Сегіз саныңың этимологиясы мен тарихы

Integer number 8

8 (eight) is the natural number following 7 and preceding 9.

English eight, from Old English eahta, æhta, Proto Germanic *ahto is a direct continuation of Proto Indo European *oḱtṓ(w) , and as such cognate with Greek ὀκτώ and Latin octo , both of which stems are reflected by the English prefix oct(o) , as in the ordinal adjective octaval or octavary, the distributive adjective is octonary. The adjective octuple (Latin octu plus) may also be used as a noun, meaning "a set of eight items"; the diminutive octuplet is mostly used to refer to eight siblings delivered in one birth. The Semitic numeral is based on a root *θmn , whence Akkadian smn , Arabic ṯmn , Hebrew šmn etc. The Chinese numeral, written 八 (Mandarin: bā; Cantonese: baat), is from Old Chinese *priāt , ultimately from Sino Tibetan b r gyat or b g ryat which also yielded Tibetan brgyat. It has been argued that, as the cardinal number is the highest number of items that can universally be cognitively processed as a single set, the etymology of the numeral eight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar. The Turkic words for "eight" are from a Proto Turkic stem *sekiz, which has been suggested as originating as a negation of eki "two", as in "without two fingers" (i. e., "two short of ten; two fingers are not being held up");
this same principle is found in Finnic *kakte ksa, which conveys a meaning of "two before (ten)". The Proto Indo European reconstruction *oḱtṓ(w) itself has been argued as representing an old dual, which would correspond to an original meaning of "twice four". Proponents of this "quaternary hypothesis" adduce the numeral , which might be built on the stem new , meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight).

The modern digit 8, like all modern Arabic numerals other than zero, originates with the Brahmi numerals. The Brahmi digit for eight by the 1st century was written in one stroke as a curve └┐ looking like an uppercase H with the bottom half of the left line and the upper half of the right line removed. However, the digit for eight used in India in the early centuries of the Common Era developed considerable graphic variation, and in some cases took the shape of a single wedge, which was adopted into the Perso Arabic tradition as ٨ (and also gave rise to the later Devanagari form ८); the alternative curved glyph also existed as a variant in Perso Arabic tradition, where it came to look similar to our digit 5. The digits as used in Al Andalus by the 10th century were a distinctive western variant of the glyphs used in the Arabic speaking world, known as ghubār numerals (ghubār translating to "sand table"). In these digits, the line of the 5 like glyph used in Indian manuscripts for eight came to be formed in ghubār as a closed loop, which was the 8 shape that became adopted into European use in the 10th century. Just as in most modern typefaces, in typefaces with text figures the character for the digit 8 usually has an ascender, as, for example, in
The infinity symbol ∞, described as a "sideways figure eight", is unrelated to the digit 8 in origin; it is first used (in the mathematical meaning "infinity") in the 17th century, and it may be derived from the Roman numeral for "one thousand" CIƆ, or alternatively from the final Greek letter, ω.

Eight is the third composite number, lying between the fourth prime number (7) and the fourth composite number (9). 8 is the first non unitary cube prime of the form p3. With proper divisors , , and , it is the third power of two (2). 8 is the first number which is neither prime nor semiprime and the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem. 8 is the first proper Leyland number of the form x^(y) + y^(x), where in its case x and y both equal 2. 8 is the sum between the first pair of twin primes (3, 5), and the only twin prime sum that is not a multiple of 3 or 12. 8 is the sixth Fibonacci number and the first even, non prime Fibonacci number. It is also the only positive Fibonacci number aside from 1 that is a perfect cube. 8 is the third refactorable number, as it has exactly four positive divisors, and 4 is one of them. 8 is the only composite number with a prime aliquot sum of 7 (1 + 2 + 4) that is part of the aliquot sequence (8, 7, 1, 0). 8 is the first number to be the aliquot sum of two numbers: the discrete semiprime 10 = 5 × 2, and squared prime 49 = 72. 8 is surrounded by (7, 9) which multiply to equal the forty fourth composite number 63, where the eighth triangular number and twenty fourth composite is 36. 8 is the number of known primary pseudoperfect numbers, the smallest four (2, 6, 42, 1806) are one less than the first four numbers in Sylvester's sequence. Sphenic numbers always have exactly eight divisors.

A polygon with eight sides is an octagon. The sides and span of a regular octagon, or truncated square, are in silver ratio, and its circumscribing square has a side and diagonal length ratio of ; with both the silver ratio and the square root of two intimately interconnected through Pell numbers, where in particular the quotient of successive Pell numbers generates rational approximations for coordinates of a regular octagon. With a central angle of 45 degrees and an internal angle of 135 degrees, a regular octagon can fill a plane vertex with a regular triangle and a regular icositetragon, as well as tessellate two dimensional space alongside squares in the truncated square tiling. This tiling is one of eight Archimedean tilings that are semi regular, or made of more than one type of regular polygon, and the only tiling that can admit a regular octagon. The Ammann–Beenker tiling is a nonperiodic tesselation of prototiles that feature prominent octagonal silver eightfold symmetry, that is the two dimensional orthographic projection of the four dimensional 8 8 duoprism. In number theory, figurate numbers representing octagons are called octagonal numbers.

A tesseract or 8 cell is the four dimensional analogue of the cube. It is one of six regular polychora, with a total of eight cubical cells, hence its name. Its dual figure is the analogue of the octahedron, with twice the amount of cells and simply termed the 16 cell, that is the orthonormal basis of vectors in four dimensions. Whereas a tesseractic honeycomb is self dual, a 16 cell honeycomb is dual to a 24 cell honeycomb that is made of 24 cells. The 24 cell is also regular, and made purely of octahedra whose vertex arrangement represents the ring of Hurwitz integral quaternions. Both the tesseract and the 16 cell can fit inside a 24 cell, and in a 24 cell honeycomb, eight 24 cells meet at a vertex. Also, the Petrie polygon of the tesseract and the 16 cell is a regular octagon.

The octonions are a hypercomplex normed division algebra that are an extension of the complex numbers. They are realized in eight dimensions, where they have an isotopy group over the real numbers that is spin group Spin(8), the unique such group that exhibits a phenomenon of triality. As a double cover of special orthogonal group SO(8), Spin(8) contains the special orthogonal Lie algebra D4 as its Dynkin diagram, whose order three outer automorphism is isomorphic to the symmetric group S3, giving rise to its triality. Over finite fields, the eight dimensional Steinberg group 3D4(q3) is simple, and one of sixteen such groups in the classification of finite simple groups. As is Lie algebra E8, whose complex form in 248 dimensions is the largest of five exceptional Lie algebras that include E7 and E6, which are held inside E8. The smallest such algebra is G2, that is the automorphism group of the octonions. In mathematical physics, special unitary group SO(3) has an eight dimensional adjoint representation whose colors are ascribed gauge symmetries that represent the vectors of the eight gluons in the Standard Model. The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. If is the direct limit of the inclusions of real orthogonal groups , the following holds:

Clifford algebras also display a periodicity of 8. For example, the algebra Cl(p + 8,q) is isomorphic to the algebra of 16 by 16 matrices with entries in Cl(p,q). We also see a period of 8 in the K theory of spheres and in the representation theory of the rotation groups, the latter giving rise to the 8 by 8 spinorial chessboard. All of these properties (that also tie with Lorentzian geometry, and Jordan algebras) are closely related to the properties of the octonions, which occupy the highest possible dimension for a normed division algebra.

The lattice Γ8 is the smallest positive even unimodular lattice. As a lattice, it holds the optimal structure for the densest packing of 240 spheres in eight dimensions, whose lattice points also represent the root system of Lie group E8. This honeycomb arrangement is shared by a unique complex tessellation of Witting polytopes, also with 240 vertices. Each complex Witting polytope is made of Hessian polyhedral cells that have Möbius–Kantor polygons as faces, each with eight vertices and eight complex equilateral triangles as edges, whose Petrie polygons form regular octagons. In general, positive even unimodular lattices only exist in dimensions proportional to eight. In the 16th dimension, there are two such lattices : Γ8 ⊕ Γ8 and Γ16, while in the 24th dimension there are precisely twenty four such lattices that are called the Niemeier lattices, the most important being the Leech lattice, which can be constructed using the octonions as well as with three copies of the ring of icosians that are isomorphic to the lattice. The order of the smallest non abelian group all of whose subgroups are normal is 8. Vertex transitive semiregular polytopes whose facets are finite exist up through the 8th dimension. In the third dimension, they include the Archimedean solids and the infinite family of uniform prisms and antiprisms, while in the fourth dimension, only the rectified 5 cell, the rectified 600 cell, and the snub 24 cell are semiregular polytopes. For dimensions five through eight, the demipenteract and the k21 polytopes 221, 321, and 421 are the only semiregular (Gosset) polytopes. Collectively, the k21 family of polytopes contains eight figures that are rooted in the triangular prism, which is the simplest semiregular polytope that is made of three cubes and two equilateral triangles. It also includes one of only three semiregular Euclidean honeycombs: the affine 521 honeycomb that represents the arrangement of vertices of the eight dimensional lattice, and made of 421 facets. The culminating figure is the ninth dimensional 621 honeycomb, which is the only affine semiregular paracompact hyperbolic honeycomb with infinite facets and vertex figures in the k21 family. There are no other finite semiregular polytopes or honeycombs in dimensions n > 8.

In the classification of sporadic groups, the third generation consists of eight groups, four of which are centralizers of (itself the largest group of this generation), with another three transpositions of Fischer group 8 is the difference between 53 and 61, which are the two smallest prime numbers that do not divide the order of any sporadic group. The largest supersingular prime that divides the order of is 71, which is the eighth self convolution of Fibonacci numbers (where 744, which is essential to Moonshine theory, is the twelfth). While only two sporadic groups have eight prime factors in their order (Lyons group and Fischer group ), Mathieu group holds a semi presentation whose order is equal to .

A number is divisible by 8 if its last three digits, when written in decimal, are also divisible by 8, or its last three digits are 0 when written in binary. 8 is the base of the octal number system, which is mostly used with computers. In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an octet.

In nuclear physics, the second magic number. In particle physics, the eightfold way is used to classify sub atomic particles. In statistical mechanics, the eight vertex model has 8 possible configurations of arrows at each vertex.

Messier object M8, a magnitude 5.0 nebula in the constellation of Sagittarius. The New General Catalogue object NGC 8, a double star in the constellation Pegasus. Since the demotion of Pluto to a dwarf planet on 24 August 2006, in our Solar System, eight of the bodies orbiting the Sun are considered to be planets.

The atomic number of oxygen. The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form. The maximum number of electrons that can occupy a valence shell (except for transitional elements), see the octet rule. The red pigment lycopene consists of eight isoprene units.

A disphenoid crystal is bounded by eight scalene triangles arranged in pairs. A ditetragonal prism in the tetragonal crystal system has eight similar faces whose alternate interfacial angles only are equal.

All spiders, and more generally all arachnids, have eight legs. Orb weaver spiders of the cosmopolitan family Areneidae have eight similar eyes. The octopus and its cephalopod relatives in genus Argonauta have eight arms (tentacles). Compound coelenterates of the subclass or order Alcyonaria have polyps with eight branched tentacles and eight septa. Sea anemones of genus Edwardsia have eight mesenteries. Animals of phylum Ctenophora swim by means of eight meridional bands of transverse ciliated plates, each plate representing a row of large modified cilia. The eight spotted forester (genus Alypia, family Zygaenidae) is a diurnal moth having black wings with brilliant white spots. The ascus in fungi of the class Ascomycetes, following nuclear fusion, bears within it typically eight ascospores. Herbs of genus Coreopsis (tickseed) have showy flower heads with involucral bracts in two distinct series of eight each. In human adult dentition there are eight teeth in each quadrant. The eighth tooth is the so called wisdom tooth. There are eight cervical nerves on each side in man and most mammals.

There are eight Jungian cognitive functions, according to the MBTI models by John Beebe and Linda Berens. Timothy Leary identified a hierarchy of eight levels of consciousness.

A byte is eight bits. Many (mostly historic) computer architectures are eight bit, among them the Nintendo Entertainment System. Standard 8 and Super 8 are 8 mm film formats. Video8, Hi8 and Digital8 are related 8 mm video formats. On most phones, the 8 key is associated with the letters T, U, and V, but on the BlackBerry Pearl it is the key for B and N.
An eight may refer to an eight cylinder engine or automobile. A V8 engine is an internal combustion engine with eight cylinders configured in two banks (rows) of four forming a "V" when seen from the end. A figure eight knot (so named for its configuration) is a kind of stopper knot. The number eight written in parentheses is the code for the musical note in Windows Live Messenger. In a seven segment display, when an 8 is illuminated, all the display bulbs are on.

The SI prefix for 10008 is yotta (Y), and for its reciprocal, yocto (y). In liquid measurement (United States customary units), there are eight fluid ounces in a cup, eight pints in a gallon and eight tablespoonfuls in a gill. There are eight furlongs in a mile. The clove, an old English unit of weight, was equal to eight pounds when measuring cheese. An eight may be an article of clothing of the eighth size. Force eight is the first wind strength attributed to a gale on the Beaufort scale when announced on a Shipping Forecast.

Sailors and civilians alike from the 1500s onward referred to evenly divided parts of the Spanish dollar as "pieces of eight", or "bits".

Various types of buildings are usually eight sided (octagonal), such as single roomed gazebos and multi roomed pagodas (descended from stupas; see religion section below). Eight caulicoles rise out of the leafage in a Corinthian capital, ending in leaves that support the volutes.

The Dharmacakra, a Buddhist symbol, has eight spokes. The Buddha's principal teaching—the Four Noble Truths—ramifies as the Noble Eightfold Path and the Buddha emphasizes the importance of the eight attainments or jhanas. In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas: (Manjusri, Vajrapani, Avalokiteśvara, Maitreya, Ksitigarbha, Nivaranavishkambhi, Akasagarbha, and Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogacara school of thought: consciousness in the five senses, thought consciousness, self consciousness, and unconsciousness "consciousness" or "store house consciousness" (alaya vijñana). The "irreversible" state of enlightenment, at which point a Bodhisattva goes on "autopilot", is the Eight Ground or bhūmi. In general, "eight" seems to be an auspicious number for Buddhists, e. g., the "eight auspicious symbols" (the jewel encrusted parasol; the goldfish (always shown as a pair, e. g., the glyph of Pisces); the self replenishing amphora; the white kamala lotus flower; the white conch; the eternal (Celtic style, infinitely looping) knot; the banner of imperial victory; the eight spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching). Similarly, Buddha's birthday falls on the 8th day of the 4th month of the Chinese calendar.

The religious rite of brit milah (commonly known as circumcision) is held on a baby boy's eighth day of life. Hanukkah is an eight day Jewish holiday that starts on the 25th day of Kislev. Shemini Atzeret (Hebrew: "Eighth Day of Assembly") is a one day Jewish holiday immediately following the seven day holiday of Sukkot.

The spiritual Eighth Day, because the number 7 refers to the days of the week (which repeat themselves). The number of Beatitudes. 1 Peter 3:20 states that there were eight people on Noah's Ark. The Antichrist is the eighth king in the Book of Revelation.

In Islam, eight is the number of angels carrying the throne of Allah in heaven. The number of gates of heaven. The octagram Rub el Hizb is often used in Islamic symbology.

In Wicca, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year. In Ancient Egyptian mythology, the Ogdoad represents the eight primordial deities of creation. In Scientology there are eight dynamics of existence. There is also the Ogdoad in Gnosticism.

The number eight is considered to be a lucky number in Chinese and other Asian cultures. Eight (八; accounting 捌; pinyin bā) is considered a lucky number in Chinese culture because it sounds like the word meaning to generate wealth (發(T) 发(S); Pinyin: fā). Property with the number 8 may be valued greatly by Chinese. For example, a Hong Kong number plate with the number 8 was sold for $640,000. The opening ceremony of the Summer Olympics in Beijing started at 8 seconds and 8 minutes past 8 pm (local time) on 8 August 2008. In Pythagorean numerology the number 8 represents victory, prosperity and overcoming. Eight (八) is also considered a lucky number in Japan, but the reason is different from that in Chinese culture. Eight gives an idea of growing prosperous, because the letter broadens gradually. The Japanese thought of eight (や) as a holy number in the ancient times. The reason is less well understood, but it is thought that it is related to the fact they used eight to express large numbers vaguely such as manyfold (やえはたえ) (literally, eightfold and twentyfold), many clouds (やくも) (literally, eight clouds), millions and millions of Gods (やおよろずのかみ) (literally, eight millions of Gods), etc. It is also guessed that the ancient Japanese gave importance to pairs, so some researchers guess twice as four (よ), which is also guessed to be a holy number in those times because it indicates the world (north, south, east, and west) might be considered a very holy number. In numerology, 8 is the number of building, and in some theories, also the number of destruction.

In astrology, Scorpio is the 8th astrological sign of the Zodiac. In the Middle Ages, 8 was the number of "unmoving" stars in the sky, and symbolized the perfection of incoming planetary energy.

A note played for one eighth the duration of a whole note is called an eighth note, or quaver. An octave, the interval between two musical notes with the same letter name (where one has double the frequency of the other), is so called because there are eight notes between the two on a standard major or minor diatonic scale, including the notes themselves and without chromatic deviation. The ecclesiastical modes are ascending diatonic musical scales of eight notes or tones comprising an octave. There are eight notes in the octatonic scale. There are eight musicians in a double quartet or an octet. Both terms may also refer to a musical composition for eight voices or instruments. Caledonians is a square dance for eight, resembling the quadrille. Albums with the number eight in their title include 8 by the Swedish band Arvingarna, 8 by the American rock band Incubus, The Meaning of 8 by Minnesota indie rock band Cloud Cult and 8ight by Anglo American singer songwriter Beatie Wolfe. Dream Theater's eighth album Octavarium contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork. "Eight maids a milking" is the gift on the eighth day of Christmas in the carol "The Twelve Days of Christmas". The 8 track cartridge is a musical recording format. "#8" is the stage name of Slipknot vocalist Corey Taylor. "Too Many Eights" is a song by Athens, Georgia's Supercluster. Eight Seconds, a Canadian musical group popular in the 1980s with their most notable song "Kiss You (When It's Dangerous)". "Eight Days a Week" is a #1 single for the music group the Beatles. Figure 8 is the fifth studio album by singer songwriter Elliott Smith, released in the year 2000, an album released by Julia Darling in 1999, and an album released by Outasight in 2011. Ming Hao from the k pop group Seventeen goes by the name "The8". "8 (circle)" is the eighth song on the album 22, A Million by the American band Bon Iver. "8" is the eighth song on the album When We All Fall Asleep, Where Do We Go? by Billie Eilish.

8 Guys is a 2003 short film written and directed by Dane Cook. 8 Man (or Eightman): 1963 Japanese manga and anime superhero. 8 Mile is a 2002 film directed by Curtis Hanson. 8 mm is a 1999 film directed by Joel Schumacher. 8 Women (Original French title: 8 femmes) is a 2001 film directed by François Ozon. Eight Below is a 2006 film directed by Frank Marshall. Eight Legged Freaks is a 2002 film directed by Ellory Elkayem. Eight Men Out is a 1988 film directed by John Sayles. Jennifer Eight, also known as Jennifer 8, is a 1992 film written and directed by Bruce Robinson. Eight Is Enough is an American television comedy drama series. In Stargate SG 1 and Stargate Atlantis, dialing an 8 chevron address will open a wormhole to another galaxy. The Hateful Eight is a 2015 American western mystery film written and directed by Quentin Tarantino. Kate Plus 8 is an American reality television show. Ocean's 8 is an American heist comedy film directed by Gary Ross.

Nestlé sells a brand of chocolates filled with peppermint flavoured cream called After Eight, referring to the time 8 p. m.
There are eight vegetables in V8 juice.

Eights may refer to octosyllabic, usually iambic, lines of verse. The drott kvaett, an Old Icelandic verse, consisted of a stanza of eight regular lines. In Terry Pratchett's Discworld series, eight is a magical number and is considered taboo. Eight is not safe to be said by wizards on the Discworld and is the number of Bel Shamharoth. Also, there are eight days in a Disc week and eight colours in a Disc spectrum, the eighth one being octarine. Lewis Carroll's poem The Hunting of the Snark has 8 "fits" (cantos), which is noted in the full name "The Hunting of the Snark – An Agony, in Eight Fits". Eight apparitions appear to Macbeth in Act 4 scene 1 of Shakespeare's Macbeth as representations of the eight descendants of Banquo.

An "eighth" is a common measurement of marijuana, meaning an eighth of an ounce. It is also a common unit of sale for psilocybin mushrooms. Avril Lavigne's song "Sk8er Boi" uses this convention in the title. The Housing Choice Voucher Program, operated by the United States Department of Housing and Urban Development, is commonly referred to as the Section 8 program, as this was the original section of the Act which instituted the program. In Colombia and Venezuela, "volverse un ocho" (meaning to tie oneself in a figure 8) refers to getting in trouble or contradicting oneself. In China, "8" is used in chat speak as a term for parting. This is due to the closeness in pronunciation of "8" (bā) and the English word "bye".

A figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating. Figure eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something.