8 (number)

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8

0 1 2 3 4 5 6 7 8 9 →
Cardinal 8
eight
Ordinal 8th
eighth
Numeral system octal
Factorization 23
Divisors 1, 2, 4, 8
Roman numeral VIII
Roman numeral (Unicode) Ⅷ, ⅷ
Arabic ٨
Amharic ፰
Bengali ৮
Chinese numeral 八
Devanāgarī ८
Hebrew ח (Het)
Khmer ៨
Thai ๘
prefixes octa-/oct- (from Greek)

octo-/oct- (from Latin)
Binary 1000
Octal 10
Duodecimal 8
Hexadecimal 8
Look up eight in
Wiktionary, the free dictionary.

8 (eight) is the natural number following 7 and preceding 9. The SI prefix for 10008 is yotta (Y), and for its reciprocal yocto (y).

Contents

[edit] In mathematics

8 is a composite number, its proper divisors being 1, 2, and 4. Eight is a power of two, being 23, or two cubed. It has an aliquot sum of 7. All powers of 2 have an aliquot sum of one less than themselves.

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 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.

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 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

In binary code eight is 1000; in ternary code eight is 22; in quaternary numeral system code eight is 20; in quinary eight is 13; in senary eight is 12; in septenary eight is 11; in octal eight is 10; in novenary code and all codes above (such as decimal and hexadecimal) eight is 8.

A fallen or lying down 8 (∞, the lemniscate) is used to represent infinity in mathematics. This interpretation of 8 may be related to the representation of the caduceus (where two snakes form several figure eights) as stability or balance of opposing forces.

Eight is the number of Thurston model geometries. Eight is not a prime number

E8 has rank 8.

As of 2008, there are only eight known Stern primes.

[edit] In numeral systems

Base Numeral system
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

[edit] List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
8 \times x 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160 168 176 184 192 200 400 800 8000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8 \div x 8 4 2.\overline{6} 2 1.6 1.\overline{3} 1.\overline{142857} 1 0.\overline{8} 0.8 0.\overline{72} 0.\overline{6} 0.\overline{615384} 0.\overline{571428} 0.5\overline{3}
x \div 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
8 ^ x\, 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 68719476736 549755813888
x ^ 8\, 1 256 6561 65536 390625 1679616 5764801 16777216 43046721 100000000 214358881 429981696 815730721
Radix 1 5 10 15 20 25 30 40 50 60 70 80 90 100
110 120 130 140 150 200 250 500 1000 10000 100000 1000000
x_{8} \ 1 5 12_{8} \ 17_{8} \ 24_{8} \ 31_{8} \ 36_{8} \ 50_{8} \ 62_{8} \ 74_{8} \ 106_{8} \ 120_{8} \ 132_{8} \ 144_{8} \
156_{8} \ 170_{8} \ 202_{8} \ 214_{8} \ 226_{8} \ 310_{8} \ 372_{8} \ 764_{8} \ 1750_{8} \ 23420_{8} \ 303240_{8} \ 3641100_{8} \

[edit] 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.[1]

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in Image:TextFigs148.png. The "1" and "4" are old-style figures; the "8" is the same height in both old-style and modern figures. 1234567890 are all the same height; they are modern figures.

[edit] In science

[edit] Physics

[edit] Astronomy

[edit] Chemistry

[edit] Biology

[edit] 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).

[edit] In religion

  • The Jewish religious rite of brit milah 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
  • The Noble Eightfold Path in the Buddhist faith has eight steps
  • The Eight Immortals are Chinese deities
  • Members of The Church of Jesus Christ of Latter-day Saints believe that humans are responsible for their actions by the age of 8. Before that age, children lack sufficient knowledge to commit sin and are therefore exempt from judgment for their actions.
  • The Dharmachakra, a Buddhist symbol, has eight spokes. The Buddha's principal teaching -- the Four Noble Truths -- ramifies as the Eightfold Noble Path. In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas (Manjushri, Vajrapani, Avalokiteshvara, Maitreya, Kshitigarbha, Nivaranavishkambhi, Akashagarbha, and Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogachara 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.
  • In Christianity, it is allegoric to:
    • what is beyond time (because the number 7 refers to the days of the week which repeat themselves),
    • and is the number of Beatitudes.
  • In Islam, It is the number of Angels carrying The Holy Throne of Allah in heavens.
  • In Neopaganism, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year.
  • In Hinduism its the number of wealth , abundance. The Goddess Lakshmi has eightfold forms. There are eight nidhis - seats of wealth.

[edit] In superstition and divination

  • If each of the classical elements is assigned a cosmic projection, the resulting number (8) represents them.


[edit] As a lucky or unlucky number

  • Eight (八; accounting 捌; pinyin bā) is considered a lucky number in Asian culture because it sounds like the word "prosper" or "wealth" (發; Pinyin: fā). Additionally, it is considered lucky in Japan because the Chinese numeral character resembles a mountain, specifically Fujisan.
  • In numerology, 8 is the number of building, and in some theories, also the number of destruction.

[edit] In astrology

[edit] In music

  • 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 on a western scale between the two, including the notes themselves
  • There are eight notes in an octatonic scale
  • There are eight musicians in an octet
  • 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 (band).
  • Eight Seconds, a Canadian musical group popular in the 1980s with their most notable song "Kiss You (When It's Dangerous)"

[edit] In sports

In football, the number 8 has historically been the number of the Central Midfielder while in rugby union the number eight central back row position wears the 8 shirt. Similarly in baseball, in its numbering system used to record defensive plays, eight represents the center fielder's position. The Philadelphia Flyers once had a line called the Crazy Eights with Eric Lindros at center (88); Mark Recchi (8); and Brent Fedyk (18). Kobe Bryant wore this number for most parts of his career. 49ers Quarterback Steve Young wore this number. 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.

Eight ball billiards is played with 15 balls; the black ball numbered 8 being the middle and most important one. Magic 8 Ball is a randomized process of predicting the future or answering various questions, packaged to resemble this ball and often sold as a fortune-telling device.

In rowing an 'eight' refers to a sweep oar boat with eight rowers plus a coxswain.

In rugby union, the only position without a proper name is the Number 8, a forward position.

It is the retired jersey number of Baseball Hall of Fame players Cal Ripken, Jr., Joe Morgan, Willie Stargell, Carl Yastrzemski, and Yogi Berra.

8 is also the record number of goals conceded by a soccer team in the Champions League. Liverpool FC defeated Besiktas JK 8-0 at Anfield Road on November 6, 2007. Besiktas JK is therefore sometimes referred to as 8esiktas.

[edit] In technology

[edit] In measurement

[edit] In foods

  • There is 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

[edit] In literature

  • 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

[edit] In slang

  • An Eighth is a common measurement of marijuana, meaning an eighth of an ounce
  • 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. 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
  • 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'.
  • In Washington, DC, seductively patting the bed covers in a figure-eight pattern in an invitation for sexual relations.
  • Eight is symbolic for lesbian sexual relations.

[edit] In other fields

International maritime signal flag for 8
International maritime signal flag for 8
Four playing cards showing the "8" of all four suits
Four playing cards showing the "8" of all four suits
  • 08/08/2008 - Games of the XXIX Olympiad will be celebrated in Beijing, China. Also, it is the official birth date of Jao, whose founding figure will turn 33.
  • The number of tentacles on an octopus.
  • 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
  • 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
  • There are Eight Principles of Yong in Chinese calligraphy
  • 8 is the number of days one can expect to wait for approval on Devilshire.
  • 8 is one of the "Lost Numbers" on the television show, Lost, along with 4, 15, 16, 23, and 42
  • In Stargate SG-1 and Stargate Atlantis, dialing an 8-chevron address will open a wormhole to another galaxy.
  • 8vo is shorthand for "octavo", a book size.
  • Eight is an often significant number in video games, particularly Mario games (8 worlds in Super Mario Bros., 8 chapters in Paper Mario, etc).
  • 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).

[edit] References

  1. ^ 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

[edit] External links

  • Flickr 8, the infinite beauty of - photo group
  • 8by8 an art community based on the geometry of 8
  • Dictionary of numbers - online tool for converting numerals to word equivalents in multiple languages