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← 7 8 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 numeralTám, bát
Devanāgarī
Kannada
Malayalam
Telugu
Tamil
Hebrewח
Khmer
Thai
ArmenianԸ ը
Babylonian numeral𒐜
Egyptian hieroglyph𓐁
Morse code_ _ _..

8(eight) is thenatural numberfollowing7and preceding9.

Etymology

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

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

It has been argued that, as thecardinal number7is the highest number of items that can universally becognitively processedas a single set, the etymology of the numeraleightmight be the first to be considered composite, either as "twice four" or as "two short of ten", or similar. TheTurkicwords for "eight" are from aProto-Turkicstem*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 inFinnic*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 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 numeralsto theArabic numerals

The modern digit 8, like all modernArabic numeralsother than zero, originates with theBrahmi numerals. The Brahmi digit foreightby 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-Andalusby the 10th century were a distinctive western variant of the glyphs used in the Arabic-speaking world, known asghubārnumerals (ghubārtranslating 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 figuresthe 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 numeralfor "one thousand" CIƆ, or alternatively from the final Greek letter,ω.

In Mathematics

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8 is acomposite numberand the first number which is neitherprimenorsemiprime.ByMihăilescu's Theorem,it is the only nonzeroperfect powerthat is one less than another perfect power. 8 is the first properLeyland numberof the formxy+ yx,where in its casexandyboth equal 2.[4]8 is aFibonacci numberand the only nontrivial Fibonacci number that is aperfect cube.[5]Sphenic numbersalways have exactly eight divisors.[6]8 is the base of theoctalnumber system.[7]

Geometry

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Apolygonwith eight sides is anoctagon.[8]A regular octagon can fill aplane-vertexwith a regulartriangleand a regularicositetragon,as well astessellatetwo-dimensional space alongside squares in thetruncated square tiling.This tiling is one of eightArchimedean tilingsthat 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 tilingis a nonperiodic tesselation ofprototilesthat feature prominent octagonalsilvereightfold symmetry, that is the two-dimensionalorthographic projectionof the four-dimensional8-8 duoprism.[10]

Anoctahedronis aregular polyhedronwith eightequilateral trianglesasfaces.is thedual polyhedronto the cube and one of eightconvex deltahedra.[11][12]Thestella octangula,oreight-pointed star,is the onlystellationwithoctahedral symmetry.It has eight triangular faces alongside eight vertices that forms a cubicfaceting,composed of two self-dualtetrahedrathat makes it the simplest of fiveregular compounds.Thecuboctahedron,on the other hand, is arectifiedcube or rectified octahedron, and one of only two convexquasiregular polyhedra.It contains eight equilateral triangular faces, whose firststellationis thecube-octahedron compound.[13][14]

Vector Spaces

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Theoctonionsare ahypercomplexnormed division algebrathat are an extension of thecomplex numbers.They are adouble coverofspecial orthogonal groupSO(8). Thespecial unitary groupSO(3) has an eight-dimensionaladjoint representationwhose colors are ascribedgauge symmetriesthat represent thevectorsof the eightgluonsin theStandard Model.Clifford algebrasdisplay a periodicity of 8.[15]

Group Theory

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Thelie groupE8is one of 5 exceptional lie groups.[16][17]The order of the smallestnon-abelian groupwhose subgroups are all normal is 8.[citation needed]

List of basic calculations

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Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8 ×x 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8 ÷x 8 4 2.6 2 1.6 1.3 1.142857 1 0.8 0.8 0.72 0.6 0.615384 0.571428 0.53
x÷ 8 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.125 1.25 1.375 1.5 1.625 1.75 1.875
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
8x 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 68719476736 549755813888
x8 1 256 6561 65536 390625 1679616 5764801 16777216 43046721 100000000 214358881 429981696 815730721

In science

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Physics

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Astronomy

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Chemistry

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Geology

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  • Adisphenoidcrystal is bounded by eight scalene triangles arranged in pairs. A ditetragonal prism in thetetragonal crystal systemhas eight similar faces whose alternate interfacial angles only are equal.

Biology

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Psychology

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In technology

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NATO signal flagfor 8

In measurement

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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 dollaras "pieces of eight", or "bits".

Architecture

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In religion, folk belief and divination

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Hinduism

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  • As sourced from the Mahabharata, there are 8 vasus who are given elemental names:[45]
    1. Anala or Agni (fire)
    2. Dhara or Prithvi (earth)
    3. Anila or Vayudeva (wind)
    4. Apa (water)
    5. Prabhasa or Dyauh (sky)
    6. Pratyusha
    7. Soma
    8. Dhruva
  • The goddess of wealth and prosperity,Lakshmi,has eight forms known asAshta Lakshmiand worshipped as:
    "Maha-lakshmi, Dhana-lakshmi, Dhanya-lakshmi, Gaja-lakshmi,
    Santana-lakshmi, Veera-lakshmi, Vijaya-lakshmi and Vidhya-lakshmi
    "[46]
  • There are eightnidhi,or seats of wealth, according toHinduism.
  • There are eightguardians of the directionsknown asAstha-dikpalas.[47]
  • There are eightHindumonasteries established by the saintMadhvacharyainUdupi,Indiapopularly known as theAshta Mathas of Udupi.[48]

Buddhism

[edit]
In Buddhism, the 8-spokedDharmacakrarepresents theNoble Eightfold Path.
  • TheDharmacakra,aBuddhistsymbol, has eight spokes.[49]The Buddha's principal teaching—theFour Noble Truths—ramifies as theNoble Eightfold Pathand the Buddha emphasizes the importance of the eight attainments or jhanas.
  • InMahayanaBuddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas: (Manjusri,Vajrapani,Avalokiteśvara,Maitreya,Ksitigarbha,Nivaranavishkambhi,Akasagarbha,andSamantabhadra).[50]These are later (controversially) associated with the Eight Consciousnesses according to theYogacaraschool 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 orbhūmi.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 whitekamalalotus-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 birthdayfalls on the 8th day of the 4th month of theChinese calendar.

Judaism

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Christianity

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Islam

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TheoctagramRub el Hizb

Taoism

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Other

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As a lucky number

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  • The number eight is considered to be alucky number in Chineseand other Asian cultures.[65]Eight (Tám;accountingBát;pinyin) is considered alucky number in Chinese culturebecause it sounds like the word meaning to generate wealth (Phát (T) phát (S);Pinyin:). Property with the number 8 may be valued greatly by Chinese. For example, a Hong Kongnumber platewith the number 8 was sold for $640,000.[66]The opening ceremony of theSummer Olympics in Beijingstarted at 8 seconds and 8 minutes past 8 pm (local time) on 8 August 2008.[67]
  • In Pythagoreannumerologythe number 8 represents victory, prosperity and overcoming.
  • Eight(Tám,hachi, ya)is also considered a lucky number inJapan,but the reason is different from that in Chinese culture.[68]Eight gives an idea of growing prosperous, because the letter (Tám) 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 music and dance

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In film and television

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In sports and other games

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An 8-ball in pool

In foods

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  • Nestlésells a brand of chocolates filled with peppermint-flavoured cream calledAfter Eight,referring to the time 8 p.m.[97]
  • There are eight vegetables inV8juice.[98]

In literature

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In slang

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Other uses

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  • A figure 8 is the common name of ageometricshape,often used in the context of sports, such as skating.[104]Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something.[105]

See also

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References

[edit]
  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.ruArchived31 October 2007 at theWayback 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 Computertransl. 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.Retrieved7 August2020....then every sphenic number n=pqr has precisely eight positive divisors
  7. ^Weisstein, Eric W."Octal".mathworld.wolfram.Retrieved7 August2020.
  8. ^Weisstein, Eric W."Octagon".mathworld.wolfram.Retrieved7 August2020.
  9. ^Weisstein, Eric W."Regular Octagon".mathworld.wolfram.Retrieved25 June2022.
  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.ISBN978-3-540-59251-8.
  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 June2022.
  13. ^Weisstein, Eric W."Cuboctahedron".mathworld.wolfram.Retrieved25 June2022.
  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.ISBN978-0-521-00551-7....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.MR2542837.
  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.eISSN2196-9701.ISBN978-1-4757-2016-7.
  18. ^Ilangovan, K. (10 June 2019).Nuclear Physics.MJP Publisher. p. 30.
  19. ^Gell-Mann, M. (15 March 1961).THE EIGHTFOLD WAY: A THEORY OF STRONG INTERACTION SYMMETRY(Technical report).OSTI4008239.
  20. ^Baxter, R. J. (5 April 1971)."Eight-Vertex Model in Lattice Statistics".Physical Review Letters.26(14): 832–833.Bibcode:1971PhRvL..26..832B.doi:10.1103/PhysRevLett.26.832.
  21. ^"Messier Object 8".messier.seds.org.Retrieved7 August2020.
  22. ^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,
  23. ^Choppin, Gregory R.; Johnsen, Russell H. (1972).Introductory chemistry.Addison-Wesley Pub. Co. p. 366.ISBN978-0-201-01022-0.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...
  24. ^Puri, Basant; Hall, Anne (16 December 1998).Phytochemical Dictionary: A Handbook of Bioactive Compounds from Plants, Second Edition.CRC Press. p. 810.ISBN978-0-203-48375-6.The chemical structure of lycopene consists of a long chain of eight isoprene units joined head to tail
  25. ^Parker, Barbara Keevil (28 December 2006).Ticks.Lerner Publications. p. 7.ISBN978-0-8225-6464-5.Arachnids have eight legs
  26. ^Jackman, J. A. (1997).A Field Guide to Spiders & Scorpions of Texas.Gulf Publishing Company. p. 70.ISBN978-0-87719-264-0.Araneids have eight eyes
  27. ^Fisher, James; Huxley, Julian (1961).The Doubleday Pictorial Library of Nature: Earth, Plants, Animals.Doubleday. p. 311.Polyps with eight branched tentacles and eight septa
  28. ^Bourne, Gilbert Charles(1911)."Anthozoa".InChisholm, Hugh(ed.).Encyclopædia Britannica.Vol. 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
  29. ^The Century Dictionary and Cyclopedia: A work of Universal Reference in all Departments of Knowledge with a New Atlas of the World.1906. p. 1384....are radially symmetrical, and swim by means of eight meridional ciliated bands,...
  30. ^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,...
  31. ^Dofka, Charline M. (1996).Competency Skills for the Dental Assistant.Cengage Learning. p. 83.ISBN978-0-8273-6685-5....In each quadrant of the permanent set of teeth (dentition), there are eight teeth
  32. ^Quain, Jones (1909).Quain's Elements of Anatomy.Longmans, Green, & Company. p. 52.These eight pairs are usually reckoned as eight cervical nerves...
  33. ^Beebe, John (17 June 2016).Energies and Patterns in Psychological Type: The reservoir of consciousness.Routledge. p. 124.ISBN978-1-317-41366-0.Linda Berens used the term 'cognitive processes' (1999) to refer to the eight types of consciousness that Jung discovered.
  34. ^"Definition of byte | Dictionary".dictionary.Retrieved8 August2020.
  35. ^Kindem, Gorham; PhD, Robert B. Musburger (21 August 2012).Introduction to Media Production: The Path to Digital Media Production.CRC Press. p. 320.ISBN978-1-136-05322-1.There used to be two 8 mm formats: standard 8 mm and Super-8 mm.
  36. ^The Library of Congress Veterans History Project: Field Kit: Conducting and Preserving Interviews.Veterans History Project, American Folklife Center, Library of Congress. 2008. p. 15.Betacam SX 8 mm Hi8, Digital8, Video8 DVD-Video ";
  37. ^"Definition of eight | Dictionary".dictionary.Retrieved8 August2020.
  38. ^Griffiths, Garth (1971).Boating in Canada: Practical Piloting and Seamanship.University of Toronto Press. p. 32.ISBN978-0-8020-1817-5.First is a stopper knot, the figure of eight,...
  39. ^The Milwaukee Cook Book.Press of Houtkamp Printing. 1907.
  40. ^"Definition of furlong | Dictionary".dictionary.Retrieved8 August2020.
  41. ^"Definition of clove | Dictionary".dictionary.Retrieved8 August2020.
  42. ^Fairhall, David; Peyton, Mike (17 May 2013).Pass Your Yachtmaster.A&C Black.ISBN978-1-4081-5627-8.Gale warnings will be given if mean wind speeds of force 8 (34–40 knots)
  43. ^Sayers, William (2003)."Eastern Prospects: Kiosks, Belvederes, Gazebos".Neophilologus.87(2): 299–305.doi:10.1023/A:1022691123957.S2CID159542713.
  44. ^Halstead, Frank (1927).The Orders of Architecture.New York: John Wiley & Sons, Inc.
  45. ^"Who are the eight vasus?".Hinduism Stack Exchange.Retrieved19 December2023.
  46. ^Hatcher, Brian A. (5 October 2015).Hinduism in the Modern World.Routledge.ISBN978-1-135-04630-9.a group manifestation of eight forms
  47. ^Jeyaraj, Daniel (23 September 2004).Genealogy of the South Indian Deities: An English Translation of Bartholomäus Ziegenbalg's Original German Manuscript with a Textual Analysis and Glossary.Routledge. p. 168.ISBN978-1-134-28703-1.He is one of the eight guardians of the world
  48. ^Ramachandran, Nirmala (2000).Hindu Heritage.Stamford Lake Publication. p. 72.ISBN978-955-8733-09-7.The temple has eight monasteries, founded by Madhvacharya
  49. ^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.ISBN978-1-61069-478-0.The dharmachakra is typically depicted with eight spokes,
  50. ^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...
  51. ^Rosten, Leo (14 April 2010).The New Joys of Yiddish: Completely Updated.Potter/Ten Speed/Harmony/Rodale. p. 48.ISBN978-0-307-56604-1.Brit Milah is observed on a boy's eighth day of life
  52. ^Ross, Kathy (1 August 2012).Crafts for Hanukkah.Millbrook Press. p. 7.ISBN978-0-7613-6836-6.Hanukkah is an eight-day Jewish holiday
  53. ^Axelrod, Cantor Matt (24 December 2013).Your Guide to the Jewish Holidays: From Shofar to Seder.Rowman & Littlefield. p. 58.ISBN978-0-7657-0990-5.Shemini Atzeret—literally, "the eighth day of assembly"
  54. ^"CATHOLIC ENCYCLOPEDIA: The Eight Beatitudes".newadvent.org.Retrieved9 August2020.
  55. ^Akintola, Olufolahan Olatoye (2011).Nations of the World…How They Evolved!: Families and Nations That Came Out of Ham.Hilldew View International Limited. p. 8.ISBN978-0-9569702-2-0.These eight souls in Noah's ark were the survivors...
  56. ^Livingstone (2001).Life Application New Testament Commentary.Tyndale House Publishers, Inc.ISBN978-0-8423-7066-0.
  57. ^Mahmutćehajić, Rusmir (2011).Maintaining the Sacred Center: The Bosnian City of Stolac.World Wisdom, Inc. p. 201.ISBN978-1-935493-91-4.... at the last, eight Angels will carry the Throne...
  58. ^"Names of the Gates of Heaven".islamweb.net.Retrieved19 December2023.
  59. ^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...
  60. ^Ho, Peter Kwok Man; Kwok, Man-Ho; O'Brien, Joanne (1990).The Eight Immortals of Taoism: Legends and Fables of Popular Taoism.Meridian. p. 7.ISBN978-0-452-01070-3....famous Eight Immortals of China...
  61. ^Zimmermann, Denise; Gleason, Katherine; Liguana, Miria (2006).The Complete Idiot's Guide to Wicca and Witchcraft.Penguin. p. 172.ISBN978-1-59257-533-6.There are eight Sabbats
  62. ^Remler, Pat (2010).Egyptian Mythology, A to Z.Infobase Publishing. p. 79.ISBN978-1-4381-3180-1....of the gods of the Ogdoad, or the eight deities of the Egyptian creation...
  63. ^Wallis, Roy(1977).The Road to Total Freedom: A Sociological Analysis of Scientology.Columbia University Press.ISBN0231042000.OL4596322M.
  64. ^David, Fideler (1993).Jesus Christ, Sun of God: Ancient Cosmology and Early Christian Symbolism.Quest Books. p. 128.ISBN978-0-8356-0696-7.
  65. ^Ang, Swee Hoon (1997)."Chinese consumers' perception of Alpha -numeric brand names".Journal of Consumer Marketing.14(3): 220–233.doi:10.1108/07363769710166800.Archivedfrom the original on 5 December 2011.
  66. ^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 May2011.
  67. ^"Olympics opening ceremony: China makes its point with greatestshow".the Guardian.8 August 2008.Retrieved29 November2022.
  68. ^Jefkins, Frank (6 December 2012).Modern Marketing Communications.Springer Science & Business Media. p. 36.ISBN978-94-011-6868-7....eight being a lucky number in Japanese.
  69. ^"Definition of SCORPIO".merriam-webster.Retrieved10 August2020.
  70. ^"Definition of eighth note | Dictionary".dictionary.Retrieved9 August2020.
  71. ^"Definition of OCTAVE".merriam-webster.Retrieved9 August2020.a tone or note that is eight steps above or below another note or tone
  72. ^"Definition of octet | Dictionary".dictionary.Retrieved9 August2020.a company of eight singers or musicians.
  73. ^"Definition of octet | Dictionary".dictionary.Retrieved9 August2020.a musical composition for eight voices or instruments.
  74. ^"Incubus Premiere New Song" Glitterbomb ", Detail New Album" 8 "".Theprp.17 March 2017.Retrieved9 August2020.
  75. ^Beatie Wolfe-8ight,retrieved9 August2020
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  77. ^Too Many Eights – Supercluster | Song Info | AllMusic,retrieved10 August2020
  78. ^"Eight Seconds | Biography & History".AllMusic.Retrieved10 August2020.
  79. ^Eight Days a Week – The Beatles | Song Info | AllMusic,retrieved10 August2020
  80. ^Figure 8 – Elliott Smith | Songs, Reviews, Credits | AllMusic,retrieved10 August2020
  81. ^Figure 8 – Julia Darling | Songs, Reviews, Credits | AllMusic,retrieved10 August2020
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  83. ^"The8 | Credits".AllMusic.Retrieved10 August2020.
  84. ^22, A Million – Bon Iver | Songs, Reviews, Credits | AllMusic,retrieved10 August2020
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