The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example, if O(∞) is the direct limit of the inclusions of real orthogonal groups
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 are closely related to the properties of the octonions.
The lowest-dimensional even unimodular lattice is the 8-dimensional E8 lattice. Even positive definite unimodular lattices exist only in dimensions divisible by 8.
A figure 8 is the common name of a geometricshape, 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.
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.
It has been argued that, as the cardinal number 7 is the highest number of item 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 9, which might be built on the stem new-, meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight).
Evolution of the Arabic digit
Evolution of the numeral 8 from the Indians to the Europeans
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.[year needed]
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.
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.
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.
Also known as Ashtha, Aṣṭa, or Ashta in Sanskrit, it is the number of wealth and abundance.
The Goddess of wealth and prosperity Lakshmi has eight forms which is known as Ashta Lakshmi and worshipped as: "Maha-lakshmi, Dhana-lakshmi, Dhanya-lakshmi, Gaja-lakshmi, Santana-lakshmi, Veera-lakshmi, Vijaya-lakshmi and Vidhya-lakshmi"
There are eight nidhi, or seats of wealth according to Hinduism.
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.
Eight (八, hachi, ya) 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 (八) broadens gradually.
The Japanese thought of 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 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.
Eight-ballpool 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)).
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.
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.
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.
^Inc, Boy Scouts of America (1931). Boys' Life. Boy Scouts of America, Inc. p. 20. lunge forward upon this skate in a left outside forward circle, in just the reverse of your right outside forward circle, until you complete a figure 8.
^Etymological Dictionary of Turkic Languages: Common Turkic and Interturkic stems starting with letters «L», «M», «N», «P», «S», Vostochnaja Literatura RAS, 2003, 241f. (altaica.ruArchived 31 October 2007 at the Wayback Machine)
^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.
^Thomas, Mary Ann (15 August 2004). Oxygen. The Rosen Publishing Group, Inc. p. 12. ISBN978-1-4042-0159-0. Knowing that oxygen has an atomic number of 8,
^Choppin, Gregory R.; Johnsen, Russell H. (1972). Introductory chemistry. Addison-Wesley Pub. Co. p. 366. ISBN9780201010220. under normal conditions the most stable allotropic form (Fig. 23-8a). Sulfur molecules within the crystal consist of puckered rings of eight sulfur atoms linked by single...
^Bourne, Gilbert Charles (1911). "Anthozoa" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. 02 (11th ed.). Cambridge University Press. pp. 97–105, see page 100. Zoantharia.....It is not known whether all the eight mesenteries of Edwardsia are developed simultaneously or not, but in the youngest form which has been studied all the eight mesenteries were present
^Parrish, Fred K. (1975). Keys to Water Quality Indicative Organisms of the Southeastern United States. Environmental Protection Agency, Office of Research and Development, Environmental Monitoring and Support Laboratory, Biological Methods Branch, Aquatics Biology Section. p. 11. ... the ascospores, are borne in sac like structures termed asci. The ascus usually contains eight as cospores,...
^Hay, Jeff (6 March 2009). World Religions. Greenhaven Publishing LLC. p. 61. ISBN978-0-7377-4627-3. The focus of ordinary believers' religious life is on following a relevant version of the Eightfold Path ...
^Little, Stephen; Eichman, Shawn; Shipper, Kristofer; Ebrey, Patricia Buckley (1 January 2000). Taoism and the Arts of China. University of California Press. p. 139. ISBN978-0-520-22785-9. Evidence for the early use of the Eight Trigrams in a religious Taoist...