the power to dissolve parliament or refuse the royal assent of a bill into law).[74] The powers of the monarch and the governor-general are limited by constitutional constraints and they cannot normally be exercised without the advice of ministers.[74]
+
+The New Zealand Parliament holds legislative power and consists of the queen and the House of Representatives.[75] It also included an upper house, the Legislative Council, until this was abolished in 1950.[75] The supremacy of parliament over the Crown and other government institutions was established in England by the Bill of Rights 1689 and has been ratified as law in New Zealand.[75] The House of Representatives is democratically elected and a government is formed from the party or coalition with the majority of seats. If no majority is formed, a minority government can be formed if support from other parties during confidence and supply votes is assured.[75] The governor-general appoints ministers under advice from the prime minister, who is by convention the parliamentary leader of the governing party or coalition.[76] Cabinet, formed by ministers and led by the prime minister, is the highest policy-making body in government and responsible for deciding significant government actions.[77] Members of Cabinet make major decisions collectively, and are therefore collectively responsible for the consequences of these decisions.[78]
+
+A parliamentary general election must be called no later than three years after the previous election.[79] Almost all general elections between 1853 and 1993 were held under the first-past-the-post voting system.[80] Since the 1996 election, a form of proportional representation called mixed-member proportional (MMP) has been used.[69] Under the MMP system, each person has two votes; one is for a candidate standing in the voter's electorate and the other is for a party. Since the 2014 election, there have been 71 electorates (which include seven Māori electorates in which only Māori can optionally vote),[81] and the remaining 49 of the 120 seats are assigned so that representation in parliament reflects the party vote, with the threshold that a party must win at least one electorate or 5% of the total party vote before it is eligible for a seat.[82]
+
+Elections since the 1930s have been dominated by two political parties, National and Labour.[80] Between March 2005 and August 2006, New Zealand became the first country in the world in which all the highest offices in the land—head of state, governor-general, prime minister, speaker and chief justice—were occupied simultaneously by women.[83] The current prime minister is Jacinda Ardern, who has been in office since 26 October 2017.[84] She is the country's third female prime minister.[85]
+
+New Zealand's judiciary, headed by the chief justice,[86] includes the Supreme Court, Court of Appeal, the High Court, and subordinate courts.[87] Judges and judicial officers are appointed non-politically and under strict rules regarding tenure to help maintain judicial independence.[69] This theoretically allows the judiciary to interpret the law based solely on the legislation enacted by Parliament without other influences on their decisions.[88]
+
+New Zealand is identified as one of the world's most stable and well-governed states.[89] As at 2017[update], the country was ranked fourth in the strength of its democratic institutions,[90] and first in government transparency and lack of corruption.[91] A 2017 Human Rights Report by the U.S. Department of State noted that the government generally respected the rights of individuals, but voiced concerns regarding the social status of the Māori population.[92] New Zealand ranks highly for civic participation in the political process, with 80% voter turnout during recent elections, compared to an OECD average of 68%.[93]
+
+Early colonial New Zealand allowed the British Government to determine external trade and be responsible for foreign policy.[94] The 1923 and 1926 Imperial Conferences decided that New Zealand should be allowed to negotiate its own political treaties and the first commercial treaty was ratified in 1928 with Japan. On 3 September 1939 New Zealand allied itself with Britain and declared war on Germany with Prime Minister Michael Joseph Savage proclaiming, "Where she goes, we go; where she stands, we stand."[95]
+
+In 1951 the United Kingdom became increasingly focused on its European interests,[96] while New Zealand joined Australia and the United States in the ANZUS security treaty.[97] The influence of the United States on New Zealand weakened following protests over the Vietnam War,[98] the refusal of the United States to admonish France after the sinking of the Rainbow Warrior,[99] disagreements over environmental and agricultural trade issues and New Zealand's nuclear-free policy.[100][101] Despite the United States' suspension of ANZUS obligations the treaty remained in effect between New Zealand and Australia, whose foreign policy has followed a similar historical trend.[102] Close political contact is maintained between the two countries, with free trade agreements and travel arrangements that allow citizens to visit, live and work in both countries without restrictions.[103] In 2013[update] there were about 650,000 New Zealand citizens living in Australia, which is equivalent to 15% of the resident population of New Zealand.[104]
+
+New Zealand has a strong presence among the Pacific Island countries. A large proportion of New Zealand's aid goes to these countries and many Pacific people migrate to New Zealand for employment.[105] Permanent migration is regulated under the 1970 Samoan Quota Scheme and the 2002 Pacific Access Category, which allow up to 1,100 Samoan nationals and up to 750 other Pacific Islanders respectively to become permanent New Zealand residents each year. A seasonal workers scheme for temporary migration was introduced in 2007 and in 2009 about 8,000 Pacific Islanders were employed under it.[106] New Zealand is involved in the Pacific Islands Forum, the Pacific Community, Asia-Pacific Economic Cooperation and the Association of Southeast Asian Nations Regional Forum (including the East Asia Summit).[103] New Zealand has been described as an emerging power.[107][108] The country is a member of the United Nations,[109] the Commonwealth of Nations[110] and the Organisation for Economic Co-operation and Development (OECD),[111] and participates in the Five Power Defence Arrangements.[112]
+
+New Zealand's military services—the Defence Force—comprise the New Zealand Army, the Royal New Zealand Air Force and the Royal New Zealand Navy.[113] New Zealand's national defence needs are modest, since a direct attack is unlikely.[114] However, its military has had a global presence. The country fought in both world wars, with notable campaigns in Gallipoli, Crete,[115] El Alamein[116] and Cassino.[117] The Gallipoli campaign played an important part in fostering New Zealand's national identity[118][119] and strengthened the ANZAC tradition it shares with Australia.[120]
+
+In addition to Vietnam and the two world wars, New Zealand fought in the Second Boer War,[121] the Korean War,[122] the Malayan Emergency,[123] the Gulf War and the Afghanistan War. It has contributed forces to several regional and global peacekeeping missions, such as those in Cyprus, Somalia, Bosnia and Herzegovina, the Sinai, Angola, Cambodia, the Iran–Iraq border, Bougainville, East Timor, and the Solomon Islands.[124]
+
+The early European settlers divided New Zealand into provinces, which had a degree of autonomy.[125] Because of financial pressures and the desire to consolidate railways, education, land sales and other policies, government was centralised and the provinces were abolished in 1876.[126] The provinces are remembered in regional public holidays[127] and sporting rivalries.[128]
+
+Since 1876, various councils have administered local areas under legislation determined by the central government.[125][129] In 1989, the government reorganised local government into the current two-tier structure of regional councils and territorial authorities.[130] The 249 municipalities[130] that existed in 1975 have now been consolidated into 67 territorial authorities and 11 regional councils.[131] The regional councils' role is to regulate "the natural environment with particular emphasis on resource management",[130] while territorial authorities are responsible for sewage, water, local roads, building consents and other local matters.[132][133] Five of the territorial councils are unitary authorities and also act as regional councils.[133] The territorial authorities consist of 13 city councils, 53 district councils, and the Chatham Islands Council. While officially the Chatham Islands Council is not a unitary authority, it undertakes many functions of a regional council.[134]
+
+The Realm of New Zealand, one of 16 Commonwealth realms,[135] is the entire area over which the queen of New Zealand is sovereign, and comprises New Zealand, Tokelau, the Ross Dependency, the Cook Islands and Niue.[68] The Cook Islands and Niue are self-governing states in free association with New Zealand.[136][137] The New Zealand Parliament cannot pass legislation for these countries, but with their consent can act on behalf of them in foreign affairs and defence. Tokelau is classified as a non-self-governing territory, but is administered by a council of three elders (one from each Tokelauan atoll).[138] The Ross Dependency is New Zealand's territorial claim in Antarctica, where it operates the Scott Base research facility.[139] New Zealand nationality law treats all parts of the realm equally, so most people born in New Zealand, the Cook Islands, Niue, Tokelau and the Ross Dependency are New Zealand citizens.[140][n 7]
+
+New Zealand is located near the centre of the water hemisphere and is made up of two main islands and a number of smaller islands. The two main islands (the North Island, or Te Ika-a-Māui, and the South Island, or Te Waipounamu) are separated by Cook Strait, 22 kilometres (14 mi) wide at its narrowest point.[142] Besides the North and South Islands, the five largest inhabited islands are Stewart Island (across the Foveaux Strait), Chatham Island, Great Barrier Island (in the Hauraki Gulf),[143] D'Urville Island (in the Marlborough Sounds)[144] and Waiheke Island (about 22 km (14 mi) from central Auckland).[145]
+
+New Zealand is long and narrow—over 1,600 kilometres (990 mi) along its north-north-east axis with a maximum width of 400 kilometres (250 mi)[146]—with about 15,000 km (9,300 mi) of coastline[147] and a total land area of 268,000 square kilometres (103,500 sq mi).[148] Because of its far-flung outlying islands and long coastline, the country has extensive marine resources. Its exclusive economic zone is one of the largest in the world, covering more than 15 times its land area.[149]
+
+The South Island is the largest landmass of New Zealand. It is divided along its length by the Southern Alps.[150] There are 18 peaks over 3,000 metres (9,800 ft), the highest of which is Aoraki / Mount Cook at 3,724 metres (12,218 ft).[151] Fiordland's steep mountains and deep fiords record the extensive ice age glaciation of this southwestern corner of the South Island.[152] The North Island is less mountainous but is marked by volcanism.[153] The highly active Taupo Volcanic Zone has formed a large volcanic plateau, punctuated by the North Island's highest mountain, Mount Ruapehu (2,797 metres (9,177 ft)). The plateau also hosts the country's largest lake, Lake Taupo,[154] nestled in the caldera of one of the world's most active supervolcanoes.[155]
+
+The country owes its varied topography, and perhaps even its emergence above the waves, to the dynamic boundary it straddles between the Pacific and Indo-Australian Plates.[156] New Zealand is part of Zealandia, a microcontinent nearly half the size of Australia that gradually submerged after breaking away from the Gondwanan supercontinent.[157][158] About 25 million years ago, a shift in plate tectonic movements began to contort and crumple the region. This is now most evident in the Southern Alps, formed by compression of the crust beside the Alpine Fault. Elsewhere the plate boundary involves the subduction of one plate under the other, producing the Puysegur Trench to the south, the Hikurangi Trench east of the North Island, and the Kermadec and Tonga Trenches[159] further north.[156]
+
+New Zealand is part of a region known as Australasia, together with Australia.[160] It also forms the southwestern extremity of the geographic and ethnographic region called Polynesia.[161] The term Oceania is often used to denote the wider region encompassing the Australian continent, New Zealand and various islands in the Pacific Ocean that are not included in the seven-continent model.[162]
+
+Rural scene near Queenstown
+
+The Emerald Lakes, Mt Tongariro
+
+Lake Gunn
+
+Pencarrow Head, Wellington
+
+New Zealand's climate is predominantly temperate maritime (Köppen: Cfb), with mean annual temperatures ranging from 10 °C (50 °F) in the south to 16 °C (61 °F) in the north.[163] Historical maxima and minima are 42.4 °C (108.32 °F) in Rangiora, Canterbury and −25.6 °C (−14.08 °F) in Ranfurly, Otago.[164] Conditions vary sharply across regions from extremely wet on the West Coast of the South Island to almost semi-arid in Central Otago and the Mackenzie Basin of inland Canterbury, and subtropical in Northland.[165][166] Of the seven largest cities, Christchurch is the driest, receiving on average only 640 millimetres (25 in) of rain per year and Wellington the wettest, receiving almost twice that amount.[167] Auckland, Wellington and Christchurch all receive a yearly average of more than 2,000 hours of sunshine. The southern and southwestern parts of the South Island have a cooler and cloudier climate, with around 1,400–1,600 hours; the northern and northeastern parts of the South Island are the sunniest areas of the country and receive about 2,400–2,500 hours.[168] The general snow season is early June until early October, though cold snaps can occur outside this season.[169] Snowfall is common in the eastern and southern parts of the South Island and mountain areas across the country.[163]
+
+The table below lists climate normals for the warmest and coldest months in New Zealand's six largest cities. North Island cities are generally warmest in February. South Island cities are warmest in January.
+
+New Zealand's geographic isolation for 80 million years[171] and island biogeography has influenced evolution of the country's species of animals, fungi and plants. Physical isolation has caused biological isolation, resulting in a dynamic evolutionary ecology with examples of very distinctive plants and animals as well as populations of widespread species.[172][173] About 82% of New Zealand's indigenous vascular plants are endemic, covering 1,944 species across 65 genera.[174][175] The number of fungi recorded from New Zealand, including lichen-forming species, is not known, nor is the proportion of those fungi which are endemic, but one estimate suggests there are about 2,300 species of lichen-forming fungi in New Zealand[174] and 40% of these are endemic.[176] The two main types of forest are those dominated by broadleaf trees with emergent podocarps, or by southern beech in cooler climates.[177] The remaining vegetation types consist of grasslands, the majority of which are tussock.[178]
+
+Before the arrival of humans, an estimated 80% of the land was covered in forest, with only high alpine, wet, infertile and volcanic areas without trees.[179] Massive deforestation occurred after humans arrived, with around half the forest cover lost to fire after Polynesian settlement.[180] Much of the remaining forest fell after European settlement, being logged or cleared to make room for pastoral farming, leaving forest occupying only 23% of the land.[181]
+
+The forests were dominated by birds, and the lack of mammalian predators led to some like the kiwi, kakapo, weka and takahē evolving flightlessness.[182] The arrival of humans, associated changes to habitat, and the introduction of rats, ferrets and other mammals led to the extinction of many bird species, including large birds like the moa and Haast's eagle.[183][184]
+
+Other indigenous animals are represented by reptiles (tuatara, skinks and geckos), frogs,[185] spiders,[186] insects (wētā)[187] and snails.[188] Some, such as the tuatara, are so unique that they have been called living fossils.[189] Three species of bats (one since extinct) were the only sign of native land mammals in New Zealand until the 2006 discovery of bones from a unique, mouse-sized land mammal at least 16 million years old.[190][191] Marine mammals however are abundant, with almost half the world's cetaceans (whales, dolphins, and porpoises) and large numbers of fur seals reported in New Zealand waters.[192] Many seabirds breed in New Zealand, a third of them unique to the country.[193] More penguin species are found in New Zealand than in any other country.[194]
+
+Since human arrival, almost half of the country's vertebrate species have become extinct, including at least fifty-one birds, three frogs, three lizards, one freshwater fish, and one bat. Others are endangered or have had their range severely reduced.[183] However, New Zealand conservationists have pioneered several methods to help threatened wildlife recover, including island sanctuaries, pest control, wildlife translocation, fostering and ecological restoration of islands and other protected areas.[195][196][197][198]
+
+New Zealand has an advanced market economy,[199] ranked 16th in the 2018[update] Human Development Index[8] and third in the 2018[update] Index of Economic Freedom.[200] It is a high-income economy with a nominal gross domestic product (GDP) per capita of US$36,254.[6] The currency is the New Zealand dollar, informally known as the "Kiwi dollar"; it also circulates in the Cook Islands (see Cook Islands dollar), Niue, Tokelau, and the Pitcairn Islands.[201]
+
+Historically, extractive industries have contributed strongly to New Zealand's economy, focussing at different times on sealing, whaling, flax, gold, kauri gum, and native timber.[202] The first shipment of refrigerated meat on the Dunedin in 1882 led to the establishment of meat and dairy exports to Britain, a trade which provided the basis for strong economic growth in New Zealand.[203] High demand for agricultural products from the United Kingdom and the United States helped New Zealanders achieve higher living standards than both Australia and Western Europe in the 1950s and 1960s.[204] In 1973, New Zealand's export market was reduced when the United Kingdom joined the European Economic Community[205] and other compounding factors, such as the 1973 oil and 1979 energy crises, led to a severe economic depression.[206] Living standards in New Zealand fell behind those of Australia and Western Europe, and by 1982 New Zealand had the lowest per-capita income of all the developed nations surveyed by the World Bank.[207] In the mid-1980s New Zealand deregulated its agricultural sector by phasing out subsidies over a three-year period.[208][209] Since 1984, successive governments engaged in major macroeconomic restructuring (known first as Rogernomics and then Ruthanasia), rapidly transforming New Zealand from a protected and highly regulated economy to a liberalised free-trade economy.[210][211]
+
+Unemployment peaked above 10% in 1991 and 1992,[213] following the 1987 share market crash, but eventually fell to a record low (since 1986) of 3.7% in 2007 (ranking third from twenty-seven comparable OECD nations).[213] However, the global financial crisis that followed had a major impact on New Zealand, with the GDP shrinking for five consecutive quarters, the longest recession in over thirty years,[214][215] and unemployment rising back to 7% in late 2009.[216] Unemployment rates for different age groups follow similar trends, but are consistently higher among youth. In the December 2014 quarter, the general unemployment rate was around 5.8%, while the unemployment rate for youth aged 15 to 21 was 15.6%.[213] New Zealand has experienced a series of "brain drains" since the 1970s[217] that still continue today.[218] Nearly one quarter of highly skilled workers live overseas, mostly in Australia and Britain, which is the largest proportion from any developed nation.[219] In recent decades, however, a "brain gain" has brought in educated professionals from Europe and less developed countries.[220][221] Today New Zealand's economy benefits from a high level of innovation.[222]
+
+New Zealand is heavily dependent on international trade,[223] particularly in agricultural products.[224] Exports account for 24% of its output,[147] making New Zealand vulnerable to international commodity prices and global economic slowdowns. Food products made up 55% of the value of all the country's exports in 2014; wood was the second largest earner (7%).[225] New Zealand's main trading partners, as at June 2018[update], are China (NZ$27.8b), Australia ($26.2b), the European Union ($22.9b), the United States ($17.6b), and Japan ($8.4b).[226] On 7 April 2008, New Zealand and China signed the New Zealand–China Free Trade Agreement, the first such agreement China has signed with a developed country.[227] The service sector is the largest sector in the economy, followed by manufacturing and construction and then farming and raw material extraction.[147] Tourism plays a significant role in the economy, contributing $12.9 billion (or 5.6%) to New Zealand's total GDP and supporting 7.5% of the total workforce in 2016.[228] International visitor arrivals are expected to increase at a rate of 5.4% annually up to 2022.[228]
+
+Wool was New Zealand's major agricultural export during the late 19th century.[202] Even as late as the 1960s it made up over a third of all export revenues,[202] but since then its price has steadily dropped relative to other commodities[229] and wool is no longer profitable for many farmers.[230] In contrast dairy farming increased, with the number of dairy cows doubling between 1990 and 2007,[231] to become New Zealand's largest export earner.[232] In the year to June 2018, dairy products accounted for 17.7% ($14.1 billion) of total exports,[226] and the country's largest company, Fonterra, controls almost one-third of the international dairy trade.[233] Other exports in 2017-18 were meat (8.8%), wood and wood products (6.2%), fruit (3.6%), machinery (2.2%) and wine (2.1%).[226] New Zealand's wine industry has followed a similar trend to dairy, the number of vineyards doubling over the same period,[234] overtaking wool exports for the first time in 2007.[235][236]
+
+In 2015, renewable energy generated 40.1% of New Zealand's gross energy supply.[237]  The majority of the country's electricity supply is generated from hydroelectric power, with major schemes on the Waikato, Waitaki and Clutha rivers, as well as at Manapouri. Geothermal power is also a significant generator of electricity, with several large stations located across the Taupo Volcanic Zone in the North Island. The five main companies in the generation and retail market are Contact Energy, Genesis Energy, Mercury Energy, Meridian Energy, and TrustPower. State-owned Transpower operates the high-voltage transmission grids in the North and South Islands, as well as the Inter-Island HVDC link connecting the two together.[237]
+
+The provision of water supply and sanitation is generally of good quality. Regional authorities provide water abstraction, treatment and distribution infrastructure to most developed areas.[238][239]
+
+New Zealand's transport network comprises 94,000 kilometres (58,410 mi) of roads, including 199 kilometres (124 mi) of motorways,[240] and 4,128 kilometres (2,565 mi) of railway lines.[147] Most major cities and towns are linked by bus services, although the private car is the predominant mode of transport.[241] The railways were privatised in 1993, but were re-nationalised by the government in stages between 2004 and 2008. The state-owned enterprise KiwiRail now operates the railways, with the exception of commuter services in Auckland and Wellington which are operated by Transdev[242] and Metlink,[243] respectively. Railways run the length of the country, although most lines now carry freight rather than passengers.[244] The road and rail networks in the two main islands are linked by roll-on/roll-off ferries between Wellington and Picton, operated by Interislander (part of KiwiRail) and Bluebridge. Most international visitors arrive via air[245] and New Zealand has six international airports, but currently[update] only the Auckland and Christchurch airports connect directly with countries other than Australia or Fiji.[246]
+
+The New Zealand Post Office had a monopoly over telecommunications in New Zealand until 1987 when Telecom New Zealand was formed, initially as a state-owned enterprise and then privatised in 1990.[247] Chorus, which was split from Telecom (now Spark) in 2011,[248] still owns the majority of the telecommunications infrastructure, but competition from other providers has increased.[247] A large-scale rollout of gigabit-capable fibre to the premises, branded as Ultra-Fast Broadband, began in 2009 with a target of being available to 87% of the population by 2022.[249] As of 2017[update], the United Nations International Telecommunication Union ranks New Zealand 13th in the development of information and communications infrastructure.[250]
+
+Early indigenous contribution to science in New Zealand was by Māori tohunga accumulating knowledge of agricultural practice and the effects of herbal remedies in the treatment of illness and disease. Cook's voyages in the 1700s and Darwin's in 1835 had important scientific botanical and zoological objectives.[251] The establishment of universities in the 19th century fostered scientific discoveries by notable New Zealanders including Ernest Rutherford for splitting the atom, William Pickering for rocket science, Maurice Wilkins for helping discover DNA, Beatrice Tinsley for galaxy formation, and Alan MacDiarmid for conducting polymers.[252]
+
+Crown Research Institutes (CRIs) were formed in 1992 from existing government-owned research organisations. Their role is to research and develop new science, knowledge, products and services across the economic, environmental, social and cultural spectrum for the benefit of New Zealand.[253] The total gross expenditure on research and development (R&D) as a proportion of GDP rose to 1.37% in 2018, up from 1.23% in 2015. New Zealand ranks 21st in the OECD for its gross R&D spending as a percentage of GDP.[254]
+
+The 2018 New Zealand census enumerated a resident population of 4,699,755, an increase of 10.8% over the 2013 figure.[3] As of July 2020, the total population has risen to an estimated 5,010,290.[n 8][5] In May 2020 Statistics New Zealand reported that New Zealand's population had climbed above 5 million people in March 2020.[256]
+
+New Zealand is a predominantly urban country, with 83.6% of the population living in urban areas, and 52.3% of the population living in the seven cities with populations exceeding 100,000.[257] Auckland, with over 1 million residents, is by far the largest city.[257] New Zealand cities generally rank highly on international livability measures. For instance, in 2016 Auckland was ranked the world's third most liveable city and Wellington the twelfth by the Mercer Quality of Living Survey.[258]
+
+Life expectancy for New Zealanders in 2012 was 84 years for females, and 80.2 years for males.[259] Life expectancy at birth is forecast to increase from 80 years to 85 years in 2050 and infant mortality is expected to decline.[260] New Zealand's fertility rate of 2.1 is relatively high for a developed country, and natural births account for a significant proportion of population growth. Consequently, the country has a young population compared to most industrialised nations, with 20% of New Zealanders being 14 years old or younger.[147] In 2018 the median age of the New Zealand population was 38.1 years.[261] By 2050 the median age is projected to rise to 43 years and the percentage of people 60 years of age and older to rise from 18% to 29%.[260] In 2008 the leading cause of premature death was cancer, at 29.8%, followed by ischaemic heart disease, 19.7%, and then cerebrovascular disease, 9.2%.[262] As of 2016[update], total expenditure on health care (including private sector spending) is 9.2% of GDP.[263]
+
+
+
+In the 2018 census, 71.8% of New Zealand residents identified ethnically as European, and 16.5% as Māori. Other major ethnic groups include Asian (15.3%) and Pacific peoples (9.0%), two-thirds of whom live in the Auckland Region.[n 3][3] The population has become more diverse in recent decades: in 1961, the census reported that the population of New Zealand was 92% European and 7% Māori, with Asian and Pacific minorities sharing the remaining 1%.[264]
+
+While the demonym for a New Zealand citizen is New Zealander, the informal "Kiwi" is commonly used both internationally[265] and by locals.[266] The Māori loanword Pākehā has been used to refer to New Zealanders of European descent, although some reject this name. The word Pākehā today is increasingly used to refer to all non-Polynesian New Zealanders.[267]
+
+The Māori were the first people to reach New Zealand, followed by the early European settlers. Following colonisation, immigrants were predominantly from Britain, Ireland and Australia because of restrictive policies similar to the White Australia policy.[268] There was also significant Dutch, Dalmatian,[269] German, and Italian immigration, together with indirect European immigration through Australia, North America, South America and South Africa.[270][271] Net migration increased after the Second World War; in the 1970s and 1980s policies were relaxed and immigration from Asia was promoted.[271][272] In 2009–10, an annual target of 45,000–50,000 permanent residence approvals was set by the New Zealand Immigration Service—more than one new migrant for every 100 New Zealand residents.[273] In the 2018 census, 27.4% of people counted were not born in New Zealand, up from 25.2% in the 2013 census. Over half (52.4%) of New Zealand's overseas-born population lives in the Auckland Region.[274] The United Kingdom remains the largest source of New Zealand's immigrant population, with around a quarter of all overseas-born New Zealanders born there; other major sources of New Zealand's overseas-born population are China, India, Australia, South Africa, Fiji and Samoa.[275] The number of fee-paying international students increased sharply in the late 1990s, with more than 20,000 studying in public tertiary institutions in 2002.[276]
+
+English is the predominant language in New Zealand, spoken by 95.4% of the population.[3] New Zealand English is similar to Australian English and many speakers from the Northern Hemisphere are unable to tell the accents apart.[278] The most prominent differences between the New Zealand English dialect and other English dialects are the shifts in the short front vowels: the short-"i" sound (as in "kit") has centralised towards the schwa sound (the "a" in "comma" and "about"); the short-"e" sound (as in "dress") has moved towards the short-"i" sound; and the short-"a" sound (as in "trap") has moved to the short-"e" sound.[279]
+
+After the Second World War, Māori were discouraged from speaking their own language (te reo Māori) in schools and workplaces and it existed as a community language only in a few remote areas.[280] It has recently undergone a process of revitalisation,[281] being declared one of New Zealand's official languages in 1987,[282] and is spoken by 4.0% of the population.[3][n 9] There are now Māori language immersion schools and two television channels that broadcast predominantly in Māori.[284] Many places have both their Māori and English names officially recognised.[285]
+
+As recorded in the 2018 census,[3] Samoan is the most widely spoken non-official language (2.2%), followed by "Northern Chinese" (including Mandarin, 2.0%), Hindi (1.5%), and French (1.2%). 22,986 people (0.5%) reported the ability to use New Zealand Sign Language, which became one of New Zealand's official languages in 2006.[286]
+
+Christianity is the predominant religion in New Zealand, although its society is among the most secular in the world.[288][289] In the 2018 census, 44.7% of respondents identified with one or more religions, including 37.0% identifying as Christians. Another 48.5% indicated that they had no religion.[n 10][3] Of those who affiliate with a particular Christian denomination, the main responses are Anglicanism (6.7%), Roman Catholicism (6.3%), and Presbyterianism (4.7%).[3] The Māori-based Ringatū and Rātana religions (1.2%) are also Christian in origin.[3][287] Immigration and demographic change in recent decades has contributed to the growth of minority religions, such as Hinduism (2.6%), Islam (1.3%), Buddhism (1.1%), and Sikhism (0.9%).[3] The Auckland Region exhibited the greatest religious diversity.[290]
+
+Primary and secondary schooling is compulsory for children aged 6 to 16, with the majority attending from the age of 5.[291] There are 13 school years and attending state (public) schools is free to New Zealand citizens and permanent residents from a person's 5th birthday to the end of the calendar year following their 19th birthday.[292] New Zealand has an adult literacy rate of 99%,[147] and over half of the population aged 15 to 29 hold a tertiary qualification.[291] There are five types of government-owned tertiary institutions: universities, colleges of education, polytechnics, specialist colleges, and wānanga,[293] in addition to private training establishments.[294] In the adult population 14.2% have a bachelor's degree or higher, 30.4% have some form of secondary qualification as their highest qualification and 22.4% have no formal qualification.[295] The OECD's Programme for International Student Assessment ranks New Zealand's education system as the seventh best in the world, with students performing exceptionally well in reading, mathematics and science.[296]
+
+Early Māori adapted the tropically based east Polynesian culture in line with the challenges associated with a larger and more diverse environment, eventually developing their own distinctive culture. Social organisation was largely communal with families (whānau), subtribes (hapū) and tribes (iwi) ruled by a chief (rangatira), whose position was subject to the community's approval.[297] The British and Irish immigrants brought aspects of their own culture to New Zealand and also influenced Māori culture,[298][299] particularly with the introduction of Christianity.[300] However, Māori still regard their allegiance to tribal groups as a vital part of their identity, and Māori kinship roles resemble those of other Polynesian peoples.[301] More recently American, Australian, Asian and other European cultures have exerted influence on New Zealand. Non-Māori Polynesian cultures are also apparent, with Pasifika, the world's largest Polynesian festival, now an annual event in Auckland.[302]
+
+The largely rural life in early New Zealand led to the image of New Zealanders being rugged, industrious problem solvers.[303] Modesty was expected and enforced through the "tall poppy syndrome", where high achievers received harsh criticism.[304] At the time New Zealand was not known as an intellectual country.[305] From the early 20th century until the late 1960s, Māori culture was suppressed by the attempted assimilation of Māori into British New Zealanders.[280] In the 1960s, as tertiary education became more available and cities expanded[306] urban culture began to dominate.[307] However, rural imagery and themes are common in New Zealand's art, literature and media.[308]
+
+New Zealand's national symbols are influenced by natural, historical, and Māori sources. The silver fern is an emblem appearing on army insignia and sporting team uniforms.[309] Certain items of popular culture thought to be unique to New Zealand are called "Kiwiana".[309]
+
+As part of the resurgence of Māori culture, the traditional crafts of carving and weaving are now more widely practised and Māori artists are increasing in number and influence.[310] Most Māori carvings feature human figures, generally with three fingers and either a natural-looking, detailed head or a grotesque head.[311] Surface patterns consisting of spirals, ridges, notches and fish scales decorate most carvings.[312] The pre-eminent Māori architecture consisted of carved meeting houses (wharenui) decorated with symbolic carvings and illustrations. These buildings were originally designed to be constantly rebuilt, changing and adapting to different whims or needs.[313]
+
+Māori decorated the white wood of buildings, canoes and cenotaphs using red (a mixture of red ochre and shark fat) and black (made from soot) paint and painted pictures of birds, reptiles and other designs on cave walls.[314] Māori tattoos (moko) consisting of coloured soot mixed with gum were cut into the flesh with a bone chisel.[315] Since European arrival paintings and photographs have been dominated by landscapes, originally not as works of art but as factual portrayals of New Zealand.[316] Portraits of Māori were also common, with early painters often portraying them as "noble savages", exotic beauties or friendly natives.[316] The country's isolation delayed the influence of European artistic trends allowing local artists to develop their own distinctive style of regionalism.[317] During the 1960s and 1970s many artists combined traditional Māori and Western techniques, creating unique art forms.[318] New Zealand art and craft has gradually achieved an international audience, with exhibitions in the Venice Biennale in 2001 and the "Paradise Now" exhibition in New York in 2004.[310][319]
+
+Māori cloaks are made of fine flax fibre and patterned with black, red and white triangles, diamonds and other geometric shapes.[320] Greenstone was fashioned into earrings and necklaces, with the most well-known design being the hei-tiki, a distorted human figure sitting cross-legged with its head tilted to the side.[321] Europeans brought English fashion etiquette to New Zealand, and until the 1950s most people dressed up for social occasions.[322] Standards have since relaxed and New Zealand fashion has received a reputation for being casual, practical and lacklustre.[323][324] However, the local fashion industry has grown significantly since 2000, doubling exports and increasing from a handful to about 50 established labels, with some labels gaining international recognition.[324]
+
+Māori quickly adopted writing as a means of sharing ideas, and many of their oral stories and poems were converted to the written form.[325] Most early English literature was obtained from Britain and it was not until the 1950s when local publishing outlets increased that New Zealand literature started to become widely known.[326] Although still largely influenced by global trends (modernism) and events (the Great Depression), writers in the 1930s began to develop stories increasingly focused on their experiences in New Zealand. During this period literature changed from a journalistic activity to a more academic pursuit.[327] Participation in the world wars gave some New Zealand writers a new perspective on New Zealand culture and with the post-war expansion of universities local literature flourished.[328] Dunedin is a UNESCO City of Literature.[329]
+
+New Zealand music has been influenced by blues, jazz, country, rock and roll and hip hop, with many of these genres given a unique New Zealand interpretation.[330] Māori developed traditional chants and songs from their ancient Southeast Asian origins, and after centuries of isolation created a unique "monotonous" and "doleful" sound.[331] Flutes and trumpets were used as musical instruments[332] or as signalling devices during war or special occasions.[333] Early settlers brought over their ethnic music, with brass bands and choral music being popular, and musicians began touring New Zealand in the 1860s.[334][335] Pipe bands became widespread during the early 20th century.[336] The New Zealand recording industry began to develop from 1940 onwards and many New Zealand musicians have obtained success in Britain and the United States.[330] Some artists release Māori language songs and the Māori tradition-based art of kapa haka (song and dance) has made a resurgence.[337] The New Zealand Music Awards are held annually by Recorded Music NZ; the awards were first held in 1965 by Reckitt & Colman as the Loxene Golden Disc awards.[338] Recorded Music NZ also publishes the country's official weekly record charts.[339]
+
+Public radio was introduced in New Zealand in 1922.[341] A state-owned television service began in 1960.[342] Deregulation in the 1980s saw a sudden increase in the numbers of radio and television stations.[343] New Zealand television primarily broadcasts American and British programming, along with many Australian and local shows.[344] The number of New Zealand films significantly increased during the 1970s. In 1978 the New Zealand Film Commission started assisting local film-makers and many films attained a world audience, some receiving international acknowledgement.[343] The highest-grossing New Zealand films are Hunt for the Wilderpeople, Boy, The World's Fastest Indian, Whale Rider, Once Were Warriors and The Piano.[345] The country's diverse scenery and compact size, plus government incentives,[346] have encouraged some producers to shoot big-budget productions in New Zealand, including The Lord of the Rings and The Hobbit film trilogies, Avatar, The Chronicles of Narnia, King Kong, Wolverine and The Last Samurai.[347] The New Zealand media industry is dominated by a small number of companies, most of which are foreign-owned, although the state retains ownership of some television and radio stations.[348] Since 1994, Freedom House has consistently ranked New Zealand's press freedom in the top twenty, with the 19th freest media in 2015[update].[349]
+
+Most of the major sporting codes played in New Zealand have British origins.[350] Rugby union is considered the national sport[351] and attracts the most spectators.[352] Golf, netball, tennis and cricket have the highest rates of adult participation, while netball, rugby union and football (soccer) are particularly popular among young people.[352][353] Around 54% of New Zealand adolescents participate in sports for their school.[353] Victorious rugby tours to Australia and the United Kingdom in the late 1880s and the early 1900s played an early role in instilling a national identity.[354] Horseracing was also a popular spectator sport and became part of the "Rugby, Racing and Beer" culture during the 1960s.[355] Māori participation in European sports was particularly evident in rugby and the country's team performs a haka, a traditional Māori challenge, before international matches.[356] New Zealand is known for its extreme sports, adventure tourism[357] and strong mountaineering tradition, as seen in the success of notable New Zealander Sir Edmund Hillary.[358][359] Other outdoor pursuits such as cycling, fishing, swimming, running, tramping, canoeing, hunting, snowsports, surfing and sailing are also popular.[360] New Zealand has seen regular sailing success in the America's Cup regatta since 1995.[361] The Polynesian sport of waka ama racing has experienced a resurgence of interest in New Zealand since the 1980s.[362]
+
+New Zealand has competitive international teams in rugby union, rugby league, netball, cricket, softball, and sailing. New Zealand participated at the Summer Olympics in 1908 and 1912 as a joint team with Australia, before first participating on its own in 1920.[363] The country has ranked highly on a medals-to-population ratio at recent Games.[364][365] The "All Blacks", the national rugby union team, are the most successful in the history of international rugby[366] and have won the World Cup three times.[367]
+
+The national cuisine has been described as Pacific Rim, incorporating the native Māori cuisine and diverse culinary traditions introduced by settlers and immigrants from Europe, Polynesia and Asia.[368] New Zealand yields produce from land and sea—most crops and livestock, such as maize, potatoes and pigs, were gradually introduced by the early European settlers.[369] Distinctive ingredients or dishes include lamb, salmon, kōura (crayfish),[370] dredge oysters, whitebait, pāua (abalone), mussels, scallops, pipis and tuatua (both are types of New Zealand shellfish),[371] kūmara (sweet potato), kiwifruit, tamarillo and pavlova (considered a national dish).[372][368] A hāngi is a traditional Māori method of cooking food using heated rocks buried in a pit oven. After European colonisation, Māori began cooking with pots and ovens and the hāngi was used less frequently, although it is still used for formal occasions such as tangihanga.[373]
+
+Click on a coloured area to see an article about English in that country or region

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+November is the eleventh month of the year in the Julian and Gregorian Calendars, the fourth and last of four months to have a length of 30 days and the fifth and last of five months to have a length of fewer than 31 days. November was the ninth month of the calendar of Romulus c. 750 BC. November retained its name (from the Latin novem meaning "nine") when January and February were added to the Roman calendar.
+November is a month of late spring in the Southern Hemisphere and late autumn in the Northern Hemisphere. Therefore, November in the Southern Hemisphere is the seasonal equivalent of May in the Northern Hemisphere and vice versa. In Ancient Rome, Ludi Plebeii was held from November 4–17, Epulum Jovis was held on November 13 and Brumalia celebrations began on November 24. These dates do not correspond to the modern Gregorian calendar.
+
+November was referred to as Blōtmōnaþ by the Anglo-Saxons. Brumaire and Frimaire were the months on which November fell in the French Republican Calendar.
+
+November meteor showers include the Andromedids, which occurs from September 25 to December 6 and generally peak around November 9–14, the Leonids, which occurs from November 15–20, the Alpha Monocerotids, which occurs from November 15–25 with the peak on November 21–22, the Northern Taurids, which occurs from October 20 to December 10, and the Southern Taurids, which occurs from September 10 – November 20, and the Phoenicids; which occur from November 29 to December 9 with the peak occurring on December 5–6. The Orionids, which occurs in late October, sometimes lasts into November.
+
+The Western zodiac signs, for the month of November, are Scorpio (October 23 – November 21) and Sagittarius (November 22 – December 21).[1][2]
+
+This list does not necessarily imply either official status or general observance.
+
+(All Baha'i, Islamic, and Jewish observances begin at the sundown prior to the date listed, and end at sundown of the date in question unless otherwise noted.)
+
+First Sunday: November 1
+
+First Monday: November 2
+
+Tuesday after the first Monday: November 3
+
+First Wednesday: November 4
+
+First Thursday: November 5
+
+First Friday: November 6
+
+First Saturday: November 7
+
+Second Sunday: November 8
+
+Week of November 8: November 8–14
+
+Week of November 11: November 8–14
+
+Second Monday: November 9
+
+Second Thursday: November 12
+
+The 13th when falling on a Friday: November 13
+
+Second Saturday: November 14
+
+Third Sunday: November 15
+
+Third week: November 15–21
+
+Third Monday: November 16
+
+Weekdays of the third week: November 16–20
+
+Wednesday of the third week: November 18
+
+Third Thursday: November 19
+
+Third Friday: November 20
+
+Third Friday until the next Monday: November 20–22
+
+Saturday before Fourth Thursday: November 21
+
+Last Week: November 22–28
+
+Day before fourth Thursday: November 25
+
+Last Wednesday: November 25
+
+Fourth Thursday: November 26
+
+Day after fourth Thursday: November 27
+
+Fourth Saturday: November 28
+
+Saturday after Thanksgiving: November 28
+
+Fourth Sunday: November 29
+
+Last Sunday: November 29
+
+Monday after fourth Thursday in November: November 30

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+
+
+
+
+An astronaut or cosmonaut is a person trained by a human spaceflight program to command, pilot, or serve as a crew member of a spacecraft. Although generally reserved for professional space travelers, the terms are sometimes applied to anyone who travels into space, including scientists, politicians, journalists and tourists.[1][2]
+The root "naut" derives from "nautes", the Greek for "sailor."
+[3]
+
+Until 2002, astronauts were sponsored and trained exclusively by governments, either by the military or by civilian space agencies. With the suborbital flight of the privately funded SpaceShipOne in 2004, a new category of astronaut was created: the commercial astronaut.
+
+The criteria for what constitutes human spaceflight vary, with some focus on the point where the atmosphere becomes so thin that centrifugal force, rather than aerodynamic force, carries a significant portion of the weight of the flight object. The Fédération Aéronautique Internationale (FAI) Sporting Code for astronautics recognizes only flights that exceed the Kármán line, at an altitude of 100 kilometers (62 mi).[4] In the United States, professional, military, and commercial astronauts who travel above an altitude of 50 miles (80 km)[5] are awarded astronaut wings.
+
+As of 17 November 2016[update], a total of 552 people from 36 countries have reached 100 km (62 mi) or more in altitude, of whom 549 reached low Earth orbit or beyond.[6]
+Of these, 24 people have traveled beyond low Earth orbit, either to lunar orbit, the lunar surface, or, in one case, a loop around the Moon.[7] Three of the 24—Jim Lovell, John Young and Eugene Cernan—did so twice.[8]
+
+As of 17 November 2016[update], under the U.S. definition, 558 people qualify as having reached space, above 50 miles (80 km) altitude. Of eight X-15 pilots who exceeded 50 miles (80 km) in altitude, only one exceeded 100 kilometers (about 62 miles).[6] Space travelers have spent over 41,790 man-days (114.5 man-years) in space, including over 100 astronaut-days of spacewalks.[9][10] As of 2016[update], the man with the longest cumulative time in space is Gennady Padalka, who has spent 879 days in space.[11] Peggy A. Whitson holds the record for the most time in space by a woman, 377 days.[12]
+
+In 1959, when both the United States and Soviet Union were planning, but had yet to launch humans into space, NASA Administrator T. Keith Glennan and his Deputy Administrator, Dr. Hugh Dryden, discussed whether spacecraft crew members should be called astronauts or cosmonauts. Dryden preferred "cosmonaut", on the grounds that flights would occur in the cosmos (near space), while the "astro" prefix suggested flight to the stars. Most NASA Space Task Group members preferred "astronaut", which survived by common usage as the preferred American term.[13] When the Soviet Union launched the first man into space, Yuri Gagarin in 1961, they chose a term which anglicizes to "cosmonaut".
+
+In English-speaking nations, a professional space traveler is called an astronaut.[14] The term derives from the Greek words ástron (ἄστρον), meaning "star", and nautes (ναύτης), meaning "sailor". The first known use of the term "astronaut" in the modern sense was by Neil R. Jones in his 1930 short story "The Death's Head Meteor". The word itself had been known earlier; for example, in Percy Greg's 1880 book Across the Zodiac, "astronaut" referred to a spacecraft. In Les Navigateurs de l'Infini (1925) by J.-H. Rosny aîné, the word astronautique (astronautic) was used. The word may have been inspired by "aeronaut", an older term for an air traveler first applied in 1784 to balloonists. An early use of "astronaut" in a non-fiction publication is Eric Frank Russell's poem "The Astronaut", appearing in the November 1934 Bulletin of the British Interplanetary Society.[15]
+
+The first known formal use of the term astronautics in the scientific community was the establishment of the annual International Astronautical Congress in 1950, and the subsequent founding of the International Astronautical Federation the following year.[16]
+
+NASA applies the term astronaut to any crew member aboard NASA spacecraft bound for Earth orbit or beyond. NASA also uses the term as a title for those selected to join its Astronaut Corps.[17] The European Space Agency similarly uses the term astronaut for members of its Astronaut Corps.[18]
+
+By convention, an astronaut employed by the Russian Federal Space Agency (or its Soviet predecessor) is called a cosmonaut in English texts.[17] The word is an anglicisation of the Russian word kosmonavt (Russian: космонавт, Russian pronunciation: [kəsmɐˈnaft]), one who works in space outside the Earth's atmosphere, a space traveler,[19] which derives from the Greek words kosmos (κόσμος), meaning "universe", and nautes (ναύτης), meaning "sailor". Other countries of the former Eastern Bloc use variations of the Russian word kosmonavt, such as the Polish kosmonauta (although Polish also uses astronauta, and the two words are considered synonyms).[20]
+
+Coinage of the term kosmonavt has been credited to Soviet aeronautics (or "cosmonautics") pioneer Mikhail Tikhonravov (1900–1974).[21][22] The first cosmonaut was Soviet Air Force pilot Yuri Gagarin, also the first person in space. He was part of the first six Russians, with German Titov, Yevgeny Khrunov, Andriyan Nikolayev, Pavel Popovich, and Grigoriy Nelyubov, who were given the title of pilot-cosmonaut in January 1961.[23] Valentina Tereshkova was the first female cosmonaut and the first and youngest woman to have flown in space with a solo mission on the Vostok 6 in 1963.[24] On March 14, 1995,[25] Norman Thagard became the first American to ride to space on board a Russian launch vehicle, and thus became the first "American cosmonaut".[26][27]
+
+Yǔ háng yuán (宇航员, "Space-universe navigating personnel") is used for astronauts and cosmonauts in general,[28][29] while hángtiān yuán (航天员, "navigating outer space personnel") is used for Chinese astronauts. Here, hángtiān (航天) is strictly defined as the navigation of outer space within the local star system, i.e. solar system. The phrase tài kōng rén (太空人, "spaceman") is often used in Hong Kong and Taiwan.[30]
+
+The term taikonaut is used by some English-language news media organizations for professional space travelers from China.[31] The word has featured in the Longman and Oxford English dictionaries, the latter of which describes it as a hybrid of the Chinese term Chinese: 太空 (tàikōng, 'space') and the Greek ναύτης (naútēs, 'sailor'); the term became more common in 2003 when China sent its first astronaut Yang Liwei into space aboard the Shenzhou 5 spacecraft.[32] This is the term used by Xinhua News Agency in the English version of the Chinese People's Daily since the advent of the Chinese space program.[33] The origin of the term is unclear; as early as May 1998, Chiew Lee Yih (趙裡昱) from Malaysia, used it in newsgroups.[34][35]
+
+With the rise of space tourism, NASA and the Russian Federal Space Agency agreed to use the term "spaceflight participant" to distinguish those space travelers from professional astronauts on missions coordinated by those two agencies.
+
+While no nation other than Russia (and previously the Soviet Union), the United States, and China have launched a manned spacecraft, several other nations have sent people into space in cooperation with one of these countries, i.e. the Soviet-led Interkosmos programme. Inspired partly by these missions, other synonyms for astronaut have entered occasional English usage. For example, the term spationaut (French spelling: spationaute) is sometimes used to describe French space travelers, from the Latin word spatium for "space", the Malay term angkasawan was used to describe participants in the Angkasawan program, and the Indian Space Research Organisation hope to launch a spacecraft in 2022 that would carry vyomanauts, coined from the Sanskrit word व्योमन् (vyoman meaning 'sky' or 'space'). In Finland, the NASA astronaut Timothy Kopra, a Finnish American, has sometimes been referred to as sisunautti, from the Finnish word sisu.[36]
+
+As of 2020 in the United States, astronaut status is conferred on a person depending on the authorizing agency:
+
+The first human in space was Soviet Yuri Gagarin, who was launched on April 12, 1961, aboard Vostok 1 and orbited around the Earth for 108 minutes. The first woman in space was Soviet Valentina Tereshkova, who launched on June 16, 1963, aboard Vostok 6 and orbited Earth for almost three days.
+
+Alan Shepard became the first American and second person in space on May 5, 1961, on a 15-minute sub-orbital flight aboard Freedom 7. The first American to orbit the Earth was John Glenn, aboard Friendship 7 on February 20, 1962. The first American woman in space was Sally Ride, during Space Shuttle Challenger's mission STS-7, on June 18, 1983.[39] In 1992 Mae Jemison became the first African American woman to travel in space aboard STS-47.
+
+Cosmonaut Alexei Leonov was the first person to conduct an extravehicular activity (EVA), (commonly called a "spacewalk"), on March 18, 1965, on the Soviet Union's Voskhod 2 mission.  This was followed two and a half months later by astronaut Ed White who made the first American EVA on NASA's Gemini 4 mission.[40]
+
+The first manned mission to orbit the Moon, Apollo 8, included American William Anders who was born in Hong Kong, making him the first Asian-born astronaut in 1968.
+
+The Soviet Union, through its Intercosmos program, allowed people from other "socialist" (i.e. Warsaw Pact and other Soviet-allied) countries to fly on its missions, with the notable exceptions of France and Austria participating in Soyuz TM-7 and Soyuz TM-13, respectively. An example is Czechoslovak Vladimír Remek, the first cosmonaut from a country other than the Soviet Union or the United States, who flew to space in 1978 on a Soyuz-U rocket.[41] Rakesh Sharma became the first Indian citizen to travel to space. He was launched aboard Soyuz T-11, on April 2, 1984.
+
+On July 23, 1980, Pham Tuan of Vietnam became the first Asian in space when he flew aboard Soyuz 37.[42] Also in 1980, Cuban Arnaldo Tamayo Méndez became the first person of Hispanic and black African descent to fly in space, and in 1983, Guion Bluford became the first African American to fly into space. In April 1985, Taylor Wang became the first ethnic Chinese person in space.[43][44] The first person born in Africa to fly in space was Patrick Baudry (France), in 1985.[45][46] In 1985, Saudi Arabian Prince Sultan Bin Salman Bin AbdulAziz Al-Saud became the first Arab Muslim astronaut in space.[47] In 1988, Abdul Ahad Mohmand became the first Afghan to reach space, spending nine days aboard the Mir space station.[48]
+
+With the increase of seats on the Space Shuttle, the U.S. began taking international astronauts. In 1983, Ulf Merbold of West Germany became the first non-US citizen to fly in a US spacecraft.  In 1984, Marc Garneau became the first of 8 Canadian astronauts to fly in space (through 2010).[49]
+In 1985, Rodolfo Neri Vela became the first Mexican-born person in space.[50] In 1991, Helen Sharman became the first Briton to fly in space.[51]
+In 2002, Mark Shuttleworth became the first citizen of an African country to fly in space, as a paying spaceflight participant.[52] In 2003, Ilan Ramon became the first Israeli to fly in space, although he died during a re-entry accident.
+
+On October 15, 2003, Yang Liwei became China's first astronaut on the Shenzhou 5 spacecraft.
+
+The youngest person to fly in space is Gherman Titov, who was 25 years old when he flew Vostok 2. (Titov was also the first person to suffer space sickness).[53][54]
+The oldest person who has flown in space is John Glenn, who was 77 when he flew on STS-95.[55]
+
+438 days is the longest time spent in space, by Russian Valeri Polyakov.[9]
+As of 2006, the most spaceflights by an individual astronaut is seven, a record held by both Jerry L. Ross and Franklin Chang-Diaz. The farthest distance from Earth an astronaut has traveled was 401,056 km (249,205 mi), when Jim Lovell, Jack Swigert, and Fred Haise went around the Moon during the Apollo 13 emergency.[9]
+
+The first civilian in space was Valentina Tereshkova[56] aboard Vostok 6 (she also became the first woman in space on that mission).
+Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the 100 kilometers (54 nautical miles) line, qualifying him by the international definition of spaceflight.[57][58] Walker had joined the US Army Air Force but was not a member during his flight. 
+The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
+
+The first non-governmental space traveler was Byron K. Lichtenberg, a researcher from the Massachusetts Institute of Technology who flew on STS-9 in 1983.[59] In December 1990, Toyohiro Akiyama became the first paying space traveler as a reporter for Tokyo Broadcasting System, a visit to Mir as part of an estimated $12 million (USD) deal with a Japanese TV station, although at the time, the term used to refer to Akiyama was "Research Cosmonaut".[60][61][62] Akiyama suffered severe space sickness during his mission, which affected his productivity.[61]
+
+The first self-funded space tourist was Dennis Tito on board the Russian spacecraft Soyuz TM-3 on April 28, 2001.
+
+The first person to fly on an entirely privately funded mission was Mike Melvill, piloting SpaceShipOne flight 15P on a suborbital journey, although he was a test pilot employed by Scaled Composites and not an actual paying space tourist.[63][64] Seven others have paid the Russian Space Agency to fly into space:
+
+The first NASA astronauts were selected for training in 1959.[65] Early in the space program, military jet test piloting and engineering training were often cited as prerequisites for selection as an astronaut at NASA, although neither John Glenn nor Scott Carpenter (of the Mercury Seven) had any university degree, in engineering or any other discipline at the time of their selection.  Selection was initially limited to military pilots.[66][67] The earliest astronauts for both America and the USSR tended to be jet fighter pilots, and were often test pilots.
+
+Once selected, NASA astronauts go through twenty months of training in a variety of areas, including training for extravehicular activity in a facility such as NASA's Neutral Buoyancy Laboratory.[1][66] Astronauts-in-training (astronaut candidates) may also experience short periods of weightlessness (microgravity) in an aircraft called the "Vomit Comet," the nickname given to a pair of modified KC-135s (retired in 2000 and 2004, respectively, and replaced in 2005 with a C-9) which perform parabolic flights.[65] Astronauts are also required to accumulate a number of flight hours in high-performance jet aircraft. This is mostly done in T-38 jet aircraft out of Ellington Field, due to its proximity to the Johnson Space Center.  Ellington Field is also where the Shuttle Training Aircraft is maintained and developed, although most flights of the aircraft are conducted from Edwards Air Force Base.
+
+Astronauts in training must learn how to control and fly the Space Shuttle and, it is vital that they are familiar with the International Space Station so they know what they must do when they get there.[68]
+
+Mission Specialist Educators, or "Educator Astronauts", were first selected in 2004, and as of 2007, there are three NASA Educator astronauts: Joseph M. Acaba, Richard R. Arnold, and Dorothy Metcalf-Lindenburger.[72][73]
+Barbara Morgan, selected as back-up teacher to Christa McAuliffe in 1985, is considered to be the first Educator astronaut by the media, but she trained as a mission specialist.[74]
+The Educator Astronaut program is a successor to the Teacher in Space program from the 1980s.[75][76]
+
+Astronauts are susceptible to a variety of health risks including decompression sickness, barotrauma, immunodeficiencies, loss of bone and muscle, loss of eyesight, orthostatic intolerance, sleep disturbances, and radiation injury.[77][78][79][80][81][82][83][84][85][86] A variety of large scale medical studies are being conducted in space via the National Space and Biomedical Research Institute (NSBRI) to address these issues. Prominent among these is the Advanced Diagnostic Ultrasound in Microgravity Study in which astronauts (including former ISS commanders Leroy Chiao and Gennady Padalka) perform ultrasound scans under the guidance of remote experts to diagnose and potentially treat hundreds of medical conditions in space. This study's techniques are now being applied to cover professional and Olympic sports injuries as well as ultrasound performed by non-expert operators in medical and high school students. It is anticipated that remote guided ultrasound will have application on Earth in emergency and rural care situations, where access to a trained physician is often rare.[87][88][89]
+
+A 2006 Space Shuttle experiment found that Salmonella typhimurium, a bacterium that can cause food poisoning, became more virulent when cultivated in space.[90] More recently, in 2017, bacteria were found to be more resistant to antibiotics and to thrive in the near-weightlessness of space.[91] Microorganisms have been observed to survive the vacuum of outer space.[92][93]
+
+On December 31, 2012, a NASA-supported study reported that human spaceflight may harm the brain and accelerate the onset of Alzheimer's disease.[94][95][96]
+
+In October 2015, the NASA Office of Inspector General issued a health hazards report related to space exploration, including a human mission to Mars.[97][98]
+
+Over the last decade, flight surgeons and scientists at NASA have seen a pattern of vision problems in astronauts on long-duration space missions. The syndrome, known as visual impairment intracranial pressure (VIIP), has been reported in nearly two-thirds of space explorers after long periods spent aboard the International Space Station (ISS).
+
+On November 2, 2017, scientists reported that significant changes in the position and structure of the brain have been found in astronauts who have taken trips in space, based on MRI studies. Astronauts who took longer space trips were associated with greater brain changes.[99][100]
+
+Being in space can be physiologically deconditioning on the body. It can affect the otolith organs and adaptive capabilities of the central nervous system. Zero gravity and cosmic rays can cause many implications for astronauts.[101]
+
+In October 2018, NASA-funded researchers found that lengthy journeys into outer space, including travel to the planet Mars, may substantially damage the gastrointestinal tissues of astronauts. The studies support earlier work that found such journeys could significantly damage the brains of astronauts, and age them prematurely.[102]
+
+Researchers in 2018 reported, after detecting the presence on the International Space Station (ISS) of five Enterobacter bugandensis bacterial strains, none pathogenic to humans, that microorganisms on ISS should be carefully monitored to continue assuring a medically healthy environment for astronauts.[103][104]
+
+A recent study by Russian scientists published in April 2019 stated that astronauts facing space radiation could face temporary hindrance of their memory centres. While this does not affect their intellectual capabilities, it temporarily hinders formation of new cells in brain's memory centers. The study conducted by Moscow Institute of Physics and Technology (MIPT) concluded this after they observed that mice exposed to neutron and gamma radiation did not impact the rodents' intellectual capabilities.[105]
+
+An astronaut on the International Space Station requires about 830 g (29 oz) mass of food inclusive of food packaging per meal each day. (The packaging mass for each meal is about 120 g or 4.2 oz) Longer-duration missions require more food.
+
+Shuttle astronauts worked with nutritionists to select menus that appeal to their individual tastes. Five months before flight, menus are selected and analyzed for nutritional content by the shuttle dietician. Foods are tested to see how they will react in a reduced gravity environment.  Caloric requirements are determined using a basal energy expenditure (BEE) formula.
+On Earth, the average American uses about 35 US gallons (130 L) of water every day.  On board the ISS astronauts limit water use to only about three US gallons (11 L) per day.[106]
+
+In Russia, cosmonauts are awarded Pilot-Cosmonaut of the Russian Federation upon completion of their missions, often accompanied with the award of Hero of the Russian Federation.  This follows the practice established in the USSR where cosmonauts were usually awarded the title Hero of the Soviet Union.
+
+At NASA, those who complete astronaut candidate training receive a silver lapel pin. Once they have flown in space, they receive a gold pin. U.S. astronauts who also have active-duty military status receive a special qualification badge, known as the Astronaut Badge, after participation on a spaceflight. The United States Air Force also presents an Astronaut Badge to its pilots who exceed 50 miles (80 km) in altitude.
+
+Eighteen astronauts (fourteen men and four women) have lost their lives during four space flights. By nationality, thirteen were American (including one born in India), four were Russian (Soviet Union), and one was Israeli.
+
+Eleven people (all men) have lost their lives training for spaceflight: eight Americans and three Russians. Six of these were in crashes of training jet aircraft, one drowned during water recovery training, and four were due to fires in pure oxygen environments.
+
+The Space Mirror Memorial, which stands on the grounds of the John F. Kennedy Space Center Visitor Complex, commemorates the lives of the men and women who have died during spaceflight and during training in the space programs of the United States. In addition to twenty NASA career astronauts, the memorial includes the names of a U.S. Air Force X-15 test pilot, a U.S. Air Force officer who died while training for a then-classified military space program, and a civilian spaceflight participant.

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+
+
+An atom is the smallest constituent unit of ordinary matter that constitutes a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small, typically around 100 picometers across. They are so small that accurately predicting their behavior using classical physics – as if they were billiard balls, for example – is not possible due to quantum effects. Current atomic models use quantum principles to better explain and predict this behavior.
+
+Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, then the atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively. These atoms are called ions.
+
+The electrons of an atom are attracted to the protons in an atomic nucleus by the electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by the nuclear force. This force is usually stronger than the electromagnetic force that repels the positively charged protons from one another. Under certain circumstances, the repelling electromagnetic force becomes stronger than the nuclear force. In this case, the nucleus splits and leaves behind different elements. This is a form of nuclear decay.
+
+The number of protons in the nucleus is the atomic number and it defines to which chemical element the atom belongs. For example, any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element. Atoms can attach to one or more other atoms by chemical bonds to form chemical compounds such as molecules or crystals. The ability of atoms to associate and dissociate is responsible for most of the physical changes observed in nature. Chemistry is the discipline that studies these changes.
+
+The basic idea that matter is made up of tiny indivisible particles is very old, appearing in many ancient cultures such as Greece and India. The word atomos, meaning "uncuttable", was coined by the ancient Greek philosophers Leucippus and his pupil Democritus (5th century BC). These ancient ideas were not based on scientific reasoning.[1][2][3][4]
+
+In the early 1800s, John Dalton compiled experimental data gathered by himself and other scientists and observed that chemical elements seemed to combine by mass in ratios of small whole numbers; he called this pattern the "law of multiple proportions". For instance, there are two types of tin oxide: one is 88.1% tin and 11.9% oxygen, and the other is 78.7% tin and 21.3% oxygen. These proportions will always be the same in any samples of these oxides — this is the law of constant proportions. Adjusting the figures, for every 100 g of tin there is either 13.5 g or 27 g of oxygen respectively. 13.5 and 27 form a ratio of 1:2, a ratio of small whole numbers. Similarly, there are two common types of iron oxide, in which for every 112 g of iron there is either 32 g or 48 g of oxygen, which gives a ratio of 2:3. This recurring pattern in the data suggested that elements always combine in multiples of discrete units, which Dalton concluded were atoms. In the case of the tin oxides, for every one tin atom, there are either one or two oxygen atoms (SnO and SnO2). In the case of the iron oxides, for every two iron atoms, there are either two or three oxygen atoms (FeO and Fe2O3).[5][6]
+
+Dalton also believed that the concept of atoms could explain why some gases dissolve in water better than other gases. For example, he observed that water absorbs nitrous oxide far better than it absorbs nitrogen. Dalton hypothesized a general pattern of solubility based on the number of particles in the chemicals and the relative weights of the particles themselves.[7]
+
+In the late 18th century, a number of scientists found that they could better explain the behavior of gases by describing them as collections of sub-microscopic particles and modelling their behavior using statistics and probability. This model worked well enough for many purposes, but some skeptical scientists cautioned that it was not solid proof that molecules and atoms literally existed. Rather, these skeptics regarded this theory as simply as a heuristic tool that was useful in certain contexts but did not necessarily reflect the true nature of matter.[8]
+
+In 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as "Brownian motion". This was thought to be caused by water molecules knocking the grains about. In 1905, Albert Einstein proved the reality of these molecules and their motions by producing the first statistical physics analysis of Brownian motion.[9][10][11] French physicist Jean Perrin used Einstein's work to experimentally determine the mass and dimensions of atoms, thereby conclusively verifying Dalton's atomic theory.[12]
+
+Prior to Perrin's verification of Einstein's equations, there had been considerable doubt among physicists that atoms and molecules were actually real. Physicists saw atomic theory as a convenient construct for chemists that worked well enough in certain applications, but that did not mean that atoms were literally real.
+
+In 1897, J.J. Thomson discovered that cathode rays are not electromagnetic waves but made of particles that are 1,800 times lighter than hydrogen (the lightest atom). Therefore, they were not atoms, but a new particle, the first subatomic particle to be discovered. He originally called these new particles corpuscles but they were later renamed electrons, after particles postulated by George Johnstone Stoney in 1874. Thomson also showed that electrons were identical to particles given off by photoelectric and radioactive materials.[13] It was quickly recognized that electrons are the particles that carry electric currents in metal wires, and carry the negative electric charge within atoms. Thus Thomson overturned the belief that atoms are the indivisible, fundamental particles of matter.[14] The misnomer "atom" is still used, even though atoms are not "uncuttable".
+
+J.J. Thomson postulated that the negatively-charged electrons were distributed throughout the atom in a uniform sea of positive charge. This was known as the plum pudding model. In 1909, Hans Geiger and Ernest Marsden, working under the direction of Ernest Rutherford, bombarded metal foil with alpha particles to observe how they scattered. They expected all the alpha particles to pass straight through with little deflection, because Thomson's model said that the charges in the atom are so diffuse that their electric fields could not affect the alpha particles much. Geiger and Marsden spotted alpha particles being deflected by angles greater than 90°, which was supposed to be impossible according to Thomson's model. To explain this, Rutherford proposed that the positive charge of the atom is concentrated in a tiny nucleus at the center. Only such an intense concentration of charge could produce an electric field strong enough to deflect alpha particles that much.[15]
+
+While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the periodic table.[16] The term isotope was coined by Margaret Todd as a suitable name for different atoms that belong to the same element. J.J. Thomson created a technique for isotope separation through his work on ionized gases, which subsequently led to the discovery of stable isotopes.[17]
+
+In 1913 the physicist Niels Bohr proposed a model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon.[18] This quantization was used to explain why the electrons' orbits are stable (given that normally, charges in acceleration, including circular motion, lose kinetic energy which is emitted as electromagnetic radiation, see synchrotron radiation) and why elements absorb and emit electromagnetic radiation in discrete spectra.[19]
+
+Later in the same year Henry Moseley provided additional experimental evidence in favor of Niels Bohr's theory. These results refined Ernest Rutherford's and Antonius Van den Broek's model, which proposed that the atom contains in its nucleus a number of positive nuclear charges that is equal to its (atomic) number in the periodic table. Until these experiments, atomic number was not known to be a physical and experimental quantity. That it is equal to the atomic nuclear charge remains the accepted atomic model today.[20]
+
+Chemical bonds between atoms were explained by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons.[21] As the chemical properties of the elements were known to largely repeat themselves according to the periodic law,[22] in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus.[23]
+
+The Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of atomic properties. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split in a way correlated with the direction of an atom's angular momentum, or spin. As this spin direction is initially random, the beam would be expected to deflect in a random direction. Instead, the beam was split into two directional components, corresponding to the atomic spin being oriented up or down with respect to the magnetic field.[24]
+
+In 1925 Werner Heisenberg published the first consistent mathematical formulation of quantum mechanics (matrix mechanics).[20] One year earlier, Louis de Broglie had proposed the de Broglie hypothesis: that all particles behave like waves to some extent,[25] and in 1926 Erwin Schrödinger used this idea to develop the Schrödinger equation, a mathematical model of the atom (wave mechanics) that described the electrons as three-dimensional waveforms rather than point particles.[26]
+
+A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at a given point in time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1927.[20] In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa.[27]
+This model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen. Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.[28][29]
+
+The development of the mass spectrometer allowed the mass of atoms to be measured with increased accuracy. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis William Aston used this instrument to show that isotopes had different masses. The atomic mass of these isotopes varied by integer amounts, called the whole number rule.[30] The explanation for these different isotopes awaited the discovery of the neutron, an uncharged particle with a mass similar to the proton, by the physicist James Chadwick in 1932. Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.[31]
+
+In 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product.[32][33] A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental nuclear fission.[34][35] In 1944, Hahn received the Nobel prize in chemistry. Despite Hahn's efforts, the contributions of Meitner and Frisch were not recognized.[36]
+
+In the 1950s, the development of improved particle accelerators and particle detectors allowed scientists to study the impacts of atoms moving at high energies.[37] Neutrons and protons were found to be hadrons, or composites of smaller particles called quarks. The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.[38]
+
+Though the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron.
+
+The electron is by far the least massive of these particles at 9.11×10−31 kg, with a negative electrical charge and a size that is too small to be measured using available techniques.[39] It was the lightest particle with a positive rest mass measured, until the discovery of neutrino mass. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom has more or fewer electrons than its atomic number, then it becomes respectively negatively or positively charged as a whole; a charged atom is called an ion. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.
+
+Protons have a positive charge and a mass 1,836 times that of the electron, at 1.6726×10−27 kg. The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920 he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton.
+
+Neutrons have no electrical charge and have a free mass of 1,839 times the mass of the electron, or 1.6749×10−27 kg.[40][41] Neutrons are the heaviest of the three constituent particles, but their mass can be reduced by the nuclear binding energy. Neutrons and protons (collectively known as nucleons) have comparable dimensions—on the order of 2.5×10−15 m—although the 'surface' of these particles is not sharply defined.[42] The neutron was discovered in 1932 by the English physicist James Chadwick.
+
+In the Standard Model of physics, electrons are truly elementary particles with no internal structure, whereas protons and neutrons are composite particles composed of elementary particles called quarks. There are two types of quarks in atoms, each having a fractional electric charge. Protons are composed of two up quarks (each with charge +2/3) and one down quark (with a charge of −1/3). Neutrons consist of one up quark and two down quarks. This distinction accounts for the difference in mass and charge between the two particles.[43][44]
+
+The quarks are held together by the strong interaction (or strong force), which is mediated by gluons. The protons and neutrons, in turn, are held to each other in the nucleus by the nuclear force, which is a residuum of the strong force that has somewhat different range-properties (see the article on the nuclear force for more). The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.[43][44]
+
+All the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 3√A fm, where A is the total number of nucleons.[45] This is much smaller than the radius of the atom, which is on the order of 105 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more powerful than the electrostatic force that causes positively charged protons to repel each other.[46]
+
+Atoms of the same element have the same number of protons, called the atomic number. Within a single element, the number of neutrons may vary, determining the isotope of that element. The total number of protons and neutrons determine the nuclide. The number of neutrons relative to the protons determines the stability of the nucleus, with certain isotopes undergoing radioactive decay.[47]
+
+The proton, the electron, and the neutron are classified as fermions. Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time. Thus, every proton in the nucleus must occupy a quantum state different from all other protons, and the same applies to all neutrons of the nucleus and to all electrons of the electron cloud.[48]
+
+A nucleus that has a different number of protons than neutrons can potentially drop to a lower energy state through a radioactive decay that causes the number of protons and neutrons to more closely match. As a result, atoms with matching numbers of protons and neutrons are more stable against decay, but with increasing atomic number, the mutual repulsion of the protons requires an increasing proportion of neutrons to maintain the stability of the nucleus.[48]
+
+The number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3–10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus.[49] Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.[50][51]
+
+If the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass–energy equivalence formula, 
+
+
+
+E
+=
+m
+
+c
+
+2
+
+
+
+
+{\displaystyle E=mc^{2}}
+
+, where 
+
+
+
+m
+
+
+{\displaystyle m}
+
+ is the mass loss and 
+
+
+
+c
+
+
+{\displaystyle c}
+
+ is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.[52]
+
+The fusion of two nuclei that create larger nuclei with lower atomic numbers than iron and nickel—a total nucleon number of about 60—is usually an exothermic process that releases more energy than is required to bring them together.[53] It is this energy-releasing process that makes nuclear fusion in stars a self-sustaining reaction. For heavier nuclei, the binding energy per nucleon in the nucleus begins to decrease. That means fusion processes producing nuclei that have atomic numbers higher than about 26, and atomic masses higher than about 60, is an endothermic process. These more massive nuclei can not undergo an energy-producing fusion reaction that can sustain the hydrostatic equilibrium of a star.[48]
+
+The electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.
+
+Electrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured.[54] Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form.[55] Orbitals can have one or more ring or node structures, and differ from each other in size, shape and orientation.[56]
+
+Each atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in a higher energy state can drop to a lower energy state while radiating the excess energy as a photon. These characteristic energy values, defined by the differences in the energies of the quantum states, are responsible for atomic spectral lines.[55]
+
+The amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom,[57] compared to 2.23 million eV for splitting a deuterium nucleus.[58] Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Electrons that are farthest from the nucleus may be transferred to other nearby atoms or shared between atoms. By this mechanism, atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.[59]
+
+By definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form,[60] also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element oganesson.[61] All known isotopes of elements with atomic numbers greater than 82 are radioactive, although the radioactivity of element 83 (bismuth) is so slight as to be practically negligible.[62][63]
+
+About 339 nuclides occur naturally on Earth,[64] of which 252 (about 74%) have not been observed to decay, and are referred to as "stable isotopes". Only 90 nuclides are stable theoretically, while another 162 (bringing the total to 252) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as "stable". An additional 34 radioactive nuclides have half-lives longer than 100 million years, and are long-lived enough to have been present since the birth of the solar system. This collection of 286 nuclides are known as primordial nuclides. Finally, an additional 53 short-lived nuclides are known to occur naturally, as daughter products of primordial nuclide decay (such as radium from uranium), or as products of natural energetic processes on Earth, such as cosmic ray bombardment (for example, carbon-14).[65][note 1]
+
+For 80 of the chemical elements, at least one stable isotope exists. As a rule, there is only a handful of stable isotopes for each of these elements, the average being 3.2 stable isotopes per element. Twenty-six elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes.[66]:1–12
+
+Stability of isotopes is affected by the ratio of protons to neutrons, and also by the presence of certain "magic numbers" of neutrons or protons that represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. Of the 252 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd–odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd–odd nuclei are highly unstable with respect to beta decay, because the decay products are even–even, and are therefore more strongly bound, due to nuclear pairing effects.[67]
+
+The large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called "nucleons") in a given atom is called the mass number. It is a positive integer and dimensionless (instead of having dimension of mass), because it expresses a count. An example of use of a mass number is "carbon-12," which has 12 nucleons (six protons and six neutrons).
+
+The actual mass of an atom at rest is often expressed in daltons (Da), also called the unified atomic mass unit (u). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately 1.66×10−27 kg.[68] Hydrogen-1 (the lightest isotope of hydrogen which is also the nuclide with the lowest mass) has an atomic weight of 1.007825 Da.[69] The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the atomic mass unit (for example the mass of a nitrogen-14 is roughly 14 Da), but this number will not be exactly an integer except (by definition) in the case of carbon-12.[70] The heaviest stable atom is lead-208,[62] with a mass of 207.9766521 Da.[71]
+
+As even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about 6.022×1023). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 Da, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.[68]
+
+Atoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus.[72] This assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin.[73] On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right).[74] Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm.[75]
+
+When subjected to external forces, like electrical fields, the shape of an atom may deviate from spherical symmetry. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystals, where large crystal-electrical fields may occur at low-symmetry lattice sites.[76][77] Significant ellipsoidal deformations have been shown to occur for sulfur ions[78] and chalcogen ions[79] in pyrite-type compounds.
+
+Atomic dimensions are thousands of times smaller than the wavelengths of light (400–700 nm) so they cannot be viewed using an optical microscope, although individual atoms can be observed using a scanning tunneling microscope. To visualize the minuteness of the atom, consider that a typical human hair is about 1 million carbon atoms in width.[80] A single drop of water contains about 2 sextillion (2×1021) atoms of oxygen, and twice the number of hydrogen atoms.[81] A single carat diamond with a mass of 2×10−4 kg contains about 10 sextillion (1022) atoms of carbon.[note 2] If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.[82]
+
+Every element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm.[83]
+
+The most common forms of radioactive decay are:[84][85]
+
+Other more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or more than one beta particle. An analog of gamma emission which allows excited nuclei to lose energy in a different way, is internal conversion—a process that produces high-speed electrons that are not beta rays, followed by production of high-energy photons that are not gamma rays. A few large nuclei explode into two or more charged fragments of varying masses plus several neutrons, in a decay called spontaneous nuclear fission.
+
+Each radioactive isotope has a characteristic decay time period—the half-life—that is determined by the amount of time needed for half of a sample to decay. This is an exponential decay process that steadily decreases the proportion of the remaining isotope by 50% every half-life. Hence after two half-lives have passed only 25% of the isotope is present, and so forth.[83]
+
+Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or "spin-½". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.[86]
+
+The magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field, but the most dominant contribution comes from electron spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons pair up with each other, with one member of each pair in a spin up state and the other in the opposite, spin down state. Thus these spins cancel each other out, reducing the total magnetic dipole moment to zero in some atoms with even number of electrons.[87]
+
+In ferromagnetic elements such as iron, cobalt and nickel, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a spontaneous process known as an exchange interaction. When the magnetic moments of ferromagnetic atoms are lined up, the material can produce a measurable macroscopic field. Paramagnetic materials have atoms with magnetic moments that line up in random directions when no magnetic field is present, but the magnetic moments of the individual atoms line up in the presence of a field.[87][88]
+
+The nucleus of an atom will have no spin when it has even numbers of both neutrons and protons, but for other cases of odd numbers, the nucleus may have a spin. Normally nuclei with spin are aligned in random directions because of thermal equilibrium, but for certain elements (such as xenon-129) it is possible to polarize a significant proportion of the nuclear spin states so that they are aligned in the same direction—a condition called hyperpolarization. This has important applications in magnetic resonance imaging.[89][90]
+
+The potential energy of an electron in an atom is negative relative to when the distance from the nucleus goes to infinity; its dependence on the electron's position reaches the minimum inside the nucleus, roughly in inverse proportion to the distance. In the quantum-mechanical model, a bound electron can occupy only a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for a theoretical explanation. An energy level can be measured by the amount of energy needed to unbind the electron from the atom, and is usually given in units of electronvolts (eV). The lowest energy state of a bound electron is called the ground state, i.e. stationary state, while an electron transition to a higher level results in an excited state.[91] The electron's energy increases along with n because the (average) distance to the nucleus increases. Dependence of the energy on ℓ is caused not by the electrostatic potential of the nucleus, but by interaction between electrons.
+
+For an electron to transition between two different states, e.g. ground state to first excited state, it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to the Niels Bohr model, what can be precisely calculated by the Schrödinger equation.
+Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.
+
+The energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum.[92] Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors.[93]
+
+When a continuous spectrum of energy is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark absorption bands in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of emission lines from the photons emitted by the atoms.) Spectroscopic measurements of the strength and width of atomic spectral lines allow the composition and physical properties of a substance to be determined.[94]
+
+Close examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron.[95] When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the Zeeman effect. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple electron configurations with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines.[96] The presence of an external electric field can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the Stark effect.[97]
+
+If a bound electron is in an excited state, an interacting photon with the proper energy can cause stimulated emission of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make lasers, which can emit a coherent beam of light energy in a narrow frequency band.[98]
+
+Valency is the combining power of an element. It is determined by the number of bonds it can form to other atoms or groups.[99] The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in
+that shell are called valence electrons. The number of valence electrons determines the bonding
+behavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells.[100] For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts. Many elements display multiple valences, or tendencies to share differing numbers of electrons in different compounds. Thus, chemical bonding between these elements takes many forms of electron-sharing that are more than simple electron transfers. Examples include the element carbon and the organic compounds.[101]
+
+The chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) The elements at the far right of the table have their outer shell completely filled with electrons, which results in chemically inert elements known as the noble gases.[102][103]
+
+Quantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas.[104] Within a state, a material can also exist in different allotropes. An example of this is solid carbon, which can exist as graphite or diamond.[105] Gaseous allotropes exist as well, such as dioxygen and ozone.
+
+At temperatures close to absolute zero, atoms can form a Bose–Einstein condensate, at which point quantum mechanical effects, which are normally only observed at the atomic scale, become apparent on a macroscopic scale.[106][107] This super-cooled collection of atoms
+then behaves as a single super atom, which may allow fundamental checks of quantum mechanical behavior.[108]
+
+The scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would be insurmountable in the classical perspective. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely packed energy levels—the Fermi level local density of states.[109][110]
+
+An atom can be ionized by removing one of its electrons. The electric charge causes the trajectory of an atom to bend when it passes through a magnetic field. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses this principle to measure the mass-to-charge ratio of ions. If a sample contains multiple isotopes, the mass spectrometer can determine the proportion of each isotope in the sample by measuring the intensity of the different beams of ions. Techniques to vaporize atoms include inductively coupled plasma atomic emission spectroscopy and inductively coupled plasma mass spectrometry, both of which use a plasma to vaporize samples for analysis.[111]
+
+A more area-selective method is electron energy loss spectroscopy, which measures the energy loss of an electron beam within a transmission electron microscope when it interacts with a portion of a sample. The atom-probe tomograph has sub-nanometer resolution in 3-D and can chemically identify individual atoms using time-of-flight mass spectrometry.[112]
+
+Spectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same element.[113] Helium was discovered in this way in the spectrum of the Sun 23 years before it was found on Earth.[114]
+
+Baryonic matter forms about 4% of the total energy density of the observable Universe, with an average density of about 0.25 particles/m3 (mostly protons and electrons).[115] Within a galaxy such as the Milky Way, particles have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 105 to 109 atoms/m3.[116] The Sun is believed to be inside the Local Bubble, so the density in the solar neighborhood is only about 103 atoms/m3.[117] Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium.
+
+Up to 95% of the Milky Way's baryonic matter are concentrated inside stars, where conditions are unfavorable for atomic matter. The total baryonic mass is about 10% of the mass of the galaxy;[118] the remainder of the mass is an unknown dark matter.[119] High temperature inside stars makes most "atoms" fully ionized, that is, separates all electrons from the nuclei. In stellar remnants—with exception of their surface layers—an immense pressure make electron shells impossible.
+
+Electrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron.[120][121][122]
+
+Ubiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma—a gas of positively charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically favorable. Atoms (complete with bound electrons) became to dominate over charged particles 380,000 years after the Big Bang—an epoch called recombination, when the expanding Universe cooled enough to allow electrons to become attached to nuclei.[123]
+
+Since the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple alpha process) the sequence of elements from carbon up to iron;[124] see stellar nucleosynthesis for details.
+
+Isotopes such as lithium-6, as well as some beryllium and boron are generated in space through cosmic ray spallation.[125] This occurs when a high-energy proton strikes an atomic nucleus, causing large numbers of nucleons to be ejected.
+
+Elements heavier than iron were produced in supernovae and colliding neutron stars through the r-process, and in AGB stars through the s-process, both of which involve the capture of neutrons by atomic nuclei.[126] Elements such as lead formed largely through the radioactive decay of heavier elements.[127]
+
+Most of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating.[128][129] Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay.[130]
+
+There are a few trace atoms on Earth that were not present at the beginning (i.e., not "primordial"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere.[131] Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors or explosions.[132][133] Of the transuranic elements—those with atomic numbers greater than 92—only plutonium and neptunium occur naturally on Earth.[134][135] Transuranic elements have radioactive lifetimes shorter than the current age of the Earth[136] and thus identifiable quantities of these elements have long since decayed, with the exception of traces of plutonium-244 possibly deposited by cosmic dust.[128] Natural deposits of plutonium and neptunium are produced by neutron capture in uranium ore.[137]
+
+The Earth contains approximately 1.33×1050 atoms.[138] Although small numbers of independent atoms of noble gases exist, such as argon, neon, and helium, 99% of the atmosphere is bound in the form of molecules, including carbon dioxide and diatomic oxygen and nitrogen. At the surface of the Earth, an overwhelming majority of atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals.[139][140] This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter.[141]
+
+All nuclides with atomic numbers higher than 82 (lead) are known to be radioactive. No nuclide with an atomic number exceeding 92 (uranium) exists on Earth as a primordial nuclide, and heavier elements generally have shorter half-lives. Nevertheless, an "island of stability" encompassing relatively long-lived isotopes of superheavy elements[142] with atomic numbers 110–114 might exist.[143] Predictions for the half-life of the most stable nuclide on the island range from a few minutes to millions of years.[144] In any case, superheavy elements (with Z > 104) would not exist due to increasing Coulomb repulsion (which results in spontaneous fission with increasingly short half-lives) in the absence of any stabilizing effects.[145]
+
+Each particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature.[146][147] In 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva.[148][149]
+
+Other exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test fundamental predictions of physics.[150][151][152]
+
+
+

en/4191.html.txt

@@ -0,0 +1,212 @@
+
+
+An atom is the smallest constituent unit of ordinary matter that constitutes a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small, typically around 100 picometers across. They are so small that accurately predicting their behavior using classical physics – as if they were billiard balls, for example – is not possible due to quantum effects. Current atomic models use quantum principles to better explain and predict this behavior.
+
+Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, then the atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively. These atoms are called ions.
+
+The electrons of an atom are attracted to the protons in an atomic nucleus by the electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by the nuclear force. This force is usually stronger than the electromagnetic force that repels the positively charged protons from one another. Under certain circumstances, the repelling electromagnetic force becomes stronger than the nuclear force. In this case, the nucleus splits and leaves behind different elements. This is a form of nuclear decay.
+
+The number of protons in the nucleus is the atomic number and it defines to which chemical element the atom belongs. For example, any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element. Atoms can attach to one or more other atoms by chemical bonds to form chemical compounds such as molecules or crystals. The ability of atoms to associate and dissociate is responsible for most of the physical changes observed in nature. Chemistry is the discipline that studies these changes.
+
+The basic idea that matter is made up of tiny indivisible particles is very old, appearing in many ancient cultures such as Greece and India. The word atomos, meaning "uncuttable", was coined by the ancient Greek philosophers Leucippus and his pupil Democritus (5th century BC). These ancient ideas were not based on scientific reasoning.[1][2][3][4]
+
+In the early 1800s, John Dalton compiled experimental data gathered by himself and other scientists and observed that chemical elements seemed to combine by mass in ratios of small whole numbers; he called this pattern the "law of multiple proportions". For instance, there are two types of tin oxide: one is 88.1% tin and 11.9% oxygen, and the other is 78.7% tin and 21.3% oxygen. These proportions will always be the same in any samples of these oxides — this is the law of constant proportions. Adjusting the figures, for every 100 g of tin there is either 13.5 g or 27 g of oxygen respectively. 13.5 and 27 form a ratio of 1:2, a ratio of small whole numbers. Similarly, there are two common types of iron oxide, in which for every 112 g of iron there is either 32 g or 48 g of oxygen, which gives a ratio of 2:3. This recurring pattern in the data suggested that elements always combine in multiples of discrete units, which Dalton concluded were atoms. In the case of the tin oxides, for every one tin atom, there are either one or two oxygen atoms (SnO and SnO2). In the case of the iron oxides, for every two iron atoms, there are either two or three oxygen atoms (FeO and Fe2O3).[5][6]
+
+Dalton also believed that the concept of atoms could explain why some gases dissolve in water better than other gases. For example, he observed that water absorbs nitrous oxide far better than it absorbs nitrogen. Dalton hypothesized a general pattern of solubility based on the number of particles in the chemicals and the relative weights of the particles themselves.[7]
+
+In the late 18th century, a number of scientists found that they could better explain the behavior of gases by describing them as collections of sub-microscopic particles and modelling their behavior using statistics and probability. This model worked well enough for many purposes, but some skeptical scientists cautioned that it was not solid proof that molecules and atoms literally existed. Rather, these skeptics regarded this theory as simply as a heuristic tool that was useful in certain contexts but did not necessarily reflect the true nature of matter.[8]
+
+In 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as "Brownian motion". This was thought to be caused by water molecules knocking the grains about. In 1905, Albert Einstein proved the reality of these molecules and their motions by producing the first statistical physics analysis of Brownian motion.[9][10][11] French physicist Jean Perrin used Einstein's work to experimentally determine the mass and dimensions of atoms, thereby conclusively verifying Dalton's atomic theory.[12]
+
+Prior to Perrin's verification of Einstein's equations, there had been considerable doubt among physicists that atoms and molecules were actually real. Physicists saw atomic theory as a convenient construct for chemists that worked well enough in certain applications, but that did not mean that atoms were literally real.
+
+In 1897, J.J. Thomson discovered that cathode rays are not electromagnetic waves but made of particles that are 1,800 times lighter than hydrogen (the lightest atom). Therefore, they were not atoms, but a new particle, the first subatomic particle to be discovered. He originally called these new particles corpuscles but they were later renamed electrons, after particles postulated by George Johnstone Stoney in 1874. Thomson also showed that electrons were identical to particles given off by photoelectric and radioactive materials.[13] It was quickly recognized that electrons are the particles that carry electric currents in metal wires, and carry the negative electric charge within atoms. Thus Thomson overturned the belief that atoms are the indivisible, fundamental particles of matter.[14] The misnomer "atom" is still used, even though atoms are not "uncuttable".
+
+J.J. Thomson postulated that the negatively-charged electrons were distributed throughout the atom in a uniform sea of positive charge. This was known as the plum pudding model. In 1909, Hans Geiger and Ernest Marsden, working under the direction of Ernest Rutherford, bombarded metal foil with alpha particles to observe how they scattered. They expected all the alpha particles to pass straight through with little deflection, because Thomson's model said that the charges in the atom are so diffuse that their electric fields could not affect the alpha particles much. Geiger and Marsden spotted alpha particles being deflected by angles greater than 90°, which was supposed to be impossible according to Thomson's model. To explain this, Rutherford proposed that the positive charge of the atom is concentrated in a tiny nucleus at the center. Only such an intense concentration of charge could produce an electric field strong enough to deflect alpha particles that much.[15]
+
+While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the periodic table.[16] The term isotope was coined by Margaret Todd as a suitable name for different atoms that belong to the same element. J.J. Thomson created a technique for isotope separation through his work on ionized gases, which subsequently led to the discovery of stable isotopes.[17]
+
+In 1913 the physicist Niels Bohr proposed a model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon.[18] This quantization was used to explain why the electrons' orbits are stable (given that normally, charges in acceleration, including circular motion, lose kinetic energy which is emitted as electromagnetic radiation, see synchrotron radiation) and why elements absorb and emit electromagnetic radiation in discrete spectra.[19]
+
+Later in the same year Henry Moseley provided additional experimental evidence in favor of Niels Bohr's theory. These results refined Ernest Rutherford's and Antonius Van den Broek's model, which proposed that the atom contains in its nucleus a number of positive nuclear charges that is equal to its (atomic) number in the periodic table. Until these experiments, atomic number was not known to be a physical and experimental quantity. That it is equal to the atomic nuclear charge remains the accepted atomic model today.[20]
+
+Chemical bonds between atoms were explained by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons.[21] As the chemical properties of the elements were known to largely repeat themselves according to the periodic law,[22] in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus.[23]
+
+The Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of atomic properties. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split in a way correlated with the direction of an atom's angular momentum, or spin. As this spin direction is initially random, the beam would be expected to deflect in a random direction. Instead, the beam was split into two directional components, corresponding to the atomic spin being oriented up or down with respect to the magnetic field.[24]
+
+In 1925 Werner Heisenberg published the first consistent mathematical formulation of quantum mechanics (matrix mechanics).[20] One year earlier, Louis de Broglie had proposed the de Broglie hypothesis: that all particles behave like waves to some extent,[25] and in 1926 Erwin Schrödinger used this idea to develop the Schrödinger equation, a mathematical model of the atom (wave mechanics) that described the electrons as three-dimensional waveforms rather than point particles.[26]
+
+A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at a given point in time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1927.[20] In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa.[27]
+This model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen. Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.[28][29]
+
+The development of the mass spectrometer allowed the mass of atoms to be measured with increased accuracy. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis William Aston used this instrument to show that isotopes had different masses. The atomic mass of these isotopes varied by integer amounts, called the whole number rule.[30] The explanation for these different isotopes awaited the discovery of the neutron, an uncharged particle with a mass similar to the proton, by the physicist James Chadwick in 1932. Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.[31]
+
+In 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product.[32][33] A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental nuclear fission.[34][35] In 1944, Hahn received the Nobel prize in chemistry. Despite Hahn's efforts, the contributions of Meitner and Frisch were not recognized.[36]
+
+In the 1950s, the development of improved particle accelerators and particle detectors allowed scientists to study the impacts of atoms moving at high energies.[37] Neutrons and protons were found to be hadrons, or composites of smaller particles called quarks. The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.[38]
+
+Though the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron.
+
+The electron is by far the least massive of these particles at 9.11×10−31 kg, with a negative electrical charge and a size that is too small to be measured using available techniques.[39] It was the lightest particle with a positive rest mass measured, until the discovery of neutrino mass. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom has more or fewer electrons than its atomic number, then it becomes respectively negatively or positively charged as a whole; a charged atom is called an ion. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.
+
+Protons have a positive charge and a mass 1,836 times that of the electron, at 1.6726×10−27 kg. The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920 he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton.
+
+Neutrons have no electrical charge and have a free mass of 1,839 times the mass of the electron, or 1.6749×10−27 kg.[40][41] Neutrons are the heaviest of the three constituent particles, but their mass can be reduced by the nuclear binding energy. Neutrons and protons (collectively known as nucleons) have comparable dimensions—on the order of 2.5×10−15 m—although the 'surface' of these particles is not sharply defined.[42] The neutron was discovered in 1932 by the English physicist James Chadwick.
+
+In the Standard Model of physics, electrons are truly elementary particles with no internal structure, whereas protons and neutrons are composite particles composed of elementary particles called quarks. There are two types of quarks in atoms, each having a fractional electric charge. Protons are composed of two up quarks (each with charge +2/3) and one down quark (with a charge of −1/3). Neutrons consist of one up quark and two down quarks. This distinction accounts for the difference in mass and charge between the two particles.[43][44]
+
+The quarks are held together by the strong interaction (or strong force), which is mediated by gluons. The protons and neutrons, in turn, are held to each other in the nucleus by the nuclear force, which is a residuum of the strong force that has somewhat different range-properties (see the article on the nuclear force for more). The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.[43][44]
+
+All the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 3√A fm, where A is the total number of nucleons.[45] This is much smaller than the radius of the atom, which is on the order of 105 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more powerful than the electrostatic force that causes positively charged protons to repel each other.[46]
+
+Atoms of the same element have the same number of protons, called the atomic number. Within a single element, the number of neutrons may vary, determining the isotope of that element. The total number of protons and neutrons determine the nuclide. The number of neutrons relative to the protons determines the stability of the nucleus, with certain isotopes undergoing radioactive decay.[47]
+
+The proton, the electron, and the neutron are classified as fermions. Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time. Thus, every proton in the nucleus must occupy a quantum state different from all other protons, and the same applies to all neutrons of the nucleus and to all electrons of the electron cloud.[48]
+
+A nucleus that has a different number of protons than neutrons can potentially drop to a lower energy state through a radioactive decay that causes the number of protons and neutrons to more closely match. As a result, atoms with matching numbers of protons and neutrons are more stable against decay, but with increasing atomic number, the mutual repulsion of the protons requires an increasing proportion of neutrons to maintain the stability of the nucleus.[48]
+
+The number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3–10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus.[49] Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.[50][51]
+
+If the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass–energy equivalence formula, 
+
+
+
+E
+=
+m
+
+c
+
+2
+
+
+
+
+{\displaystyle E=mc^{2}}
+
+, where 
+
+
+
+m
+
+
+{\displaystyle m}
+
+ is the mass loss and 
+
+
+
+c
+
+
+{\displaystyle c}
+
+ is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.[52]
+
+The fusion of two nuclei that create larger nuclei with lower atomic numbers than iron and nickel—a total nucleon number of about 60—is usually an exothermic process that releases more energy than is required to bring them together.[53] It is this energy-releasing process that makes nuclear fusion in stars a self-sustaining reaction. For heavier nuclei, the binding energy per nucleon in the nucleus begins to decrease. That means fusion processes producing nuclei that have atomic numbers higher than about 26, and atomic masses higher than about 60, is an endothermic process. These more massive nuclei can not undergo an energy-producing fusion reaction that can sustain the hydrostatic equilibrium of a star.[48]
+
+The electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.
+
+Electrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured.[54] Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form.[55] Orbitals can have one or more ring or node structures, and differ from each other in size, shape and orientation.[56]
+
+Each atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in a higher energy state can drop to a lower energy state while radiating the excess energy as a photon. These characteristic energy values, defined by the differences in the energies of the quantum states, are responsible for atomic spectral lines.[55]
+
+The amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom,[57] compared to 2.23 million eV for splitting a deuterium nucleus.[58] Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Electrons that are farthest from the nucleus may be transferred to other nearby atoms or shared between atoms. By this mechanism, atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.[59]
+
+By definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form,[60] also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element oganesson.[61] All known isotopes of elements with atomic numbers greater than 82 are radioactive, although the radioactivity of element 83 (bismuth) is so slight as to be practically negligible.[62][63]
+
+About 339 nuclides occur naturally on Earth,[64] of which 252 (about 74%) have not been observed to decay, and are referred to as "stable isotopes". Only 90 nuclides are stable theoretically, while another 162 (bringing the total to 252) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as "stable". An additional 34 radioactive nuclides have half-lives longer than 100 million years, and are long-lived enough to have been present since the birth of the solar system. This collection of 286 nuclides are known as primordial nuclides. Finally, an additional 53 short-lived nuclides are known to occur naturally, as daughter products of primordial nuclide decay (such as radium from uranium), or as products of natural energetic processes on Earth, such as cosmic ray bombardment (for example, carbon-14).[65][note 1]
+
+For 80 of the chemical elements, at least one stable isotope exists. As a rule, there is only a handful of stable isotopes for each of these elements, the average being 3.2 stable isotopes per element. Twenty-six elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes.[66]:1–12
+
+Stability of isotopes is affected by the ratio of protons to neutrons, and also by the presence of certain "magic numbers" of neutrons or protons that represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. Of the 252 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd–odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd–odd nuclei are highly unstable with respect to beta decay, because the decay products are even–even, and are therefore more strongly bound, due to nuclear pairing effects.[67]
+
+The large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called "nucleons") in a given atom is called the mass number. It is a positive integer and dimensionless (instead of having dimension of mass), because it expresses a count. An example of use of a mass number is "carbon-12," which has 12 nucleons (six protons and six neutrons).
+
+The actual mass of an atom at rest is often expressed in daltons (Da), also called the unified atomic mass unit (u). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately 1.66×10−27 kg.[68] Hydrogen-1 (the lightest isotope of hydrogen which is also the nuclide with the lowest mass) has an atomic weight of 1.007825 Da.[69] The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the atomic mass unit (for example the mass of a nitrogen-14 is roughly 14 Da), but this number will not be exactly an integer except (by definition) in the case of carbon-12.[70] The heaviest stable atom is lead-208,[62] with a mass of 207.9766521 Da.[71]
+
+As even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about 6.022×1023). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 Da, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.[68]
+
+Atoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus.[72] This assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin.[73] On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right).[74] Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm.[75]
+
+When subjected to external forces, like electrical fields, the shape of an atom may deviate from spherical symmetry. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystals, where large crystal-electrical fields may occur at low-symmetry lattice sites.[76][77] Significant ellipsoidal deformations have been shown to occur for sulfur ions[78] and chalcogen ions[79] in pyrite-type compounds.
+
+Atomic dimensions are thousands of times smaller than the wavelengths of light (400–700 nm) so they cannot be viewed using an optical microscope, although individual atoms can be observed using a scanning tunneling microscope. To visualize the minuteness of the atom, consider that a typical human hair is about 1 million carbon atoms in width.[80] A single drop of water contains about 2 sextillion (2×1021) atoms of oxygen, and twice the number of hydrogen atoms.[81] A single carat diamond with a mass of 2×10−4 kg contains about 10 sextillion (1022) atoms of carbon.[note 2] If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.[82]
+
+Every element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm.[83]
+
+The most common forms of radioactive decay are:[84][85]
+
+Other more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or more than one beta particle. An analog of gamma emission which allows excited nuclei to lose energy in a different way, is internal conversion—a process that produces high-speed electrons that are not beta rays, followed by production of high-energy photons that are not gamma rays. A few large nuclei explode into two or more charged fragments of varying masses plus several neutrons, in a decay called spontaneous nuclear fission.
+
+Each radioactive isotope has a characteristic decay time period—the half-life—that is determined by the amount of time needed for half of a sample to decay. This is an exponential decay process that steadily decreases the proportion of the remaining isotope by 50% every half-life. Hence after two half-lives have passed only 25% of the isotope is present, and so forth.[83]
+
+Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or "spin-½". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.[86]
+
+The magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field, but the most dominant contribution comes from electron spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons pair up with each other, with one member of each pair in a spin up state and the other in the opposite, spin down state. Thus these spins cancel each other out, reducing the total magnetic dipole moment to zero in some atoms with even number of electrons.[87]
+
+In ferromagnetic elements such as iron, cobalt and nickel, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a spontaneous process known as an exchange interaction. When the magnetic moments of ferromagnetic atoms are lined up, the material can produce a measurable macroscopic field. Paramagnetic materials have atoms with magnetic moments that line up in random directions when no magnetic field is present, but the magnetic moments of the individual atoms line up in the presence of a field.[87][88]
+
+The nucleus of an atom will have no spin when it has even numbers of both neutrons and protons, but for other cases of odd numbers, the nucleus may have a spin. Normally nuclei with spin are aligned in random directions because of thermal equilibrium, but for certain elements (such as xenon-129) it is possible to polarize a significant proportion of the nuclear spin states so that they are aligned in the same direction—a condition called hyperpolarization. This has important applications in magnetic resonance imaging.[89][90]
+
+The potential energy of an electron in an atom is negative relative to when the distance from the nucleus goes to infinity; its dependence on the electron's position reaches the minimum inside the nucleus, roughly in inverse proportion to the distance. In the quantum-mechanical model, a bound electron can occupy only a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for a theoretical explanation. An energy level can be measured by the amount of energy needed to unbind the electron from the atom, and is usually given in units of electronvolts (eV). The lowest energy state of a bound electron is called the ground state, i.e. stationary state, while an electron transition to a higher level results in an excited state.[91] The electron's energy increases along with n because the (average) distance to the nucleus increases. Dependence of the energy on ℓ is caused not by the electrostatic potential of the nucleus, but by interaction between electrons.
+
+For an electron to transition between two different states, e.g. ground state to first excited state, it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to the Niels Bohr model, what can be precisely calculated by the Schrödinger equation.
+Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.
+
+The energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum.[92] Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors.[93]
+
+When a continuous spectrum of energy is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark absorption bands in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of emission lines from the photons emitted by the atoms.) Spectroscopic measurements of the strength and width of atomic spectral lines allow the composition and physical properties of a substance to be determined.[94]
+
+Close examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron.[95] When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the Zeeman effect. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple electron configurations with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines.[96] The presence of an external electric field can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the Stark effect.[97]
+
+If a bound electron is in an excited state, an interacting photon with the proper energy can cause stimulated emission of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make lasers, which can emit a coherent beam of light energy in a narrow frequency band.[98]
+
+Valency is the combining power of an element. It is determined by the number of bonds it can form to other atoms or groups.[99] The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in
+that shell are called valence electrons. The number of valence electrons determines the bonding
+behavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells.[100] For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts. Many elements display multiple valences, or tendencies to share differing numbers of electrons in different compounds. Thus, chemical bonding between these elements takes many forms of electron-sharing that are more than simple electron transfers. Examples include the element carbon and the organic compounds.[101]
+
+The chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) The elements at the far right of the table have their outer shell completely filled with electrons, which results in chemically inert elements known as the noble gases.[102][103]
+
+Quantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas.[104] Within a state, a material can also exist in different allotropes. An example of this is solid carbon, which can exist as graphite or diamond.[105] Gaseous allotropes exist as well, such as dioxygen and ozone.
+
+At temperatures close to absolute zero, atoms can form a Bose–Einstein condensate, at which point quantum mechanical effects, which are normally only observed at the atomic scale, become apparent on a macroscopic scale.[106][107] This super-cooled collection of atoms
+then behaves as a single super atom, which may allow fundamental checks of quantum mechanical behavior.[108]
+
+The scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would be insurmountable in the classical perspective. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely packed energy levels—the Fermi level local density of states.[109][110]
+
+An atom can be ionized by removing one of its electrons. The electric charge causes the trajectory of an atom to bend when it passes through a magnetic field. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses this principle to measure the mass-to-charge ratio of ions. If a sample contains multiple isotopes, the mass spectrometer can determine the proportion of each isotope in the sample by measuring the intensity of the different beams of ions. Techniques to vaporize atoms include inductively coupled plasma atomic emission spectroscopy and inductively coupled plasma mass spectrometry, both of which use a plasma to vaporize samples for analysis.[111]
+
+A more area-selective method is electron energy loss spectroscopy, which measures the energy loss of an electron beam within a transmission electron microscope when it interacts with a portion of a sample. The atom-probe tomograph has sub-nanometer resolution in 3-D and can chemically identify individual atoms using time-of-flight mass spectrometry.[112]
+
+Spectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same element.[113] Helium was discovered in this way in the spectrum of the Sun 23 years before it was found on Earth.[114]
+
+Baryonic matter forms about 4% of the total energy density of the observable Universe, with an average density of about 0.25 particles/m3 (mostly protons and electrons).[115] Within a galaxy such as the Milky Way, particles have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 105 to 109 atoms/m3.[116] The Sun is believed to be inside the Local Bubble, so the density in the solar neighborhood is only about 103 atoms/m3.[117] Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium.
+
+Up to 95% of the Milky Way's baryonic matter are concentrated inside stars, where conditions are unfavorable for atomic matter. The total baryonic mass is about 10% of the mass of the galaxy;[118] the remainder of the mass is an unknown dark matter.[119] High temperature inside stars makes most "atoms" fully ionized, that is, separates all electrons from the nuclei. In stellar remnants—with exception of their surface layers—an immense pressure make electron shells impossible.
+
+Electrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron.[120][121][122]
+
+Ubiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma—a gas of positively charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically favorable. Atoms (complete with bound electrons) became to dominate over charged particles 380,000 years after the Big Bang—an epoch called recombination, when the expanding Universe cooled enough to allow electrons to become attached to nuclei.[123]
+
+Since the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple alpha process) the sequence of elements from carbon up to iron;[124] see stellar nucleosynthesis for details.
+
+Isotopes such as lithium-6, as well as some beryllium and boron are generated in space through cosmic ray spallation.[125] This occurs when a high-energy proton strikes an atomic nucleus, causing large numbers of nucleons to be ejected.
+
+Elements heavier than iron were produced in supernovae and colliding neutron stars through the r-process, and in AGB stars through the s-process, both of which involve the capture of neutrons by atomic nuclei.[126] Elements such as lead formed largely through the radioactive decay of heavier elements.[127]
+
+Most of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating.[128][129] Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay.[130]
+
+There are a few trace atoms on Earth that were not present at the beginning (i.e., not "primordial"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere.[131] Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors or explosions.[132][133] Of the transuranic elements—those with atomic numbers greater than 92—only plutonium and neptunium occur naturally on Earth.[134][135] Transuranic elements have radioactive lifetimes shorter than the current age of the Earth[136] and thus identifiable quantities of these elements have long since decayed, with the exception of traces of plutonium-244 possibly deposited by cosmic dust.[128] Natural deposits of plutonium and neptunium are produced by neutron capture in uranium ore.[137]
+
+The Earth contains approximately 1.33×1050 atoms.[138] Although small numbers of independent atoms of noble gases exist, such as argon, neon, and helium, 99% of the atmosphere is bound in the form of molecules, including carbon dioxide and diatomic oxygen and nitrogen. At the surface of the Earth, an overwhelming majority of atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals.[139][140] This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter.[141]
+
+All nuclides with atomic numbers higher than 82 (lead) are known to be radioactive. No nuclide with an atomic number exceeding 92 (uranium) exists on Earth as a primordial nuclide, and heavier elements generally have shorter half-lives. Nevertheless, an "island of stability" encompassing relatively long-lived isotopes of superheavy elements[142] with atomic numbers 110–114 might exist.[143] Predictions for the half-life of the most stable nuclide on the island range from a few minutes to millions of years.[144] In any case, superheavy elements (with Z > 104) would not exist due to increasing Coulomb repulsion (which results in spontaneous fission with increasingly short half-lives) in the absence of any stabilizing effects.[145]
+
+Each particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature.[146][147] In 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva.[148][149]
+
+Other exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test fundamental predictions of physics.[150][151][152]
+
+
+

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+
+
+In cell biology, the nucleus (pl. nuclei; from Latin nucleus or nuculeus, meaning kernel or seed) is a membrane-bound organelle found in eukaryotic cells. Eukaryotes usually have a single nucleus, but a few cell types, such as mammalian red blood cells, have no nuclei, and a few others including osteoclasts have many.
+
+The cell nucleus contains all of the cell's genome, except for a small fraction of mitochondrial DNA, organized as multiple long linear DNA molecules in a complex with a large variety of proteins, such as histones, to form chromosomes. The genes within these chromosomes are structured in such a way to promote cell function. The nucleus maintains the integrity of genes and controls the activities of the cell by regulating gene expression—the nucleus is, therefore, the control center of the cell. The main structures making up the nucleus are the nuclear envelope, a double membrane that encloses the entire organelle and isolates its contents from the cellular cytoplasm, and the nuclear matrix (which includes the nuclear lamina), a network within the nucleus that adds mechanical support, much like the cytoskeleton, which supports the cell as a whole.
+
+Because the nuclear envelope is impermeable to large molecules, nuclear pores are required to regulate nuclear transport of molecules across the envelope. The pores cross both nuclear membranes, providing a channel through which larger molecules must be actively transported by carrier proteins while allowing free movement of small molecules and ions. Movement of large molecules such as proteins and RNA through the pores is required for both gene expression and the maintenance of chromosomes. Although the interior of the nucleus does not contain any membrane-bound subcompartments, its contents are not uniform, and a number of nuclear bodies exist, made up of unique proteins, RNA molecules, and particular parts of the chromosomes. The best-known of these is the nucleolus, which is mainly involved in the assembly of ribosomes. After being produced in the nucleolus, ribosomes are exported to the cytoplasm where they translate mRNA.
+
+The nucleus was the first organelle to be discovered. What is most likely the oldest preserved drawing dates back to the early microscopist Antonie van Leeuwenhoek (1632–1723). He observed a "lumen", the nucleus, in the red blood cells of salmon.[1] Unlike mammalian red blood cells, those of other vertebrates still contain nuclei.
+
+The nucleus was also described by Franz Bauer in 1804[2] and in more detail in 1831 by Scottish botanist Robert Brown in a talk at the Linnean Society of London. Brown was studying orchids under the microscope when he observed an opaque area, which he called the "areola" or "nucleus", in the cells of the flower's outer layer.[3]
+
+He did not suggest a potential function. In 1838, Matthias Schleiden proposed that the nucleus plays a role in generating cells, thus he introduced the name "cytoblast" ("cell builder"). He believed that he had observed new cells assembling around "cytoblasts". Franz Meyen was a strong opponent of this view, having already described cells multiplying by division and believing that many cells would have no nuclei. The idea that cells can be generated de novo, by the "cytoblast" or otherwise, contradicted work by Robert Remak (1852) and Rudolf Virchow (1855) who decisively propagated the new paradigm that cells are generated solely by cells ("Omnis cellula e cellula"). The function of the nucleus remained unclear.[4]
+
+Between 1877 and 1878, Oscar Hertwig published several studies on the fertilization of sea urchin eggs, showing that the nucleus of the sperm enters the oocyte and fuses with its nucleus. This was the first time it was suggested that an individual develops from a (single) nucleated cell. This was in contradiction to Ernst Haeckel's theory that the complete phylogeny of a species would be repeated during embryonic development, including generation of the first nucleated cell from a "monerula", a structureless mass of primordial protoplasm ("Urschleim"). Therefore, the necessity of the sperm nucleus for fertilization was discussed for quite some time. However, Hertwig confirmed his observation in other animal groups, including amphibians and molluscs. Eduard Strasburger produced the same results for plants in 1884. This paved the way to assign the nucleus an important role in heredity. In 1873, August Weismann postulated the equivalence of the maternal and paternal germ cells for heredity. The function of the nucleus as carrier of genetic information became clear only later, after mitosis was discovered and the Mendelian rules were rediscovered at the beginning of the 20th century; the chromosome theory of heredity was therefore developed.[4]
+
+The nucleus is the largest organelle in animal cells.[5]
+In mammalian cells, the average diameter of the nucleus is approximately 6 micrometres (µm), which occupies about 10% of the total cell volume.[6] The contents of the        
+nucleus are held in the nucleoplasm similar to the cytoplasm in the rest of the cell. The fluid component of this is termed the nucleosol, similar to the cytosol in the cytoplasm.[7]
+
+In most types of granulocyte, a white blood cell,  the nucleus is lobated and can be bi-lobed, tri-lobed or multi-lobed.
+
+The dynamic behaviour of structures in the nucleus, such as the nuclear rotation that occurs prior to mitosis, can be visualized using label-free live cell imaging.[8]
+
+The nuclear envelope, otherwise known as nuclear membrane, consists of two cellular membranes, an inner and an outer membrane, arranged parallel to one another and separated by 10 to 50 nanometres (nm). The nuclear envelope completely encloses the nucleus and separates the cell's genetic material from the surrounding cytoplasm, serving as a barrier to prevent macromolecules from diffusing freely between the nucleoplasm and the cytoplasm.[9] The outer nuclear membrane is continuous with the membrane of the rough endoplasmic reticulum (RER), and is similarly studded with ribosomes.[9] The space between the membranes is called the perinuclear space and is continuous with the RER lumen.
+
+Nuclear pores, which provide aqueous channels through the envelope, are composed of multiple proteins, collectively referred to as nucleoporins. The pores are about 125 million daltons in molecular weight and consist of around 50 (in yeast) to several hundred proteins (in vertebrates).[5] The pores are 100 nm in total diameter; however, the gap through which molecules freely diffuse is only about 9 nm wide, due to the presence of regulatory systems within the center of the pore. This size selectively allows the passage of small water-soluble molecules while preventing larger molecules, such as nucleic acids and larger proteins, from inappropriately entering or exiting the nucleus. These large molecules must be actively transported into the nucleus instead. The nucleus of a typical mammalian cell will have about 3000 to 4000 pores throughout its envelope,[10] each of which contains an eightfold-symmetric ring-shaped structure at a position where the inner and outer membranes fuse.[11] Attached to the ring is a structure called the nuclear basket that extends into the nucleoplasm, and a series of filamentous extensions that reach into the cytoplasm. Both structures serve to mediate binding to nuclear transport proteins.[5]
+
+Most proteins, ribosomal subunits, and some DNAs are transported through the pore complexes in a process mediated by a family of transport factors known as karyopherins. Those karyopherins that mediate movement into the nucleus are also called importins, whereas those that mediate movement out of the nucleus are called exportins. Most karyopherins interact directly with their cargo, although some use adaptor proteins.[12] Steroid hormones such as cortisol and aldosterone, as well as other small lipid-soluble molecules involved in intercellular signaling, can diffuse through the cell membrane and into the cytoplasm, where they bind nuclear receptor proteins that are trafficked into the nucleus. There they serve as transcription factors when bound to their ligand; in the absence of a ligand, many such receptors function as histone deacetylases that repress gene expression.[5]
+
+In animal cells, two networks of intermediate filaments provide the nucleus with mechanical support: The nuclear lamina forms an organized meshwork on the internal face of the envelope, while less organized support is provided on the cytosolic face of the envelope. Both systems provide structural support for the nuclear envelope and anchoring sites for chromosomes and nuclear pores.[13]
+
+The nuclear lamina is composed mostly of lamin proteins. Like all proteins, lamins are synthesized in the cytoplasm and later transported to the nucleus interior, where they are assembled before being incorporated into the existing network of nuclear lamina.[14][15] Lamins found on the cytosolic face of the membrane, such as emerin and nesprin, bind to the cytoskeleton to provide structural support. Lamins are also found inside the nucleoplasm where they form another regular structure, known as the nucleoplasmic veil,[16] that is visible using fluorescence microscopy. The actual function of the veil is not clear, although it is excluded from the nucleolus and is present during interphase.[17] Lamin structures that make up the veil, such as LEM3, bind chromatin and disrupting their structure inhibits transcription of protein-coding genes.[18]
+
+Like the components of other intermediate filaments, the lamin monomer contains an alpha-helical domain used by two monomers to coil around each other, forming a dimer structure called a coiled coil. Two of these dimer structures then join side by side, in an antiparallel arrangement, to form a tetramer called a protofilament. Eight of these protofilaments form a lateral arrangement that is twisted to form a ropelike filament. These filaments can be assembled or disassembled in a dynamic manner, meaning that changes in the length of the filament depend on the competing rates of filament addition and removal.[13]
+
+Mutations in lamin genes leading to defects in filament assembly cause a group of rare genetic disorders known as laminopathies. The most notable laminopathy is the family of diseases known as progeria, which causes the appearance of premature aging in its sufferers. The exact mechanism by which the associated biochemical changes give rise to the aged phenotype is not well understood.[19]
+
+The cell nucleus contains the majority of the cell's genetic material in the form of multiple linear DNA molecules organized into structures called chromosomes. Each human cell contains roughly two meters of DNA. During most of the cell cycle these are organized in a DNA-protein complex known as chromatin, and during cell division the chromatin can be seen to form the well-defined chromosomes familiar from a karyotype. A small fraction of the cell's genes are located instead in the mitochondria.
+
+There are two types of chromatin. Euchromatin is the less compact DNA form, and contains genes that are frequently expressed by the cell.[20] The other type, heterochromatin, is the more compact form, and contains DNA that is infrequently transcribed. This structure is further categorized into facultative heterochromatin, consisting of genes that are organized as heterochromatin only in certain cell types or at certain stages of development, and constitutive heterochromatin that consists of chromosome structural components such as telomeres and centromeres.[21] During interphase the chromatin organizes itself into discrete individual patches,[22] called chromosome territories.[23] Active genes, which are generally found in the euchromatic region of the chromosome, tend to be located towards the chromosome's territory boundary.[24]
+
+Antibodies to certain types of chromatin organization, in particular, nucleosomes, have been associated with a number of autoimmune diseases, such as systemic lupus erythematosus.[25] These are known as anti-nuclear antibodies (ANA) and have also been observed in concert with multiple sclerosis as part of general immune system dysfunction.[26] As in the case of progeria, the role played by the antibodies in inducing the symptoms of autoimmune diseases is not obvious.
+
+The nucleolus is the largest of the discrete densely stained, membraneless structures known as nuclear bodies found in the nucleus. It forms around tandem repeats of rDNA, DNA coding for ribosomal RNA (rRNA). These regions are called nucleolar organizer regions (NOR). The main roles of the nucleolus are to synthesize rRNA and assemble ribosomes. The structural cohesion of the nucleolus depends on its activity, as ribosomal assembly in the nucleolus results in the transient association of nucleolar components, facilitating further ribosomal assembly, and hence further association. This model is supported by observations that inactivation of rDNA results in intermingling of nucleolar structures.[27]
+
+In the first step of ribosome assembly,  a protein called RNA polymerase I transcribes rDNA, which forms a large pre-rRNA precursor. This is cleaved into the subunits 5.8S, 18S, and 28S rRNA.[28] The transcription, post-transcriptional processing, and assembly of rRNA occurs in the nucleolus, aided by small nucleolar RNA (snoRNA) molecules, some of which are derived from spliced introns from messenger RNAs encoding genes related to ribosomal function. The assembled ribosomal subunits are the largest structures passed through the nuclear pores.[5]
+
+When observed under the electron microscope, the nucleolus can be seen to consist of three distinguishable regions: the innermost fibrillar centers (FCs), surrounded by the dense fibrillar component (DFC) (that contains fibrillarin and nucleolin), which in turn is bordered by the granular component (GC) (that contains the protein nucleophosmin). Transcription of the rDNA occurs either in the FC or at the FC-DFC boundary, and, therefore, when rDNA transcription in the cell is increased, more FCs are detected. Most of the cleavage and modification of rRNAs occurs in the DFC, while the latter steps involving protein assembly onto the ribosomal subunits occur in the GC.[28]
+
+Besides the nucleolus, the nucleus contains a number of other nuclear bodies. These include Cajal bodies, gemini of Cajal bodies, polymorphic interphase karyosomal association (PIKA), promyelocytic leukaemia (PML) bodies, paraspeckles, and splicing speckles. Although little is known about a number of these domains, they are significant in that they show that the nucleoplasm is not a uniform mixture, but rather contains organized functional subdomains.[32]
+
+Other subnuclear structures appear as part of abnormal disease processes. For example, the presence of small intranuclear rods has been reported in some cases of nemaline myopathy. This condition typically results from mutations in actin, and the rods themselves consist of mutant actin as well as other cytoskeletal proteins.[34]
+
+A nucleus typically contains between 1 and 10 compact structures called Cajal bodies or coiled bodies (CB), whose diameter measures between 0.2 µm and 2.0 µm depending on the cell type and species.[29] When seen under an electron microscope, they resemble balls of tangled thread[31] and are dense foci of distribution for the protein coilin.[35] CBs are involved in a number of different roles relating to RNA processing, specifically small nucleolar RNA (snoRNA) and small nuclear RNA (snRNA) maturation, and histone mRNA modification.[29]
+
+Similar to Cajal bodies are Gemini of Cajal bodies, or gems, whose name is derived from the Gemini constellation in reference to their close "twin" relationship with CBs. Gems are similar in size and shape to CBs, and in fact are virtually indistinguishable under the microscope.[35] Unlike CBs, gems do not contain small nuclear ribonucleoproteins (snRNPs), but do contain a protein called survival of motor neuron (SMN) whose function relates to snRNP biogenesis. Gems are believed to assist CBs in snRNP biogenesis,[36] though it has also been suggested from microscopy evidence that CBs and gems are different manifestations of the same structure.[35] Later ultrastructural studies have shown gems to be twins of Cajal bodies with the difference being in the coilin component; Cajal bodies are SMN positive and coilin positive, and gems are SMN positive and coilin negative.[37]
+
+PIKA domains, or polymorphic interphase karyosomal associations, were first described in microscopy studies in 1991. Their function remains unclear, though they were not thought to be associated with active DNA replication, transcription, or RNA processing.[38] They have been found to often associate with discrete domains defined by dense localization of the transcription factor PTF, which promotes transcription of small nuclear RNA (snRNA).[39]
+
+Promyelocytic leukemia bodies (PML bodies) are spherical bodies found scattered throughout the nucleoplasm, measuring around 0.1–1.0 µm. They are known by a number of other names, including nuclear domain 10 (ND10), Kremer bodies, and PML oncogenic domains.[40] PML bodies are named after one of their major components, the promyelocytic leukemia protein (PML). They are often seen in the nucleus in association with Cajal bodies and cleavage bodies.[32] Pml-/- mice, which are unable to create PML bodies, develop normally without obvious ill effects, showing that PML bodies are not required for most essential biological processes.[41]
+
+Speckles are subnuclear structures that are enriched in pre-messenger RNA splicing factors and are located in the interchromatin regions of the nucleoplasm of mammalian cells. At the fluorescence-microscope level they appear as irregular, punctate structures, which vary in size and shape, and when examined by electron microscopy they are seen as clusters of interchromatin granules. Speckles are dynamic structures, and both their protein and RNA-protein components can cycle continuously between speckles and other nuclear locations, including active transcription sites. Studies on the composition, structure and behaviour of speckles have provided a model for understanding the functional compartmentalization of the nucleus and the organization of the gene-expression machinery[42]
+splicing snRNPs[43][44] and other splicing proteins necessary for pre-mRNA processing.[42] Because of a cell's changing requirements, the composition and location of these bodies changes according to mRNA transcription and regulation via phosphorylation of specific proteins.[45]
+The splicing speckles are also known as nuclear speckles (nuclear specks), splicing factor compartments (SF compartments), interchromatin granule clusters (IGCs), and B snurposomes.[46]
+B snurposomes are found in the amphibian oocyte nuclei and in Drosophila melanogaster embryos. B snurposomes appear alone or attached to the Cajal bodies in the electron micrographs of the amphibian nuclei.[47]
+IGCs function as storage sites for the splicing factors.[48]
+
+Discovered by Fox et al. in 2002, paraspeckles are irregularly shaped compartments in the interchromatin space of the nucleus.[49]  First documented in HeLa cells, where there are generally 10–30 per nucleus,[50] paraspeckles are now known to also exist in all human primary cells, transformed cell lines, and tissue sections.[51] Their name is derived from their distribution in the nucleus; the "para" is short for parallel and the "speckles" refers to the splicing speckles to which they are always in close proximity.[50]
+
+Paraspeckles are dynamic structures that are altered in response to changes in cellular metabolic activity. They are transcription dependent[49] and in the absence of RNA Pol II transcription, the paraspeckle disappears and all of its associated protein components  (PSP1, p54nrb, PSP2, CFI(m)68, and PSF) form a crescent shaped perinucleolar cap in the nucleolus. This phenomenon is demonstrated during the cell cycle. In the cell cycle, paraspeckles are present during interphase and during all of mitosis except for telophase. During telophase, when the two daughter nuclei are formed, there is no RNA Pol II transcription so the protein components instead form a perinucleolar cap.[51]
+
+Perichromatin fibrils are visible only under electron microscope. They are located next to the transcriptionally active chromatin and are hypothesized to be the sites of active pre-mRNA processing.[48]
+
+Clastosomes are small nuclear bodies (0.2–0.5 µm) described as having a thick ring-shape due to the peripheral capsule around these bodies.[30] This name is derived from the Greek klastos, broken and soma, body.[30] Clastosomes are not typically present in normal cells, making them hard to detect. They form under high proteolytic conditions within the nucleus and degrade once there is a decrease in activity or if cells are treated with proteasome inhibitors.[30][52] The scarcity of clastosomes in cells indicates that they are not required for proteasome function.[53] Osmotic stress has also been shown to cause the formation of clastosomes.[54] These nuclear bodies contain catalytic and regulatory sub-units of the proteasome and its substrates, indicating that clastosomes are sites for degrading proteins.[53]
+
+The fougaro system (Greek; Fougaro, chimney) is a sub-organelle system in the nucleus that may be a mechanism to recycle or remove molecules from the cell to the external medium. The molecules or peptides are ubiquitinated before being released from the nucleus of the cells. The ubiquitinated molecules are released independently or associated with endosomal proteins such as Beclin[55][56]
+
+The nucleus provides a site for genetic transcription that is segregated from the location of translation in the cytoplasm, allowing levels of gene regulation that are not available to prokaryotes. The main function of the cell nucleus is to control gene expression and mediate the replication of DNA during the cell cycle.
+
+The nucleus is an organelle found in eukaryotic cells. Inside its fully enclosed nuclear membrane, it contains the majority of the cell's genetic material. This material is organized as DNA molecules, along with a variety of proteins, to form chromosomes.
+
+The nuclear envelope allows the nucleus to control its contents, and separate them from the rest of the cytoplasm where necessary. This is important for controlling processes on either side of the nuclear membrane. In most cases where a cytoplasmic process needs to be restricted, a key participant is removed to the nucleus, where it interacts with transcription factors to downregulate the production of certain enzymes in the pathway. This regulatory mechanism occurs in the case of glycolysis, a cellular pathway for breaking down glucose to produce energy. Hexokinase is an enzyme responsible for the first the step of glycolysis, forming glucose-6-phosphate from glucose. At high concentrations of fructose-6-phosphate, a molecule made later from glucose-6-phosphate, a regulator protein removes hexokinase to the nucleus,[57] where it forms a transcriptional repressor complex with nuclear proteins to reduce the expression of genes involved in glycolysis.[58]
+
+In order to control which genes are being transcribed, the cell separates some transcription factor proteins responsible for regulating gene expression from physical access to the DNA until they are activated by other signaling pathways. This prevents even low levels of inappropriate gene expression. For example, in the case of NF-κB-controlled genes, which are involved in most inflammatory responses, transcription is induced in response to a signal pathway such as that initiated by the signaling molecule TNF-α, binds to a cell membrane receptor, resulting in the recruitment of signalling proteins, and eventually activating the transcription factor NF-κB. A nuclear localisation signal on the NF-κB protein allows it to be transported through the nuclear pore and into the nucleus, where it stimulates the transcription of the target genes.[13]
+
+The compartmentalization allows the cell to prevent translation of unspliced mRNA.[59] Eukaryotic mRNA contains introns that must be removed before being translated to produce functional proteins. The splicing is done inside the nucleus before the mRNA can be accessed by ribosomes for translation. Without the nucleus, ribosomes would translate newly transcribed (unprocessed) mRNA, resulting in malformed and nonfunctional proteins.
+
+Gene expression first involves transcription, in which DNA is used as a template to produce RNA. In the case of genes encoding proteins, that RNA produced from this process is messenger RNA (mRNA), which then needs to be translated by ribosomes to form a protein. As ribosomes are located outside the nucleus, mRNA produced needs to be exported.[60]
+
+Since the nucleus is the site of transcription, it also contains a variety of proteins that either directly mediate transcription or are involved in regulating the process. These proteins include helicases, which unwind the double-stranded DNA molecule to facilitate access to it, RNA polymerases, which bind to the DNA promoter to synthesize the growing RNA molecule, topoisomerases, which change the amount of supercoiling in DNA, helping it wind and unwind, as well as a large variety of transcription factors that regulate expression.[61]
+
+Newly synthesized mRNA molecules are known as primary transcripts or pre-mRNA. They must undergo post-transcriptional modification in the nucleus before being exported to the cytoplasm; mRNA that appears in the cytoplasm without these modifications is degraded rather than used for protein translation. The three main modifications are 5' capping, 3' polyadenylation, and RNA splicing. While in the nucleus, pre-mRNA is associated with a variety of proteins in complexes known as heterogeneous ribonucleoprotein particles (hnRNPs). Addition of the 5' cap occurs co-transcriptionally and is the first step in post-transcriptional modification. The 3' poly-adenine tail is only added after transcription is complete.
+
+RNA splicing, carried out by a complex called the spliceosome, is the process by which introns, or regions of DNA that do not code for protein, are removed from the pre-mRNA and the remaining exons connected to re-form a single continuous molecule. This process normally occurs after 5' capping and 3' polyadenylation but can begin before synthesis is complete in transcripts with many exons.[5] Many pre-mRNAs, including those encoding antibodies, can be spliced in multiple ways to produce different mature mRNAs that encode different protein sequences. This process is known as alternative splicing, and allows production of a large variety of proteins from a limited amount of DNA.
+
+The entry and exit of large molecules from the nucleus is tightly controlled by the nuclear pore complexes. Although small molecules can enter the nucleus without regulation,[62] macromolecules such as RNA and proteins require association karyopherins called importins to enter the nucleus and exportins to exit. "Cargo" proteins that must be translocated from the cytoplasm to the nucleus contain short amino acid sequences known as nuclear localization signals, which are bound by importins, while those transported from the nucleus to the cytoplasm carry nuclear export signals bound by exportins. The ability of importins and exportins to transport their cargo is regulated by GTPases, enzymes that hydrolyze the molecule guanosine triphosphate (GTP) to release energy. The key GTPase in nuclear transport is Ran, which can bind either GTP or GDP (guanosine diphosphate), depending on whether it is located in the nucleus or the cytoplasm. Whereas importins depend on RanGTP to dissociate from their cargo, exportins require RanGTP in order to bind to their cargo.[12]
+
+Nuclear import depends on the importin binding its cargo in the cytoplasm and carrying it through the nuclear pore into the nucleus. Inside the nucleus, RanGTP acts to separate the cargo from the importin, allowing the importin to exit the nucleus and be reused. Nuclear export is similar, as the exportin binds the cargo inside the nucleus in a process facilitated by RanGTP, exits through the nuclear pore, and separates from its cargo in the cytoplasm.
+
+Specialized export proteins exist for translocation of mature mRNA and tRNA to the cytoplasm after post-transcriptional modification is complete. This quality-control mechanism is important due to these molecules' central role in protein translation. Mis-expression of a protein due to incomplete excision of exons or mis-incorporation of amino acids could have negative consequences for the cell; thus, incompletely modified RNA that reaches the cytoplasm is degraded rather than used in translation.[5]
+
+During its lifetime, a nucleus may be broken down or destroyed, either in the process of cell division or as a consequence of apoptosis (the process of programmed cell death). During these events, the structural components of the nucleus — the envelope and lamina — can be systematically degraded.
+In most cells, the disassembly of the nuclear envelope marks the end of the prophase of mitosis. However, this disassembly of the nucleus is not a universal feature of mitosis and does not occur in all cells. Some unicellular eukaryotes (e.g., yeasts) undergo so-called closed mitosis, in which the nuclear envelope remains intact. In closed mitosis, the daughter chromosomes migrate to opposite poles of the nucleus, which then divides in two. The cells of higher eukaryotes, however, usually undergo open mitosis, which is characterized by breakdown of the nuclear envelope. The daughter chromosomes then migrate to opposite poles of the mitotic spindle, and new nuclei reassemble around them.
+
+At a certain point during the cell cycle in open mitosis, the cell divides to form two cells. In order for this process to be possible, each of the new daughter cells must have a full set of genes, a process requiring replication of the chromosomes as well as segregation of the separate sets. This occurs by the replicated chromosomes, the sister chromatids, attaching to microtubules, which in turn are attached to different centrosomes. The sister chromatids can then be pulled to separate locations in the cell. In many cells, the centrosome is located in the cytoplasm, outside the nucleus; the microtubules would be unable to attach to the chromatids in the presence of the nuclear envelope.[63] Therefore, the early stages in the cell cycle, beginning in prophase and until around prometaphase, the nuclear membrane is dismantled.[16] Likewise, during the same period, the nuclear lamina is also disassembled, a process regulated by phosphorylation of the lamins by protein kinases such as the CDC2 protein kinase.[64] Towards the end of the cell cycle, the nuclear membrane is reformed, and around the same time, the nuclear lamina are reassembled by dephosphorylating the lamins.[64]
+
+However, in dinoflagellates, the nuclear envelope remains intact, the centrosomes are located in the cytoplasm, and the microtubules come in contact with chromosomes, whose centromeric regions are incorporated into the nuclear envelope (the so-called closed mitosis with extranuclear spindle). In many other protists (e.g., ciliates, sporozoans) and fungi, the centrosomes are intranuclear, and their nuclear envelope also does not disassemble during cell division.
+
+Apoptosis is a controlled process in which the cell's structural components are destroyed, resulting in death of the cell. Changes associated with apoptosis directly affect the nucleus and its contents, for example, in the condensation of chromatin and the disintegration of the nuclear envelope and lamina. The destruction of the lamin networks is controlled by specialized apoptotic proteases called caspases, which cleave the lamin proteins and, thus, degrade the nucleus' structural integrity. Lamin cleavage is sometimes used as a laboratory indicator of caspase activity in assays for early apoptotic activity.[16] Cells that express mutant caspase-resistant lamins are deficient in nuclear changes related to apoptosis, suggesting that lamins play a role in initiating the events that lead to apoptotic degradation of the nucleus.[16] Inhibition of lamin assembly itself is an inducer of apoptosis.[65]
+
+The nuclear envelope acts as a barrier that prevents both DNA and RNA viruses from entering the nucleus. Some viruses require access to proteins inside the nucleus in order to replicate and/or assemble. DNA viruses, such as herpesvirus replicate and assemble in the cell nucleus, and exit by budding through the inner nuclear membrane. This process is accompanied by disassembly of the lamina on the nuclear face of the inner membrane.[16]
+
+Initially, it has been suspected that immunoglobulins in general and autoantibodies in particular do not enter the nucleus. Now there is a body of evidence that under pathological conditions (e.g. lupus erythematosus) IgG can enter the nucleus.[66]
+
+Most eukaryotic cell types usually have a single nucleus, but some have no nuclei, while others have several. This can result from normal development, as in the maturation of mammalian red blood cells, or from faulty cell division.
+
+An anucleated cell contains no nucleus and is, therefore, incapable of dividing to produce daughter cells. The best-known anucleated cell is the mammalian red blood cell, or erythrocyte, which also lacks other organelles such as mitochondria, and serves primarily as a transport vessel to ferry oxygen from the lungs to the body's tissues. Erythrocytes mature through erythropoiesis in the bone marrow, where they lose their nuclei, organelles, and ribosomes. The nucleus is expelled during the process of differentiation from an erythroblast to a reticulocyte, which is the immediate precursor of the mature erythrocyte.[67] The presence of mutagens may induce the release of some immature "micronucleated" erythrocytes into the bloodstream.[68][69] Anucleated cells can also arise from flawed cell division in which one daughter lacks a nucleus and the other has two nuclei.
+
+In flowering plants, this condition occurs in sieve tube elements.
+
+Multinucleated cells contain multiple nuclei. Most acantharean species of protozoa[70] and some fungi in mycorrhizae[71] have naturally multinucleated cells. Other examples include the intestinal parasites in the genus Giardia, which have two nuclei per cell.[72] In humans, skeletal muscle cells, called myocytes and syncytium, become multinucleated during development; the resulting arrangement of nuclei near the periphery of the cells allows maximal intracellular space for myofibrils.[5] Other multinucleate cells in the human are osteoclasts a type of bone cell. Multinucleated and binucleated cells can also be abnormal in humans; for example, cells arising from the fusion of monocytes and macrophages, known as giant multinucleated cells, sometimes accompany inflammation[73] and are also implicated in tumor formation.[74]
+
+A number of dinoflagellates are known to have two nuclei.[75] Unlike other multinucleated cells these nuclei contain two distinct lineages of DNA: one from the dinoflagellate and the other from a symbiotic diatom. The mitochondria and the plastids of the diatom somehow remain functional.
+
+As the major defining characteristic of the eukaryotic cell, the nucleus' evolutionary origin has been the subject of much speculation. Four major hypotheses have been proposed to explain the existence of the nucleus, although none have yet earned widespread support.[76]
+
+The first model known as the "syntrophic model" proposes that a symbiotic relationship between the archaea and bacteria created the nucleus-containing eukaryotic cell. (Organisms of the Archaea and Bacteria domain have no cell nucleus.[77]) It is hypothesized that the symbiosis originated when ancient archaea, similar to modern methanogenic archaea, invaded and lived within bacteria similar to modern myxobacteria, eventually forming the early nucleus. This theory is analogous to the accepted theory for the origin of eukaryotic mitochondria and chloroplasts, which are thought to have developed from a similar endosymbiotic relationship between proto-eukaryotes and aerobic bacteria.[78] The archaeal origin of the nucleus is supported by observations that archaea and eukarya have similar genes for certain proteins, including histones. Observations that myxobacteria are motile, can form multicellular complexes, and possess kinases and G proteins similar to eukarya, support a bacterial origin for the eukaryotic cell.[79]
+
+A second model proposes that proto-eukaryotic cells evolved from bacteria without an endosymbiotic stage. This model is based on the existence of modern planctomycetes bacteria that possess a nuclear structure with primitive pores and other compartmentalized membrane structures.[80]  A similar proposal states that a eukaryote-like cell, the chronocyte, evolved first and phagocytosed archaea and bacteria to generate the nucleus and the eukaryotic cell.[81]
+
+The most controversial model, known as viral eukaryogenesis, posits that the membrane-bound nucleus, along with other eukaryotic features, originated from the infection of a prokaryote by a virus. The suggestion is based on similarities between eukaryotes and viruses such as linear DNA strands, mRNA capping, and tight binding to proteins (analogizing histones to viral envelopes). One version of the proposal suggests that the nucleus evolved in concert with phagocytosis to form an early cellular "predator".[82] Another variant proposes that eukaryotes originated from early archaea infected by poxviruses, on the basis of observed similarity between the DNA polymerases in modern poxviruses and eukaryotes.[83][84] It has been suggested that the unresolved question of the evolution of sex could be related to the viral eukaryogenesis hypothesis.[85]
+
+A more recent proposal, the exomembrane hypothesis, suggests that the nucleus instead originated from a single ancestral cell that evolved a second exterior cell membrane; the interior membrane enclosing the original cell then became the nuclear membrane and evolved increasingly elaborate pore structures for passage of internally synthesized cellular components such as ribosomal subunits.[86]
+

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+In cell biology, the nucleus (pl. nuclei; from Latin nucleus or nuculeus, meaning kernel or seed) is a membrane-bound organelle found in eukaryotic cells. Eukaryotes usually have a single nucleus, but a few cell types, such as mammalian red blood cells, have no nuclei, and a few others including osteoclasts have many.
+
+The cell nucleus contains all of the cell's genome, except for a small fraction of mitochondrial DNA, organized as multiple long linear DNA molecules in a complex with a large variety of proteins, such as histones, to form chromosomes. The genes within these chromosomes are structured in such a way to promote cell function. The nucleus maintains the integrity of genes and controls the activities of the cell by regulating gene expression—the nucleus is, therefore, the control center of the cell. The main structures making up the nucleus are the nuclear envelope, a double membrane that encloses the entire organelle and isolates its contents from the cellular cytoplasm, and the nuclear matrix (which includes the nuclear lamina), a network within the nucleus that adds mechanical support, much like the cytoskeleton, which supports the cell as a whole.
+
+Because the nuclear envelope is impermeable to large molecules, nuclear pores are required to regulate nuclear transport of molecules across the envelope. The pores cross both nuclear membranes, providing a channel through which larger molecules must be actively transported by carrier proteins while allowing free movement of small molecules and ions. Movement of large molecules such as proteins and RNA through the pores is required for both gene expression and the maintenance of chromosomes. Although the interior of the nucleus does not contain any membrane-bound subcompartments, its contents are not uniform, and a number of nuclear bodies exist, made up of unique proteins, RNA molecules, and particular parts of the chromosomes. The best-known of these is the nucleolus, which is mainly involved in the assembly of ribosomes. After being produced in the nucleolus, ribosomes are exported to the cytoplasm where they translate mRNA.
+
+The nucleus was the first organelle to be discovered. What is most likely the oldest preserved drawing dates back to the early microscopist Antonie van Leeuwenhoek (1632–1723). He observed a "lumen", the nucleus, in the red blood cells of salmon.[1] Unlike mammalian red blood cells, those of other vertebrates still contain nuclei.
+
+The nucleus was also described by Franz Bauer in 1804[2] and in more detail in 1831 by Scottish botanist Robert Brown in a talk at the Linnean Society of London. Brown was studying orchids under the microscope when he observed an opaque area, which he called the "areola" or "nucleus", in the cells of the flower's outer layer.[3]
+
+He did not suggest a potential function. In 1838, Matthias Schleiden proposed that the nucleus plays a role in generating cells, thus he introduced the name "cytoblast" ("cell builder"). He believed that he had observed new cells assembling around "cytoblasts". Franz Meyen was a strong opponent of this view, having already described cells multiplying by division and believing that many cells would have no nuclei. The idea that cells can be generated de novo, by the "cytoblast" or otherwise, contradicted work by Robert Remak (1852) and Rudolf Virchow (1855) who decisively propagated the new paradigm that cells are generated solely by cells ("Omnis cellula e cellula"). The function of the nucleus remained unclear.[4]
+
+Between 1877 and 1878, Oscar Hertwig published several studies on the fertilization of sea urchin eggs, showing that the nucleus of the sperm enters the oocyte and fuses with its nucleus. This was the first time it was suggested that an individual develops from a (single) nucleated cell. This was in contradiction to Ernst Haeckel's theory that the complete phylogeny of a species would be repeated during embryonic development, including generation of the first nucleated cell from a "monerula", a structureless mass of primordial protoplasm ("Urschleim"). Therefore, the necessity of the sperm nucleus for fertilization was discussed for quite some time. However, Hertwig confirmed his observation in other animal groups, including amphibians and molluscs. Eduard Strasburger produced the same results for plants in 1884. This paved the way to assign the nucleus an important role in heredity. In 1873, August Weismann postulated the equivalence of the maternal and paternal germ cells for heredity. The function of the nucleus as carrier of genetic information became clear only later, after mitosis was discovered and the Mendelian rules were rediscovered at the beginning of the 20th century; the chromosome theory of heredity was therefore developed.[4]
+
+The nucleus is the largest organelle in animal cells.[5]
+In mammalian cells, the average diameter of the nucleus is approximately 6 micrometres (µm), which occupies about 10% of the total cell volume.[6] The contents of the        
+nucleus are held in the nucleoplasm similar to the cytoplasm in the rest of the cell. The fluid component of this is termed the nucleosol, similar to the cytosol in the cytoplasm.[7]
+
+In most types of granulocyte, a white blood cell,  the nucleus is lobated and can be bi-lobed, tri-lobed or multi-lobed.
+
+The dynamic behaviour of structures in the nucleus, such as the nuclear rotation that occurs prior to mitosis, can be visualized using label-free live cell imaging.[8]
+
+The nuclear envelope, otherwise known as nuclear membrane, consists of two cellular membranes, an inner and an outer membrane, arranged parallel to one another and separated by 10 to 50 nanometres (nm). The nuclear envelope completely encloses the nucleus and separates the cell's genetic material from the surrounding cytoplasm, serving as a barrier to prevent macromolecules from diffusing freely between the nucleoplasm and the cytoplasm.[9] The outer nuclear membrane is continuous with the membrane of the rough endoplasmic reticulum (RER), and is similarly studded with ribosomes.[9] The space between the membranes is called the perinuclear space and is continuous with the RER lumen.
+
+Nuclear pores, which provide aqueous channels through the envelope, are composed of multiple proteins, collectively referred to as nucleoporins. The pores are about 125 million daltons in molecular weight and consist of around 50 (in yeast) to several hundred proteins (in vertebrates).[5] The pores are 100 nm in total diameter; however, the gap through which molecules freely diffuse is only about 9 nm wide, due to the presence of regulatory systems within the center of the pore. This size selectively allows the passage of small water-soluble molecules while preventing larger molecules, such as nucleic acids and larger proteins, from inappropriately entering or exiting the nucleus. These large molecules must be actively transported into the nucleus instead. The nucleus of a typical mammalian cell will have about 3000 to 4000 pores throughout its envelope,[10] each of which contains an eightfold-symmetric ring-shaped structure at a position where the inner and outer membranes fuse.[11] Attached to the ring is a structure called the nuclear basket that extends into the nucleoplasm, and a series of filamentous extensions that reach into the cytoplasm. Both structures serve to mediate binding to nuclear transport proteins.[5]
+
+Most proteins, ribosomal subunits, and some DNAs are transported through the pore complexes in a process mediated by a family of transport factors known as karyopherins. Those karyopherins that mediate movement into the nucleus are also called importins, whereas those that mediate movement out of the nucleus are called exportins. Most karyopherins interact directly with their cargo, although some use adaptor proteins.[12] Steroid hormones such as cortisol and aldosterone, as well as other small lipid-soluble molecules involved in intercellular signaling, can diffuse through the cell membrane and into the cytoplasm, where they bind nuclear receptor proteins that are trafficked into the nucleus. There they serve as transcription factors when bound to their ligand; in the absence of a ligand, many such receptors function as histone deacetylases that repress gene expression.[5]
+
+In animal cells, two networks of intermediate filaments provide the nucleus with mechanical support: The nuclear lamina forms an organized meshwork on the internal face of the envelope, while less organized support is provided on the cytosolic face of the envelope. Both systems provide structural support for the nuclear envelope and anchoring sites for chromosomes and nuclear pores.[13]
+
+The nuclear lamina is composed mostly of lamin proteins. Like all proteins, lamins are synthesized in the cytoplasm and later transported to the nucleus interior, where they are assembled before being incorporated into the existing network of nuclear lamina.[14][15] Lamins found on the cytosolic face of the membrane, such as emerin and nesprin, bind to the cytoskeleton to provide structural support. Lamins are also found inside the nucleoplasm where they form another regular structure, known as the nucleoplasmic veil,[16] that is visible using fluorescence microscopy. The actual function of the veil is not clear, although it is excluded from the nucleolus and is present during interphase.[17] Lamin structures that make up the veil, such as LEM3, bind chromatin and disrupting their structure inhibits transcription of protein-coding genes.[18]
+
+Like the components of other intermediate filaments, the lamin monomer contains an alpha-helical domain used by two monomers to coil around each other, forming a dimer structure called a coiled coil. Two of these dimer structures then join side by side, in an antiparallel arrangement, to form a tetramer called a protofilament. Eight of these protofilaments form a lateral arrangement that is twisted to form a ropelike filament. These filaments can be assembled or disassembled in a dynamic manner, meaning that changes in the length of the filament depend on the competing rates of filament addition and removal.[13]
+
+Mutations in lamin genes leading to defects in filament assembly cause a group of rare genetic disorders known as laminopathies. The most notable laminopathy is the family of diseases known as progeria, which causes the appearance of premature aging in its sufferers. The exact mechanism by which the associated biochemical changes give rise to the aged phenotype is not well understood.[19]
+
+The cell nucleus contains the majority of the cell's genetic material in the form of multiple linear DNA molecules organized into structures called chromosomes. Each human cell contains roughly two meters of DNA. During most of the cell cycle these are organized in a DNA-protein complex known as chromatin, and during cell division the chromatin can be seen to form the well-defined chromosomes familiar from a karyotype. A small fraction of the cell's genes are located instead in the mitochondria.
+
+There are two types of chromatin. Euchromatin is the less compact DNA form, and contains genes that are frequently expressed by the cell.[20] The other type, heterochromatin, is the more compact form, and contains DNA that is infrequently transcribed. This structure is further categorized into facultative heterochromatin, consisting of genes that are organized as heterochromatin only in certain cell types or at certain stages of development, and constitutive heterochromatin that consists of chromosome structural components such as telomeres and centromeres.[21] During interphase the chromatin organizes itself into discrete individual patches,[22] called chromosome territories.[23] Active genes, which are generally found in the euchromatic region of the chromosome, tend to be located towards the chromosome's territory boundary.[24]
+
+Antibodies to certain types of chromatin organization, in particular, nucleosomes, have been associated with a number of autoimmune diseases, such as systemic lupus erythematosus.[25] These are known as anti-nuclear antibodies (ANA) and have also been observed in concert with multiple sclerosis as part of general immune system dysfunction.[26] As in the case of progeria, the role played by the antibodies in inducing the symptoms of autoimmune diseases is not obvious.
+
+The nucleolus is the largest of the discrete densely stained, membraneless structures known as nuclear bodies found in the nucleus. It forms around tandem repeats of rDNA, DNA coding for ribosomal RNA (rRNA). These regions are called nucleolar organizer regions (NOR). The main roles of the nucleolus are to synthesize rRNA and assemble ribosomes. The structural cohesion of the nucleolus depends on its activity, as ribosomal assembly in the nucleolus results in the transient association of nucleolar components, facilitating further ribosomal assembly, and hence further association. This model is supported by observations that inactivation of rDNA results in intermingling of nucleolar structures.[27]
+
+In the first step of ribosome assembly,  a protein called RNA polymerase I transcribes rDNA, which forms a large pre-rRNA precursor. This is cleaved into the subunits 5.8S, 18S, and 28S rRNA.[28] The transcription, post-transcriptional processing, and assembly of rRNA occurs in the nucleolus, aided by small nucleolar RNA (snoRNA) molecules, some of which are derived from spliced introns from messenger RNAs encoding genes related to ribosomal function. The assembled ribosomal subunits are the largest structures passed through the nuclear pores.[5]
+
+When observed under the electron microscope, the nucleolus can be seen to consist of three distinguishable regions: the innermost fibrillar centers (FCs), surrounded by the dense fibrillar component (DFC) (that contains fibrillarin and nucleolin), which in turn is bordered by the granular component (GC) (that contains the protein nucleophosmin). Transcription of the rDNA occurs either in the FC or at the FC-DFC boundary, and, therefore, when rDNA transcription in the cell is increased, more FCs are detected. Most of the cleavage and modification of rRNAs occurs in the DFC, while the latter steps involving protein assembly onto the ribosomal subunits occur in the GC.[28]
+
+Besides the nucleolus, the nucleus contains a number of other nuclear bodies. These include Cajal bodies, gemini of Cajal bodies, polymorphic interphase karyosomal association (PIKA), promyelocytic leukaemia (PML) bodies, paraspeckles, and splicing speckles. Although little is known about a number of these domains, they are significant in that they show that the nucleoplasm is not a uniform mixture, but rather contains organized functional subdomains.[32]
+
+Other subnuclear structures appear as part of abnormal disease processes. For example, the presence of small intranuclear rods has been reported in some cases of nemaline myopathy. This condition typically results from mutations in actin, and the rods themselves consist of mutant actin as well as other cytoskeletal proteins.[34]
+
+A nucleus typically contains between 1 and 10 compact structures called Cajal bodies or coiled bodies (CB), whose diameter measures between 0.2 µm and 2.0 µm depending on the cell type and species.[29] When seen under an electron microscope, they resemble balls of tangled thread[31] and are dense foci of distribution for the protein coilin.[35] CBs are involved in a number of different roles relating to RNA processing, specifically small nucleolar RNA (snoRNA) and small nuclear RNA (snRNA) maturation, and histone mRNA modification.[29]
+
+Similar to Cajal bodies are Gemini of Cajal bodies, or gems, whose name is derived from the Gemini constellation in reference to their close "twin" relationship with CBs. Gems are similar in size and shape to CBs, and in fact are virtually indistinguishable under the microscope.[35] Unlike CBs, gems do not contain small nuclear ribonucleoproteins (snRNPs), but do contain a protein called survival of motor neuron (SMN) whose function relates to snRNP biogenesis. Gems are believed to assist CBs in snRNP biogenesis,[36] though it has also been suggested from microscopy evidence that CBs and gems are different manifestations of the same structure.[35] Later ultrastructural studies have shown gems to be twins of Cajal bodies with the difference being in the coilin component; Cajal bodies are SMN positive and coilin positive, and gems are SMN positive and coilin negative.[37]
+
+PIKA domains, or polymorphic interphase karyosomal associations, were first described in microscopy studies in 1991. Their function remains unclear, though they were not thought to be associated with active DNA replication, transcription, or RNA processing.[38] They have been found to often associate with discrete domains defined by dense localization of the transcription factor PTF, which promotes transcription of small nuclear RNA (snRNA).[39]
+
+Promyelocytic leukemia bodies (PML bodies) are spherical bodies found scattered throughout the nucleoplasm, measuring around 0.1–1.0 µm. They are known by a number of other names, including nuclear domain 10 (ND10), Kremer bodies, and PML oncogenic domains.[40] PML bodies are named after one of their major components, the promyelocytic leukemia protein (PML). They are often seen in the nucleus in association with Cajal bodies and cleavage bodies.[32] Pml-/- mice, which are unable to create PML bodies, develop normally without obvious ill effects, showing that PML bodies are not required for most essential biological processes.[41]
+
+Speckles are subnuclear structures that are enriched in pre-messenger RNA splicing factors and are located in the interchromatin regions of the nucleoplasm of mammalian cells. At the fluorescence-microscope level they appear as irregular, punctate structures, which vary in size and shape, and when examined by electron microscopy they are seen as clusters of interchromatin granules. Speckles are dynamic structures, and both their protein and RNA-protein components can cycle continuously between speckles and other nuclear locations, including active transcription sites. Studies on the composition, structure and behaviour of speckles have provided a model for understanding the functional compartmentalization of the nucleus and the organization of the gene-expression machinery[42]
+splicing snRNPs[43][44] and other splicing proteins necessary for pre-mRNA processing.[42] Because of a cell's changing requirements, the composition and location of these bodies changes according to mRNA transcription and regulation via phosphorylation of specific proteins.[45]
+The splicing speckles are also known as nuclear speckles (nuclear specks), splicing factor compartments (SF compartments), interchromatin granule clusters (IGCs), and B snurposomes.[46]
+B snurposomes are found in the amphibian oocyte nuclei and in Drosophila melanogaster embryos. B snurposomes appear alone or attached to the Cajal bodies in the electron micrographs of the amphibian nuclei.[47]
+IGCs function as storage sites for the splicing factors.[48]
+
+Discovered by Fox et al. in 2002, paraspeckles are irregularly shaped compartments in the interchromatin space of the nucleus.[49]  First documented in HeLa cells, where there are generally 10–30 per nucleus,[50] paraspeckles are now known to also exist in all human primary cells, transformed cell lines, and tissue sections.[51] Their name is derived from their distribution in the nucleus; the "para" is short for parallel and the "speckles" refers to the splicing speckles to which they are always in close proximity.[50]
+
+Paraspeckles are dynamic structures that are altered in response to changes in cellular metabolic activity. They are transcription dependent[49] and in the absence of RNA Pol II transcription, the paraspeckle disappears and all of its associated protein components  (PSP1, p54nrb, PSP2, CFI(m)68, and PSF) form a crescent shaped perinucleolar cap in the nucleolus. This phenomenon is demonstrated during the cell cycle. In the cell cycle, paraspeckles are present during interphase and during all of mitosis except for telophase. During telophase, when the two daughter nuclei are formed, there is no RNA Pol II transcription so the protein components instead form a perinucleolar cap.[51]
+
+Perichromatin fibrils are visible only under electron microscope. They are located next to the transcriptionally active chromatin and are hypothesized to be the sites of active pre-mRNA processing.[48]
+
+Clastosomes are small nuclear bodies (0.2–0.5 µm) described as having a thick ring-shape due to the peripheral capsule around these bodies.[30] This name is derived from the Greek klastos, broken and soma, body.[30] Clastosomes are not typically present in normal cells, making them hard to detect. They form under high proteolytic conditions within the nucleus and degrade once there is a decrease in activity or if cells are treated with proteasome inhibitors.[30][52] The scarcity of clastosomes in cells indicates that they are not required for proteasome function.[53] Osmotic stress has also been shown to cause the formation of clastosomes.[54] These nuclear bodies contain catalytic and regulatory sub-units of the proteasome and its substrates, indicating that clastosomes are sites for degrading proteins.[53]
+
+The fougaro system (Greek; Fougaro, chimney) is a sub-organelle system in the nucleus that may be a mechanism to recycle or remove molecules from the cell to the external medium. The molecules or peptides are ubiquitinated before being released from the nucleus of the cells. The ubiquitinated molecules are released independently or associated with endosomal proteins such as Beclin[55][56]
+
+The nucleus provides a site for genetic transcription that is segregated from the location of translation in the cytoplasm, allowing levels of gene regulation that are not available to prokaryotes. The main function of the cell nucleus is to control gene expression and mediate the replication of DNA during the cell cycle.
+
+The nucleus is an organelle found in eukaryotic cells. Inside its fully enclosed nuclear membrane, it contains the majority of the cell's genetic material. This material is organized as DNA molecules, along with a variety of proteins, to form chromosomes.
+
+The nuclear envelope allows the nucleus to control its contents, and separate them from the rest of the cytoplasm where necessary. This is important for controlling processes on either side of the nuclear membrane. In most cases where a cytoplasmic process needs to be restricted, a key participant is removed to the nucleus, where it interacts with transcription factors to downregulate the production of certain enzymes in the pathway. This regulatory mechanism occurs in the case of glycolysis, a cellular pathway for breaking down glucose to produce energy. Hexokinase is an enzyme responsible for the first the step of glycolysis, forming glucose-6-phosphate from glucose. At high concentrations of fructose-6-phosphate, a molecule made later from glucose-6-phosphate, a regulator protein removes hexokinase to the nucleus,[57] where it forms a transcriptional repressor complex with nuclear proteins to reduce the expression of genes involved in glycolysis.[58]
+
+In order to control which genes are being transcribed, the cell separates some transcription factor proteins responsible for regulating gene expression from physical access to the DNA until they are activated by other signaling pathways. This prevents even low levels of inappropriate gene expression. For example, in the case of NF-κB-controlled genes, which are involved in most inflammatory responses, transcription is induced in response to a signal pathway such as that initiated by the signaling molecule TNF-α, binds to a cell membrane receptor, resulting in the recruitment of signalling proteins, and eventually activating the transcription factor NF-κB. A nuclear localisation signal on the NF-κB protein allows it to be transported through the nuclear pore and into the nucleus, where it stimulates the transcription of the target genes.[13]
+
+The compartmentalization allows the cell to prevent translation of unspliced mRNA.[59] Eukaryotic mRNA contains introns that must be removed before being translated to produce functional proteins. The splicing is done inside the nucleus before the mRNA can be accessed by ribosomes for translation. Without the nucleus, ribosomes would translate newly transcribed (unprocessed) mRNA, resulting in malformed and nonfunctional proteins.
+
+Gene expression first involves transcription, in which DNA is used as a template to produce RNA. In the case of genes encoding proteins, that RNA produced from this process is messenger RNA (mRNA), which then needs to be translated by ribosomes to form a protein. As ribosomes are located outside the nucleus, mRNA produced needs to be exported.[60]
+
+Since the nucleus is the site of transcription, it also contains a variety of proteins that either directly mediate transcription or are involved in regulating the process. These proteins include helicases, which unwind the double-stranded DNA molecule to facilitate access to it, RNA polymerases, which bind to the DNA promoter to synthesize the growing RNA molecule, topoisomerases, which change the amount of supercoiling in DNA, helping it wind and unwind, as well as a large variety of transcription factors that regulate expression.[61]
+
+Newly synthesized mRNA molecules are known as primary transcripts or pre-mRNA. They must undergo post-transcriptional modification in the nucleus before being exported to the cytoplasm; mRNA that appears in the cytoplasm without these modifications is degraded rather than used for protein translation. The three main modifications are 5' capping, 3' polyadenylation, and RNA splicing. While in the nucleus, pre-mRNA is associated with a variety of proteins in complexes known as heterogeneous ribonucleoprotein particles (hnRNPs). Addition of the 5' cap occurs co-transcriptionally and is the first step in post-transcriptional modification. The 3' poly-adenine tail is only added after transcription is complete.
+
+RNA splicing, carried out by a complex called the spliceosome, is the process by which introns, or regions of DNA that do not code for protein, are removed from the pre-mRNA and the remaining exons connected to re-form a single continuous molecule. This process normally occurs after 5' capping and 3' polyadenylation but can begin before synthesis is complete in transcripts with many exons.[5] Many pre-mRNAs, including those encoding antibodies, can be spliced in multiple ways to produce different mature mRNAs that encode different protein sequences. This process is known as alternative splicing, and allows production of a large variety of proteins from a limited amount of DNA.
+
+The entry and exit of large molecules from the nucleus is tightly controlled by the nuclear pore complexes. Although small molecules can enter the nucleus without regulation,[62] macromolecules such as RNA and proteins require association karyopherins called importins to enter the nucleus and exportins to exit. "Cargo" proteins that must be translocated from the cytoplasm to the nucleus contain short amino acid sequences known as nuclear localization signals, which are bound by importins, while those transported from the nucleus to the cytoplasm carry nuclear export signals bound by exportins. The ability of importins and exportins to transport their cargo is regulated by GTPases, enzymes that hydrolyze the molecule guanosine triphosphate (GTP) to release energy. The key GTPase in nuclear transport is Ran, which can bind either GTP or GDP (guanosine diphosphate), depending on whether it is located in the nucleus or the cytoplasm. Whereas importins depend on RanGTP to dissociate from their cargo, exportins require RanGTP in order to bind to their cargo.[12]
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+Nuclear import depends on the importin binding its cargo in the cytoplasm and carrying it through the nuclear pore into the nucleus. Inside the nucleus, RanGTP acts to separate the cargo from the importin, allowing the importin to exit the nucleus and be reused. Nuclear export is similar, as the exportin binds the cargo inside the nucleus in a process facilitated by RanGTP, exits through the nuclear pore, and separates from its cargo in the cytoplasm.
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+Specialized export proteins exist for translocation of mature mRNA and tRNA to the cytoplasm after post-transcriptional modification is complete. This quality-control mechanism is important due to these molecules' central role in protein translation. Mis-expression of a protein due to incomplete excision of exons or mis-incorporation of amino acids could have negative consequences for the cell; thus, incompletely modified RNA that reaches the cytoplasm is degraded rather than used in translation.[5]
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+During its lifetime, a nucleus may be broken down or destroyed, either in the process of cell division or as a consequence of apoptosis (the process of programmed cell death). During these events, the structural components of the nucleus — the envelope and lamina — can be systematically degraded.
+In most cells, the disassembly of the nuclear envelope marks the end of the prophase of mitosis. However, this disassembly of the nucleus is not a universal feature of mitosis and does not occur in all cells. Some unicellular eukaryotes (e.g., yeasts) undergo so-called closed mitosis, in which the nuclear envelope remains intact. In closed mitosis, the daughter chromosomes migrate to opposite poles of the nucleus, which then divides in two. The cells of higher eukaryotes, however, usually undergo open mitosis, which is characterized by breakdown of the nuclear envelope. The daughter chromosomes then migrate to opposite poles of the mitotic spindle, and new nuclei reassemble around them.
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+At a certain point during the cell cycle in open mitosis, the cell divides to form two cells. In order for this process to be possible, each of the new daughter cells must have a full set of genes, a process requiring replication of the chromosomes as well as segregation of the separate sets. This occurs by the replicated chromosomes, the sister chromatids, attaching to microtubules, which in turn are attached to different centrosomes. The sister chromatids can then be pulled to separate locations in the cell. In many cells, the centrosome is located in the cytoplasm, outside the nucleus; the microtubules would be unable to attach to the chromatids in the presence of the nuclear envelope.[63] Therefore, the early stages in the cell cycle, beginning in prophase and until around prometaphase, the nuclear membrane is dismantled.[16] Likewise, during the same period, the nuclear lamina is also disassembled, a process regulated by phosphorylation of the lamins by protein kinases such as the CDC2 protein kinase.[64] Towards the end of the cell cycle, the nuclear membrane is reformed, and around the same time, the nuclear lamina are reassembled by dephosphorylating the lamins.[64]
+
+However, in dinoflagellates, the nuclear envelope remains intact, the centrosomes are located in the cytoplasm, and the microtubules come in contact with chromosomes, whose centromeric regions are incorporated into the nuclear envelope (the so-called closed mitosis with extranuclear spindle). In many other protists (e.g., ciliates, sporozoans) and fungi, the centrosomes are intranuclear, and their nuclear envelope also does not disassemble during cell division.
+
+Apoptosis is a controlled process in which the cell's structural components are destroyed, resulting in death of the cell. Changes associated with apoptosis directly affect the nucleus and its contents, for example, in the condensation of chromatin and the disintegration of the nuclear envelope and lamina. The destruction of the lamin networks is controlled by specialized apoptotic proteases called caspases, which cleave the lamin proteins and, thus, degrade the nucleus' structural integrity. Lamin cleavage is sometimes used as a laboratory indicator of caspase activity in assays for early apoptotic activity.[16] Cells that express mutant caspase-resistant lamins are deficient in nuclear changes related to apoptosis, suggesting that lamins play a role in initiating the events that lead to apoptotic degradation of the nucleus.[16] Inhibition of lamin assembly itself is an inducer of apoptosis.[65]
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+The nuclear envelope acts as a barrier that prevents both DNA and RNA viruses from entering the nucleus. Some viruses require access to proteins inside the nucleus in order to replicate and/or assemble. DNA viruses, such as herpesvirus replicate and assemble in the cell nucleus, and exit by budding through the inner nuclear membrane. This process is accompanied by disassembly of the lamina on the nuclear face of the inner membrane.[16]
+
+Initially, it has been suspected that immunoglobulins in general and autoantibodies in particular do not enter the nucleus. Now there is a body of evidence that under pathological conditions (e.g. lupus erythematosus) IgG can enter the nucleus.[66]
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+Most eukaryotic cell types usually have a single nucleus, but some have no nuclei, while others have several. This can result from normal development, as in the maturation of mammalian red blood cells, or from faulty cell division.
+
+An anucleated cell contains no nucleus and is, therefore, incapable of dividing to produce daughter cells. The best-known anucleated cell is the mammalian red blood cell, or erythrocyte, which also lacks other organelles such as mitochondria, and serves primarily as a transport vessel to ferry oxygen from the lungs to the body's tissues. Erythrocytes mature through erythropoiesis in the bone marrow, where they lose their nuclei, organelles, and ribosomes. The nucleus is expelled during the process of differentiation from an erythroblast to a reticulocyte, which is the immediate precursor of the mature erythrocyte.[67] The presence of mutagens may induce the release of some immature "micronucleated" erythrocytes into the bloodstream.[68][69] Anucleated cells can also arise from flawed cell division in which one daughter lacks a nucleus and the other has two nuclei.
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+In flowering plants, this condition occurs in sieve tube elements.
+
+Multinucleated cells contain multiple nuclei. Most acantharean species of protozoa[70] and some fungi in mycorrhizae[71] have naturally multinucleated cells. Other examples include the intestinal parasites in the genus Giardia, which have two nuclei per cell.[72] In humans, skeletal muscle cells, called myocytes and syncytium, become multinucleated during development; the resulting arrangement of nuclei near the periphery of the cells allows maximal intracellular space for myofibrils.[5] Other multinucleate cells in the human are osteoclasts a type of bone cell. Multinucleated and binucleated cells can also be abnormal in humans; for example, cells arising from the fusion of monocytes and macrophages, known as giant multinucleated cells, sometimes accompany inflammation[73] and are also implicated in tumor formation.[74]
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+A number of dinoflagellates are known to have two nuclei.[75] Unlike other multinucleated cells these nuclei contain two distinct lineages of DNA: one from the dinoflagellate and the other from a symbiotic diatom. The mitochondria and the plastids of the diatom somehow remain functional.
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+As the major defining characteristic of the eukaryotic cell, the nucleus' evolutionary origin has been the subject of much speculation. Four major hypotheses have been proposed to explain the existence of the nucleus, although none have yet earned widespread support.[76]
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+The first model known as the "syntrophic model" proposes that a symbiotic relationship between the archaea and bacteria created the nucleus-containing eukaryotic cell. (Organisms of the Archaea and Bacteria domain have no cell nucleus.[77]) It is hypothesized that the symbiosis originated when ancient archaea, similar to modern methanogenic archaea, invaded and lived within bacteria similar to modern myxobacteria, eventually forming the early nucleus. This theory is analogous to the accepted theory for the origin of eukaryotic mitochondria and chloroplasts, which are thought to have developed from a similar endosymbiotic relationship between proto-eukaryotes and aerobic bacteria.[78] The archaeal origin of the nucleus is supported by observations that archaea and eukarya have similar genes for certain proteins, including histones. Observations that myxobacteria are motile, can form multicellular complexes, and possess kinases and G proteins similar to eukarya, support a bacterial origin for the eukaryotic cell.[79]
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+A second model proposes that proto-eukaryotic cells evolved from bacteria without an endosymbiotic stage. This model is based on the existence of modern planctomycetes bacteria that possess a nuclear structure with primitive pores and other compartmentalized membrane structures.[80]  A similar proposal states that a eukaryote-like cell, the chronocyte, evolved first and phagocytosed archaea and bacteria to generate the nucleus and the eukaryotic cell.[81]
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+The most controversial model, known as viral eukaryogenesis, posits that the membrane-bound nucleus, along with other eukaryotic features, originated from the infection of a prokaryote by a virus. The suggestion is based on similarities between eukaryotes and viruses such as linear DNA strands, mRNA capping, and tight binding to proteins (analogizing histones to viral envelopes). One version of the proposal suggests that the nucleus evolved in concert with phagocytosis to form an early cellular "predator".[82] Another variant proposes that eukaryotes originated from early archaea infected by poxviruses, on the basis of observed similarity between the DNA polymerases in modern poxviruses and eukaryotes.[83][84] It has been suggested that the unresolved question of the evolution of sex could be related to the viral eukaryogenesis hypothesis.[85]
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+A more recent proposal, the exomembrane hypothesis, suggests that the nucleus instead originated from a single ancestral cell that evolved a second exterior cell membrane; the interior membrane enclosing the original cell then became the nuclear membrane and evolved increasingly elaborate pore structures for passage of internally synthesized cellular components such as ribosomal subunits.[86]
+