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# 8 (number)

8
Cardinal 8
eight
Ordinal 8th
eighth
Numeral system octal
Factorization $2^3$
Divisors 1, 2, 4, 8
Roman numeral VIII
Roman numeral (Unicode) Ⅷ, ⅷ
Arabic ٨
Amharic
Bengali
Chinese numeral 八，捌
Devanāgarī
Hebrew ח (Het)
Khmer
Korean
Thai
prefixes octa-/oct- (from Greek) octo-/oct- (from Latin)
Binary 1000
Octal 10
Duodecimal 8

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). It is the root of two other numbers: eighteen (eight and ten) and eighty (eight tens). Linguistically, it 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 $p^3$. 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) 8.

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

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 Fibonacci number that is a perfect cube.

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.

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 $O\left(infty\right)$ is the direct limit of the inclusions of real orthogonal groups $O\left(1\right)hookrightarrow O\left(2\right)hookrightarrowldotshookrightarrow O\left(k\right)hookrightarrowldots$ then $pi_\left\{k+8\right\}\left(O\left(infty\right)\right)congpi_\left\{k\right\}\left(O\left(infty\right)\right)$. Clifford algebras also display a periodicity of 8. For example the algebra $Cl\left(p+8,q\right)$ is isomorphic to the algebra of 16 by 16 matrices with entries in $Cl\left(p,q\right)$. 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. Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something.

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

### In numeral systems

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

### 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 $2.overline\left\{6\right\}$ 2 1.6 $1.overline\left\{3\right\}$ $1.overline\left\{142857\right\}$ 1 $0.overline\left\{8\right\}$ 0.8 $0.overline\left\{72\right\}$ $0.overline\left\{6\right\}$ $0.overline\left\{615384\right\}$ $0.overline\left\{571428\right\}$ $0.5overline\left\{3\right\}$
$x div 8$ 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
$x_\left\{8\right\}$ 1 5 $12_\left\{8\right\}$ $17_\left\{8\right\}$ $24_\left\{8\right\}$ $31_\left\{8\right\}$ $36_\left\{8\right\}$ $50_\left\{8\right\}$ $62_\left\{8\right\}$ $74_\left\{8\right\}$ $106_\left\{8\right\}$ $120_\left\{8\right\}$ $132_\left\{8\right\}$ $144_\left\{8\right\}$
$156_\left\{8\right\}$ $170_\left\{8\right\}$ $202_\left\{8\right\}$ $214_\left\{8\right\}$ $226_\left\{8\right\}$ $310_\left\{8\right\}$ $372_\left\{8\right\}$ $764_\left\{8\right\}$ $1750_\left\{8\right\}$ $23420_\left\{8\right\}$ $303240_\left\{8\right\}$ $3641100_\left\{8\right\}$

## 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.

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

## In science

### 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 the 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 Dharmachakra, a Buddhist symbol, has eight spokes. The Buddha's principal teaching -- the Four Noble Truths -- ramifies as the Noble Eightfold 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.Judeo-Christianity
• 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
• 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.
• 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.Other
• The Eight Immortals are Chinese deities
• In Neopaganism, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year.
• In Hinduism it's the number of wealth , abundance. The Goddess Lakshmi has eightfold forms. There are eight nidhis - seats of wealth. Also, there are eight Guardians of the directions.

## In superstition and divination

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

## 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.
• The lowest stop on a pipe-organ is the eight-foot stop, which is approximately eight feet in length.
• 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 (band).
• 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 sports and other games

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.

In rugby union, the only position without a proper name is the Number 8, a forward position. In rowing an "eight" refers to a sweep-oar racing boat with a crew of eight rowers plus a coxswain.

In the 2008 Games of the XXIX Olympiad, the official opening was on 08/08/08 (in the dd/mm/yy format) at 8:08:08 p.m. local time in Beijing, China.

Eight ball pool billiards is played with a cue ball and 15 numbered balls, the black ball numbered 8 being the middle and most important one, as the winner is the player or side that legally pockets it after first pocketing its numerical group of 7 object balls. (For other meanings see Eight ball (disambiguation)).

Balklines divide a billiards table into eight outside compartments or divisions called balks. In balkline billiards the table also has eight anchor spaces.

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.

• In the game of eights or crazy eights, each successive player must play a card either of the same suit or of the same rank as that played by the preceding player, or may play an eight and call for any suit. The object is to get rid of all one's cards first.
• In poker, a "dead man's hand" contains two pairs of either aces and eights or jacks and eights.

The throw of eight in craps is called (in rhyming slang) an eighter from Decatur.

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

## In technology

• Many (mostly historic) computer architectures are eight-bit, among them the Nintendo Entertainment System
• A byte is eight bits
• On most phones, the 8 key is associated with the letters T, U, and V, but on the BlackBerry it is the key for B , N, and X.
• An eight may refer to an eight-cylinder engine or automobile. A V8 engine is an internal combustion engine with eight cylinders configured in two banks (rows) of four forming a "V" when seen from the end.
• A figure eight is a type of knot frequently used by climbers.

## 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

## 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. It is also a common unit of sale for psilocybin mushrooms. Also, an eighth of an ounce of cocaine is commonly referred to as an "8-ball.
• 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
• 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.