8 (number)

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"8th", "Eight" and "Eighth" redirect here. For other uses see 8 (disambiguation)
← 7 8 9 →
−1 0 1 2 3 4 5 6 7 8 9 →
Cardinal eight
Ordinal 8th
(eighth)
Factorization 23
Divisors 1, 2, 4, 8
Roman numeral VIII
Roman numeral (unicode) Ⅷ, ⅷ
Greek prefix octa-/oct-
Latin prefix octo-/oct-
Binary 10002
Ternary 223
Quaternary 204
Quinary 135
Senary 126
Octal 108
Duodecimal 812
Hexadecimal 816
Vigesimal 820
Base 36 836
Greek η (or Η)
Arabic ٨,8
Urdu ۸
Amharic ፰
Bengali ৮
Chinese numeral 八，捌
Devanāgarī ८
Kannada ೮
Telugu ౮
Tamil ௮
Hebrew ח (Het)
Hebrew שמונה (shmoneh)
Khmer ៨
Korean 팔
Thai ๘

8 (eight /ˈeɪt/) is the natural number following 7 and preceding 9. It is the root word of two other numbers: eighteen (eight and ten) and eighty (eight tens). The word is derived from Middle English eighte.

In mathematics

8 is a composite number, its proper divisors being 1, 2, and 4. It is twice 4 or four times 2. Eight is a power of two, being 2^{3} (two cubed), and is the first number of the form p^{3}, p being an integer greater than 1. It has an aliquot sum of 7 in the 4 member aliquot sequence (8,7,1,0) being the first member of 7-aliquot tree. It is symbolized by the Arabic numeral (figure)

All powers of 2 ;(2^{x}), have an aliquot sum of one less than themselves.

A number is divisible by 8 if its last 3 digits are also divisible by 8.

Eight is the first number to be the aliquot sum of two numbers other than itself; the discrete biprime 10, and the square number 49.

8 is the base of the octal number system, which is mostly used with computers. In octal, one digit represents 3 bits. In modern computers, a byte is a grouping of eight bits, also called an octet.

The number 8 is a Fibonacci number, being 3 plus 5. The next Fibonacci number is 13. 8 is the only positive Fibonacci number, aside from 1, that is a perfect cube.[1]

8 is the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem.

8 is the order of the smallest non-abelian group all of whose subgroups are normal.

8 and 9 form a Ruth–Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

A polygon with eight sides is an octagon. Figurate numbers representing octagons (including eight) are called octagonal numbers. A polyhedron with eight faces is an octahedron. A cuboctahedron has as faces six equal squares and eight equal regular triangles.

A cube has eight vertices.

Sphenic numbers always have exactly eight divisors.

8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra.

The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example if O(\infty ) is the direct limit of the inclusions of real orthogonal groups O(1)\hookrightarrow O(2)\hookrightarrow \ldots \hookrightarrow O(k)\hookrightarrow \ldots then \pi _{{k+8}}(O(\infty ))\cong \pi _{{k}}(O(\infty )). 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 spin group Spin(8) is the unique such group that exhibits the phenomenon of triality.

The lowest dimensional even unimodular lattice is the 8-dimensional E8 lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8.

A figure 8 is the common name of a geometric shape, 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.

In numeral systems

Base Numeral system Representation
2 binary 1000
3 ternary 22
4 quaternary 20
5 quinary 13
6 senary 12
7 septenary 11
8 octal 10
over 8 (decimal, hexadecimal) 8

In culture

Evolution of the glyph

In the beginning, various groups in India wrote eight more or less in one stroke as a curve that looks like an uppercase H with the bottom half of the left line and the upper half of the right line removed. At one point this glyph came close to looking like our modern five. With the western Ghubar Arabs, the similarity of the glyph to five was banished by connecting the beginning and the end of stroke together, and it was only a matter of the Europeans rounding the glyph that led to our modern eight.[3]

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in .

In science

Physics

Astronomy

Chemistry

  • The atomic number of oxygen.
  • The number of allotropes of carbon.
  • The most stable allotrope of a sulphur molecule is made of eight sulphur atoms arranged in a rhombic form.
  • The maximum number of electrons that can occupy a valence shell.
  • The red pigment lycopene consists of eight isoprene units.

Geology

  • 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.

Biology

  • All spiders, and more generally all arachnids, have eight legs. Orb-weaver spiders of the cosmopolitan family Areneidae have eight similar eyes.
  • The octopus and its cephalopod relatives in genus Argonauta have eight arms (tentacles).
  • Compound coelenterates of the subclass or order Alcyonaria have polyps with eight-branched tentacles and eight septa.
  • Sea anemones of genus Edwardsia have eight mesenteries.
  • Animals of phylum Ctenophora swim by means of eight meridional bands of transverse ciliated plates, each plate representing a row of large modified cilia.
  • The eight-spotted forester (genus Alypia, family Zygaenidae) is a diurnal moth having black wings with brilliant white spots.
  • The ascus in fungi of the class Ascomycetes, following nuclear fusion, bears within it typically eight ascospores.
  • Herbs of genus Coreopsis (tickseed) have showy flower heads with involucral bracts in two distinct series of eight each.
  • Timothy Leary identified a hierarchy of eight levels of consciousness.
  • In human adult dentition there are eight teeth in each quadrant. The eighth tooth is the so-called wisdom tooth.
  • There are eight cervical nerves on each side in man and most mammals.

Architecture and engineering

  • Various types of buildings are usually eight-sided (octagonal), such as single-roomed gazebos and multi-roomed pagodas (descended from stupas; see religion section below).
  • Eight caulicoles rise out of the leafage in a Corinthian capital, ending in leaves that support the volutes.

In religion

Buddhism
The 8-spoked Dharmacakra represents the Noble Eightfold Path
  • 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.
Judaism
  • The religious rite of brit milah (commonly known as circumcision) is held on a baby boy's eighth day of life.
  • Hanukkah is an eight-day Jewish holiday that starts on the 25th day of Kislev.
  • Shemini Atzeret (Hebrew: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of Sukkot.
Christianity
Islam
Other

In superstition and divination

As a lucky number

  • 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.[5] 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.[6]
  • 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 astrology

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.
  • There are eight notes in the octatonic scale.
  • There are eight musicians in a double quartet or an octet. Both terms may also refer to a musical composition for eight voices or instruments.
  • Caledonians is a square dance for eight, resembling the quadrille.
  • Albums with the number eight in their title include 8 by the Swedish band Arvingarna and The Meaning of 8 by Minnesota indie rock band Cloud Cult
  • Dream Theater's eighth album Octavarium contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork
  • "Eight maids a-milking" is the gift on the eighth day of Christmas in the carol "The Twelve Days of Christmas"
  • The 8-track cartridge is a musical recording format
  • "#8" is the stagename of Slipknot vocalist Corey Taylor
  • "Too Many Eights" is a song by Athens, Georgia's Supercluster.
  • Eight Seconds, a Canadian musical group popular in the 1980s with their most notable song "Kiss You (When It's Dangerous)"
  • "Eight Days a Week" is a #1 single for the music group The Beatles.

In film and television

In sports and other games

In technology

In measurement

In foods

  • Nestlé sells a brand of chocolates filled with peppermint-flavoured cream called After Eight, referring to the time 8 p.m.
  • There are eight vegetables in V8 juice
  • In cooking recipes, there are approximately 8 pinches to a teaspoon

In literature

  • Eights may refer to octosyllabic, usually iambic, lines of verse.
  • 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
  • Lewis Carroll's poem The Hunting of the Snark has 8 "fits" (cantos), which is noted in the full name "The Hunting of the Snark - An Agony, in Eight Fits
  • 8 apparitions appear to Macbeth in Act 4 scene 1 of Shakespeare's Macbeth as representations of the 8 descendants of Banquo

In slang

  • An "eighth" is a common measurement of marijuana, meaning an eighth of an ounce.[9] It is also a common unit of sale for psilocybin mushrooms.[10] Also, an eighth of an ounce of cocaine is commonly referred to as an "8-ball."[11]
  • Referring to the shape of the numeral, eight was represented in bingo slang, before political correctness, as "One Fat Lady". Eighty-eight was "Two Fat Ladies"
  • The numeral "8" is sometimes used in writing 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. The search engine "Targ8"[12] uses it to replace "et" in Target. Often found on vanity plates
  • "Section 8" is common U.S. slang for "crazy", based on the U.S. military's Section 8 discharge for mentally unfit personnel
  • The Housing Choice Voucher Program, operated by the United States Department of Housing and Urban Development, is commonly referred to as the Section 8 program, as this was the original section of the Act which instituted the program
  • In Colombia and Venezuela, "volverse un ocho" (meaning to tie oneself in a figure 8) refers to getting in trouble or contradicting one's self.
  • 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'.
  • Eight is symbolic for lesbian sexual relations.

In other fields

NATO signal flag for 8
Four playing cards showing the "8" of all four suits
  • Eight, West Virginia, a community in the United States
  • The ordinal adjective is octaval or octavary.
  • The distributive adjective is octonary.
  • Eight babies delivered in one birth are called octuplets. The first set of eight surviving babies, the Chukwu octuplets, were born in 1998
  • October was the eighth month in the Roman calendar; currently August is the eighth month
  • A double quatrefoil has eight foils used as the cadency mark of a ninth son.
  • A duke's coronet, worn by a British or Irish duke, has eight conventional strawberry leaves upon the rim of the circlet.
  • Eight extra facets are sometimes added around the culet at the lower pyramid of a brilliant diamond.
  • I-8 is the designation of the US interstate highway that runs from San Diego, California to Casa Grande, Arizona
  • Eight is the number of categories the VALS system uses to classify consumer groups, and the number of categories used by Fallon-McElligott's system for teen marketing
  • War of the Eight Princes, a war in Chinese history
  • "88" is the abbreviated terminology used by the Aryan Brotherhood for the Nazi salute, "Heil Hitler" – "H" being the eighth letter of the alphabet, twice
  • The silver piece of eight was coined in the Spanish Empire and moved trade around the world. Examples include the Carolus dollar, cob and cut. A doubloon was worth 8 gold escudos or 16 pieces of eight.
  • Eight elementary grades are included in the eight-four plan of school organization (along with four secondary grades).
  • 8 is the official number of the Bishop James Madison Society, a secret society at the College of William & Mary.
  • There are Eight Principles of Yong in Chinese calligraphy
  • 8vo is shorthand for "octavo", a book 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).
  • Astadiggajas is the collective title given to the eight Telugu poets in the court of the emperor Sri Krishnadevaraya who ruled the Vijayanagara Empire from 1509 until his death in 1529.
  • A stop sign has eight sides.
  • In mythology, the horse of the Norse god Odin has eight legs and is called Sleipnir.
  • Proposition 8, the ballot measure banning same-sex marriage in California.
  • No H8 campaign in protest of Proposition 8 in California.

See also

References

  1. ↑ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88
  2. ↑ Ang, Swee Hoon (1997). "Chinese consumers’ perception of alpha-numeric brand names". Journal of Consumer Marketing 14 (3): 220–233. doi:10.1108/07363769710166800. 
  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. ↑ "Life Application New Testament Commentary", Bruce B. Barton. Tyndale House Publishers, Inc., 2001. ISBN 0-8423-7066-8, ISBN 978-0-8423-7066-0. p. 1257
  5. ↑ Steven C. Bourassa, Vincent S. Peng (1999). "Hedonic Prices and House Numbers: The Influence of Feng Shui". International Real Estate Review 2 (1): 79–93 
  6. ↑ "Patriot games: China makes its point with greatest show" by Richard Williams, The Guardian, published 9 August 2008
  7. ↑ Barney's burp song
  8. ↑ A to Z Encyclopaedia of Ice Hockey
  9. ↑ [http://www.urbandictionary.com/define.php?term=eighth, urban dictionary]
  10. ↑ [http://www.google.com/search?hl=en&safe=off&client=safari&rls=en-us&q=%22eighth+of+shrooms%22&btnG=Search, psilocybin mushrooms]
  11. ↑ http://www.thegooddrugsguide.com/cocaine/faq.htm
  12. ↑ , Targ8 your search engine

External links

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