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8

From Wikipedia, the free encyclopedia
(Redirected from8 (number))
Natural number
This article is about the number. For the years, see8 BC andAD 8. For other uses, see8 (disambiguation) andNumber Eight (disambiguation).
"VIII" redirects here. For other uses, seeVIII (disambiguation).

Natural number
← 78 9 →
Cardinaleight
Ordinal8th
(eighth)
Numeral systemoctal
Factorization23
Divisors1, 2, 4, 8
Greek numeralΗ´
Roman numeralVIII, viii
Greekprefixocta-/oct-
Latinprefixocto-/oct-
Binary10002
Ternary223
Senary126
Octal108
Duodecimal812
Hexadecimal816
Greekη (or Η)
Arabic,Kurdish,Persian,Sindhi,Urdu٨
Amharic
Bengali
Chinese numeral八,捌
Devanāgarī
Santali
Kannada
Malayalam
Telugu
Tamil
Hebrewח
Khmer
Thai
ArmenianԸ ը
Babylonian numeral𒐜
Egyptian hieroglyph𓐁
Morse code_ _ _..

8 (eight) is thenatural number following7 and preceding9.

Etymology

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Englisheight, fromOld Englisheahta, æhta,Proto-Germanic*ahto is a direct continuation of thehypothesizedProto-Indo-European*oḱtṓ(w)-, and as such cognate with Greekὀκτώ and Latinocto-, both of which stems are reflected by the English prefixoct(o)-, as in the ordinal adjectiveoctaval oroctavary, the distributive adjective isoctonary.The adjectiveoctuple (Latinoctu-plus) may also be used as a noun, meaning "a set of eight items"; the diminutiveoctuplet is mostly used to refer to eight siblings delivered in one birth.

TheSemitic numeral is based on a root*θmn-, whence Akkadiansmn-, Arabicṯmn-, Hebrewšmn- etc.TheChinese numeral, written (Mandarin:;Cantonese:baat), is fromOld Chinese*priāt-, ultimately from Sino-Tibetanb-r-gyat orb-g-ryat which also yielded Tibetanbrgyat.

It has been argued that, as thecardinal number7 is the highest number of items that can universally becognitively processed as a single set, the etymology of the numeraleight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar.TheTurkic words for "eight" are from aProto-Turkic stem*sekiz, which has been suggested as originating as a negation ofeki "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 inUralic*kakteksa, 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 numeral9, which might be built on the stemnew-, meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight).[2]

Evolution of the Arabic digit

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Evolution of the numeral 8 from theBrahmi numerals to theArabic numerals

The modern digit 8, like all modernArabic numerals other than zero, originates with theBrahmi numerals.TheBrahmi digit foreight 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 as٨ (and also gave rise to the later Devanagari form); 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 inAl-Andalus by the 10th century were a distinctive western variant of the glyphs used in the Arabic-speaking world, known asghubār numerals (ghubār translating to "sand table"). In these digits, the line of the5-like glyph used in Indian manuscripts for eight came to be formed in ghubār as a closed loop, which was the8-shape that became adopted into European use in the 10th century.[3]

Just as in most moderntypefaces, in typefaces withtext figures the character for the digit 8 usually has anascender, as, for example, in.

Theinfinity 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 theRoman numeral for "one thousand" CIƆ, or alternatively from the final Greek letter,ω.

In mathematics

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8 is acomposite number and the first number which is neitherprime norsemiprime. ByMihăilescu's Theorem, it is the only nonzeroperfect power that is one less than another perfect power. 8 is the first properLeyland number of the formxy + yx, where in its casex andy both equal 2.[4] 8 is aFibonacci number and the only nontrivial Fibonacci number that is aperfect cube.[5]Sphenic numbers always have exactly eight divisors.[6] 8 is the base of theoctal number system.[7]

Geometry

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Apolygon with eight sides is anoctagon.[8] A regular octagon can fill aplane-vertex with a regulartriangle and a regularicositetragon, as well astessellate two-dimensional space alongside squares in thetruncated square tiling. This tiling is one of eightArchimedean tilings that are semi-regular, or made of more than one type of regularpolygon, and the only tiling that can admit a regular octagon.[9] TheAmmann–Beenker tiling is a nonperiodic tesselation ofprototiles that feature prominent octagonalsilver eightfold symmetry, that is the two-dimensionalorthographic projection of the four-dimensional8-8 duoprism.[10]

Anoctahedron is aregular polyhedron with eightequilateral triangles asfaces. is thedual polyhedron to the cube and one of eightconvex deltahedra.[11][12] Thestella octangula, oreight-pointed star, is the onlystellation withoctahedral symmetry. It has eight triangular faces alongside eight vertices that forms a cubicfaceting, composed of two self-dualtetrahedra that makes it the simplest of fiveregular compounds. Thecuboctahedron, on the other hand, is arectified cube or rectified octahedron, and one of only two convexquasiregular polyhedra. It contains eight equilateral triangular faces, whose firststellation is thecube-octahedron compound.[13][14]

Vector spaces

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Theoctonions are ahypercomplexnormed division algebra that are an extension of thecomplex numbers. They are adouble cover ofspecial orthogonal group SO(8). Thespecial unitary group SO(3) has an eight-dimensionaladjoint representation whose colors are ascribedgauge symmetries that represent thevectors of the eightgluons in theStandard Model.Clifford algebras display a periodicity of 8.[15]

Group theory

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TheLie groupE8 hasrank 8, and is one of 5 exceptional Lie groups.[16][17] The order of the smallestnon-abelian group whose subgroups are all normal is 8.[citation needed]

List of basic calculations

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Multiplication123456789101112131415
8 ×x81624324048566472808896104112120
Division123456789101112131415
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
Exponentiation12345678910111213
8x8645124096327682621442097152167772161342177281073741824858993459268719476736549755813888
x81256656165536390625167961657648011677721643046721100000000214358881429981696815730721

In science

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Physics

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In nuclear physics, the secondmagic number.[18]

Chemistry

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The number eight plays a central role inchemistry, particularly in the context of theoctet rule (also known as the eight-electron rule). According to this theory, atoms of the main group elements from the second period of theperiodic table onwards strive to have a maximum of eight outer electrons (valence electrons) inmolecules in order to achieve a stablenoble gas configuration. This rule applies in particular to the elementscarbon,nitrogen,oxygen andfluorine, as these often form compounds in which they achieve eight valence electrons. Theatomic number eight is also significant in chemistry, as it represents the element oxygen, which is in the eighth position in the periodic table.

In technology

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NATO signal flag for 8

In culture

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Currency

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

In religion, folk belief and divination

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Buddhism

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In Buddhism, the 8-spokedDharmacakra represents theNoble Eightfold Path.

In general, "eight" seems to be an auspicious number for Buddhists. TheDharmacakra, aBuddhist symbol, has eight spokes.[20] The Buddha's principal teaching—theFour Noble Truths—ramifies as theNoble Eightfold Path and the Buddha emphasizes the importance of the eight attainments or jhanas.

Islam

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TheoctagramRub el Hizb

As a lucky number

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  • The number eight is considered to be alucky number in Chinese and other Asian cultures.[21] Eight (;accounting;pinyin) is considered alucky number in Chinese culture because it sounds like the word meaning to generate wealth (發(T) 发(S);Pinyin:). Property with the number 8 may be valued greatly by Chinese. For example, a Hong Kongnumber plate with the number 8 was sold for $640,000.[22] The opening ceremony of theSummer Olympics in Beijing started at 8 seconds and 8 minutes past 8 p.m. (local time) on 8 August 2008.[23]
  • In Pythagoreannumerology the number 8 represents victory, prosperity and overcoming.
  • Eight (,hachi, ya) is also considered a lucky number inJapan, but the reason is different from that in Chinese culture.[24] Eight gives an idea of growing prosperous, because the letter () broadens gradually.
  • The Japanese thought of eight (,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 (,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.
  • Innumerology, 8 is the number of building, and in some theories, also the number of destruction.

In astrology

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

In sports and other games

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An 8-ball in pool

In literature

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  • InTerry Pratchett'sDiscworld series, eight is a magical number[25] and is considered taboo. Eight is not safe to be said by wizards on theDiscworld 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 beingoctarine.

In slang

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  • An "eighth" is a common measurement ofmarijuana, meaning an eighth of anounce. It is also a common unit of sale forpsilocybin mushrooms.[26]
  • InColombia andVenezuela, "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".

Other uses

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References

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  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.ruArchived 31 October 2007 at theWayback Machine)
  2. ^the hypothesis is discussed critically (and rejected as "without sufficient support") byWerner 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.)."Sequence A076980 (Leyland numbers)".TheOn-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. Retrieved7 August 2020....then every sphenic number n=pqr has precisely eight positive divisors
  7. ^Weisstein, Eric W."Octal".mathworld.wolfram.com. Retrieved7 August 2020.
  8. ^Weisstein, Eric W."Octagon".mathworld.wolfram.com. Retrieved7 August 2020.
  9. ^Weisstein, Eric W."Regular Octagon".mathworld.wolfram.com. Retrieved25 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. Retrieved25 June 2022.
  13. ^Weisstein, Eric W."Cuboctahedron".mathworld.wolfram.com. Retrieved25 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. ^"Definition of byte | Dictionary.com".www.dictionary.com. Retrieved8 August 2020.
  20. ^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,
  21. ^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.
  22. ^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 fromthe original(PDF) on 13 April 2015. Retrieved11 May 2011.
  23. ^"Olympics opening ceremony: China makes its point with greatestshow".the Guardian. 8 August 2008. Retrieved29 November 2022.
  24. ^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.
  25. ^Collins, Robert; Latham, Robert (1988).Science Fiction & Fantasy Book Review Annual. Meckler. p. 289.ISBN 978-0-88736-249-1.
  26. ^Franciosi, Anthony (25 October 2019)."Weed Measurements: The Marijuana Metric System".Honest Marijuana. Retrieved19 December 2023.
  27. ^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.
  28. ^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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