8

	8
	Template:Numbers (digits)
Cardinal	8 ; eight
Ordinal	8th ; eighth
Numeral system	octal
Factorization
Divisors	1, 2, 4, 8
Roman numeral	VIII
Roman numeral (Unicode)	Ⅷ, ⅷ
Arabic	٨
Amharic	፰
Bengali	৮
Chinese numeral	八，捌
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

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).

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 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 $O(\infty )$ 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. 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	$2.{\overline {6}}$	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
Radix	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}\$
$x_{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}\$

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 . 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

Physics

In nuclear physics, the second magic number.
In particle physics, the eightfold way is used to classify sub-atomic particles.

Astronomy

Messier object M8, a magnitude 5.0 nebula in the constellation of Sagittarius.
The New General Catalogue object NGC 8, a double star in the constellation Pegasus
The Saros number of the solar eclipse series which began on 2579 BCE March 7 and ended on 1281 BCE April 26. The duration of Saros series 8 was 1298.1 years, and it contained 73 solar eclipses.
The Saros number of the lunar eclipse series which began on 2512 BCE July 27 and ended on 961 BCE February 13. The duration of Saros series 7 was 1550.6 years, and it contained 87 lunar eclipses.
As of 2006, in our solar system, eight of the bodies orbiting the Sun are considered to be planets.

Chemistry

The atomic number of oxygen.
The number of allotropes of carbon.
The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.
The maximum number of electrons that can occupy a valence shell.
The red pigment Lycopene consits 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 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

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.
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 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.
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 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.

As a lucky or unlucky number

Eight (八; accounting 捌; pinyin bā) is considered a lucky number in Chinese culture because it sounds like the word "prosper" or "wealth" (發(T) 发(S); Pinyin: fā).
In numerology, 8 is the number of building, and in some theories, also the number of destruction.

In astrology

In Astrology, Scorpio is the 8th astrological sign of the Zodiac
In the middle ages, 8 was the number of "unmoving" stars in the sky, and symbolized the perfectioning of incoming planetary energy

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 (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. 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.

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.

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.

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 measurement

In liquid measurement (US customary units), there are eight fluid ounces in a cup, eight pints in a gallon and eight tablespoonfuls in a gill.
There are eight furlongs in a mile.
The clove, an old English unit of weight, was equal to eight pounds when measuring cheese.
An eight may be an article of clothing of the eighth size.

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
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.

In other fields

File:Battlestar Galactica 1x12 Number Eights.jpg

Cylon Model Number Eight

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.
8 is the official number of the Bishop James Madison Society, a secret society at the College of William and Mary.
There are Eight Principles of Yong in Chinese calligraphy
8 is one of The Numbers - 4, 8, 15, 16, 23, and 42 - featured in Lost.
In Stargate SG-1 and Stargate Atlantis, dialing an 8-chevron address will open a wormhole to another galaxy.
In Battlestar Galactica, Number Eight is a Cylon portrayed by Grace Park.
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.

References

The Octonions John C Baez

^ 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

External links

Flickr 8, the infinite beauty of - photo group
8by8 an art community based on the geometry of 8

[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

[1]