The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example if is the direct limit of the inclusions of real orthogonal groups then . Clifford algebras also display a periodicity of 8. For example the algebra is isomorphic to the algebra of 16 by 16 matrices with entries in . 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 are closely related to the properties of the octonions.
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 sibling delivered in one birth.
It has been argued that, as the cardinal number seven is the highest number of item that can universially 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 nine, 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 8 glyph, like all modern Hindu-Arabic numerals (other than zero) originates with the Brahmi numerals. The Brahmi numeral 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 eight glyph used in India in the early centuries of the Common Era developed considerable 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 numeral ८; the alternative curved glyph also existed as a variant in Perso-Arabic tradition, where it came to look similar to our glyph 5.[year needed]
The numerals 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 numerals, the line of the 5-like glyph used for eight came to be formed into a closed loop, which was the 8-shape adopted into European use in the 10th century.
The infinity symbol ∞, described as "sideways figure eight" is unrelated to the 8 glyph 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.
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.
On most phones, the 8 key is associated with the letters T, U, and V, but on the BlackBerry it is the key for B, N, and X.
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.
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' (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.
Eight (八,hachi, ya?) is also considered a lucky number in Japanese culture, but the reason is different from that in Chinese culture. Eight gives an idea of growing prosperous, because the letter (八) broadens gradually.
The Japanese thought eight (や,ya?) 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,Yae Hatae?) (literally, eightfold and twentyfold), many clouds (やくも,Yakumo?) (literally, eight clouds), millions and millions of Gods (やおよろずのかみ,Yaoyorozu no Kami?) (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,yo?), 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 the Middle Ages, 8 was the number of "unmoving" stars in the sky, and symbolized the perfection of incoming planetary energy.
In music and dance
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 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.
Eight-ballpocket billiards is played with a cue ball and 15 numbered balls, the black ball numbered 8 being the middle and most important one, as the winner is the player or side that legally pockets it after first pocketing its numerical group of 7 object balls (for other meanings see Eight ball (disambiguation)).
Balklines divide a billiards table into eight outside compartments or divisions called balks. In balkline billiards the table also has eight anchor spaces.
In most rugby league competitions (though not the European Super League, which uses static squad numbering), one of the two starting props wears the number 8.
In rowing an "eight" refers to a sweep-oar racing boat with a crew of eight rowers plus a coxswain.
In chess, each side has eight pawns and the board is made of 64 squares arranged in an eight by eight lattice. The eight queens puzzle is a challenge to arrange eight queens on the board so that none can capture any of the others.
In the game of eights or Crazy Eights, each successive player must play a card either of the same suit or of the same rank as that played by the preceding player, or may play an eight and call for any suit. The object is to get rid of all one's cards first.
In poker, a "Dead Man's Hand" consists of two pairs; aces and eights. While playing poker in a saloon in Deadwood, Dakota Territory (now South Dakota), Wild Bill Hickok held this hand when he was shot from behind and killed.
The Montreal Expos, for Hall of Famer Gary Carter. The franchise continues to honor the number in its current incarnation as the Washington Nationals (although it initially planned to reissue all of the Expos' retired numbers).
The drott-kvaett, an Old Icelandic verse, consisted of a stanza of eight regular lines.
In Terry Pratchett's Discworld series, eight is a holy 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
Referring to the shape of the numeral, eight was formerly represented in bingo slang as "One Fat Lady". Eighty-eight was "Two Fat Ladies".
The numeral "8" is sometimes used in informal writing and Internet slang to represent the syllable "ate", as in writing "H8" for "hate", or "congratul8ions" for "congratulations". Avril Lavigne's song "Sk8er Boi" uses this convention in the title.
8vo is shorthand for "octavo", a book and paper size.
The Eight - Eight American painters who exhibited together only once in 1908 in New York City. They joined this exhibition to oppose traditions upheld by the National Academy and help advance modernism in the United States. Five of the eight painters were associated with the Ashcan School: Robert Henri (1865–1929), George Luks (1867–1933), William Glackens (1870–1938), John Sloan (1871–1951), and Everett Shinn (1876–1953), along with Maurice Prendergast (1859–1924), Ernest Lawson (1873–1939), and Arthur Bowen Davies (1862–1928).
^Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88
^Etymological Dictionary of Turkic Languages: Common Turkic and Interturkic stems starting with letters «L», «M», «N», «P», «S», Vostochnaja Literatura RAS, 2003, 241f. (altaica.ru)
^the hypothesis is discussed critically (and rejected as "without sufficient support") by Werner Winter, 'Some thought about Indo-European numerals' in: Jadranka Gvozdanović (ed.), Indo-European Numerals, Walter de Gruyter, 1992, 14f.
^Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.68[clarification needed]