8

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← 7 8 9 →
−1 0 1 2 3 4 5 6 7 8 9 →
Cardinal eight
Ordinal 8th
(eighth)
Numeral system octal
Factorization 23
Divisors 1, 2, 4, 8
Greek numeral Η´
Roman numeral VIII, viii
Greek prefix octa-/oct-
Latin prefix octo-/oct-
Binary 10002
Ternary 223
Senary 126
Octal 108
Duodecimal 812
Hexadecimal 816
Greek η (or Η)
Arabic, Kurdish, Persian, Sindhi, Urdu ٨
Amharic ፰
Bengali ৮
Chinese numeral 八,捌
Devanāgarī ८
Kannada ೮
Malayalam ൮
Telugu ౮
Tamil ௮
Hebrew ח
Khmer ៨
Thai ๘
Armenian Ը ը
Babylonian numeral 𒐜
Egyptian hieroglyph 𓐁
Morse code _ _ _..

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

Contents

Etymology

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 7 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"); [1] 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). [2]

Evolution of the Arabic digit

Evolution of the numeral 8 from the Brahmi numerals to the Arabic numerals Evo8glyph.svg
Evolution of the numeral 8 from the Brahmi numerals to the Arabic numerals

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. [3]

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 TextFigs148.svg .

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.

In mathematics

8 is a composite number and the first number which is neither prime nor semiprime. By Mihăilescu's Theorem, it is the only nonzero perfect power that is one less than another perfect power. 8 is the first proper Leyland number of the form xy + yx, where in its case x and y both equal 2. [4] 8 is a Fibonacci number and the only nontrivial Fibonacci number that is a perfect cube. [5] Sphenic numbers always have exactly eight divisors. [6] 8 is the base of the octal number system. [7]

Geometry

A polygon with eight sides is an octagon. [8] 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. [9] 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. [10]

An octahedron is a regular polyhedron with eight equilateral triangles as faces. is the dual polyhedron to the cube and one of eight convex deltahedra. [11] [12] The stella octangula, or eight-pointed star, is the only stellation with octahedral symmetry. It has eight triangular faces alongside eight vertices that forms a cubic faceting, composed of two self-dual tetrahedra that makes it the simplest of five regular compounds. The cuboctahedron, on the other hand, is a rectified cube or rectified octahedron, and one of only two convex quasiregular polyhedra. It contains eight equilateral triangular faces, whose first stellation is the cube-octahedron compound. [13] [14]

Vector spaces

The octonions are a hypercomplex normed division algebra that are an extension of the complex numbers. They are a double cover of special orthogonal group SO(8). The 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. Clifford algebras display a periodicity of 8. [15]

Group theory

The lie group E8 is one of 5 exceptional lie groups. [16] [17] The order of the smallest non-abelian group whose subgroups are all normal is 8.[ citation needed ]

List of basic calculations

Multiplication 123456789101112131415
8 × x8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
Division 123456789101112131415
8 ÷ x842.621.61.31.14285710.80.80.720.60.6153840.5714280.53
x ÷ 80.1250.250.3750.50.6250.750.87511.1251.251.3751.51.6251.751.875
Exponentiation 12345678910111213
8x8645124096327682621442097152167772161342177281073741824858993459268719476736549755813888
x81256656165536390625167961657648011677721643046721100000000214358881429981696815730721

In science

Physics

Chemistry

In technology

NATO signal flag for 8 ICS Eight.svg
NATO signal flag for 8

In culture

Currency

In religion, folk belief and divination

Buddhism

In Buddhism, the 8-spoked Dharmacakra represents the Noble Eightfold Path. Dharma Wheel.svg
In Buddhism, the 8-spoked Dharmacakra represents the Noble Eightfold Path.

In general, "eight" seems to be an auspicious number for Buddhists. The Dharmacakra, a Buddhist symbol, has eight spokes. [21] 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.

Islam

The octagram Rub el Hizb Rub El Hizb.svg
The octagram Rub el Hizb

As a lucky number

  • The number eight is considered to be a lucky number in Chinese and other Asian cultures. [22] 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. [23] 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. [24]
  • In Pythagorean numerology the number 8 represents victory, prosperity and overcoming.
  • Eight (八, hachi, ya) is also considered a lucky number in Japan, but the reason is different from that in Chinese culture. [25] 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 astrology

  • In the Middle Ages, 8 was the number of "unmoving" stars in the sky, and symbolized the perfection of incoming planetary energy.

In sports and other games

An 8-ball in pool 8-Ball.jpg
An 8-ball in pool

In literature

In slang

Other uses

Related Research Articles

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References

  1. ↑ 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 Archived 31 October 2007 at the Wayback Machine )
  2. ↑ 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.
  3. ↑ 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.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA076980(Leyland numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88
  6. ↑ Weisstein, Eric W. "Sphenic Number". mathworld.wolfram.com. Retrieved 7 August 2020. ...then every sphenic number n=pqr has precisely eight positive divisors
  7. ↑ Weisstein, Eric W. "Octal". mathworld.wolfram.com. Retrieved 7 August 2020.
  8. ↑ Weisstein, Eric W. "Octagon". mathworld.wolfram.com. Retrieved 7 August 2020.
  9. ↑ Weisstein, Eric W. "Regular Octagon". mathworld.wolfram.com. Retrieved 25 June 2022.
  10. ↑ Katz, A (1995). "Matching rules and quasiperiodicity: the octagonal tilings". In Axel, F.; Gratias, D. (eds.). Beyond quasicrystals. Springer. pp. 141–189. doi:10.1007/978-3-662-03130-8_6. ISBN   978-3-540-59251-8.
  11. ↑ Freudenthal, H; van der Waerden, B. L. (1947), "Over een bewering van Euclides ("On an Assertion of Euclid")", Simon Stevin (in Dutch), 25: 115–128
  12. ↑ Roger Kaufman. "The Convex Deltahedra And the Allowance of Coplanar Faces". The Kaufman Website. Retrieved 25 June 2022.
  13. ↑ Weisstein, Eric W. "Cuboctahedron". mathworld.wolfram.com. Retrieved 25 June 2022.
  14. ↑ Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. pp. 18–19.
  15. ↑ Lounesto, Pertti (3 May 2001). Clifford Algebras and Spinors. Cambridge University Press. p. 216. ISBN   978-0-521-00551-7. ...Clifford algebras, contains or continues with two kinds of periodicities of 8...
  16. ↑ Wilson, Robert A. (2009). "Octonions and the Leech lattice". Journal of Algebra. 322 (6): 2186–2190. doi: 10.1016/j.jalgebra.2009.03.021 . MR   2542837.
  17. ↑ Conway, John H.; Sloane, N. J. A. (1988). "Algebraic Constructions for Lattices". Sphere Packings, Lattices and Groups. New York, NY: Springer. doi:10.1007/978-1-4757-2016-7. eISSN   2196-9701. ISBN   978-1-4757-2016-7.
  18. ↑ Ilangovan, K. (10 June 2019). Nuclear Physics. MJP Publisher. p. 30.
  19. ↑ Choppin, Gregory R.; Johnsen, Russell H. (1972). Introductory chemistry. Addison-Wesley Pub. Co. p. 366. ISBN   978-0-201-01022-0. 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...
  20. ↑ "Definition of byte | Dictionary.com". www.dictionary.com. Retrieved 8 August 2020.
  21. ↑ Issitt, Micah; Main, Carlyn (16 September 2014). Hidden Religion: The Greatest Mysteries and Symbols of the World's Religious Beliefs: The Greatest Mysteries and Symbols of the World's Religious Beliefs. ABC-CLIO. p. 186. ISBN   978-1-61069-478-0. The dharmachakra is typically depicted with eight spokes,
  22. ↑ Ang, Swee Hoon (1997). "Chinese consumers' perception of alpha-numeric brand names". Journal of Consumer Marketing. 14 (3): 220–233. doi:10.1108/07363769710166800. Archived from the original on 5 December 2011.
  23. ↑ Steven C. Bourassa; Vincent S. Peng (1999). "Hedonic Prices and House Numbers: The Influence of Feng Shui" (PDF). International Real Estate Review. 2 (1): 79–93. Archived from the original (PDF) on 13 April 2015. Retrieved 11 May 2011.
  24. ↑ "Olympics opening ceremony: China makes its point with greatestshow". the Guardian. 8 August 2008. Retrieved 29 November 2022.
  25. ↑ Jefkins, Frank (6 December 2012). Modern Marketing Communications. Springer Science & Business Media. p. 36. ISBN   978-94-011-6868-7. ...eight being a lucky number in Japanese.
  26. ↑ Collins, Robert; Latham, Robert (1988). Science Fiction & Fantasy Book Review Annual. Meckler. p. 289. ISBN   978-0-88736-249-1.
  27. ↑ Franciosi, Anthony (25 October 2019). "Weed Measurements: The Marijuana Metric System". Honest Marijuana. Retrieved 19 December 2023.
  28. ↑ Boys' Life. Boy Scouts of America, Inc. 1931. 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.
  29. ↑ Day, Cyrus Lawrence (1986). The Art of Knotting & Splicing. Naval Institute Press. p. 231. ISBN   978-0-87021-062-4. To make a line temporarily fast by winding it, figure – eight fashion, round a cleat, a belaying pin, or a pair of bitts.
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