8 (number)

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Cardinal	8 eight
Ordinal	8th eighth
Numeral system	octal
Factorization	$23$
Divisors	1, 2, 4, 8
Roman numeral	VIII
Roman numeral (Unicode)	Ⅷ, ⅷ
prefixes	octa-/oct- (from Greek) octo-/oct- (from Latin)
Binary	1000
Octal	10
Duodecimal	8
Hexadecimal	8
Hebrew	ח (Het)

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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).

[edit] In mathematics

It is a composite number, its proper divisors being 1, 2, and 4. Eight is a power of two, being 2³, or two cubed.

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 $C l (p + 8, q)$ is isomorphic to the algebra of 16 by 16 matrices with entries in $C l (p, q)$ . 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 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.

[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	$1.\overline{3}$	$1.\overline{1}4285\overline{7}$	1	$0.\overline{8}$	0.8		$0.\overline{7}\overline{2}$	$0.\overline{6}$	$0.\overline{6}1538\overline{4}$	$0.\overline{5}7142\overline{8}$	$0.5\overline{3}$
$x \div 8$	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
$8 ^ x\,$	8	64	512	4096	32768	262144	2097152	16777216	134217728	1073741824		8589934592	68719476736
$x ^ 8\,$	1	256	6561	65536	390625	1679616	5764801	16777216	43046721	100000000		214358881	429981696

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} \$

[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.

In fonts with text figures, eight usually has an ascender, for example, .

[edit] In science

The atomic number of oxygen.
The number of allotropes of carbon.
In physics, the second magic number.
In particle physics, the eightfold way is used to classify sub-atomic particles.
All spiders, and more generally all arachnids, have eight legs. An octopus has eight tentacles
Timothy Leary identified a hierarchy of eight levels of consciousness
The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.

[edit] 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.

[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
In Scientology, there are 8 dynamics of life. The eighth dynamic represents the Infinity, or God
In Christianity, it is allegoric to christ's sacrifice on the cross and is the number of Beatitudes.

[edit] In superstition and divination

In tarot, card No. 8 is "Strength"
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, formal writing 捌, pinyin bā) is considered a lucky number in Chinese culture because it sounds like the word "prosper" or "wealth" (發 Pinyin: fā)
In numerology, 8 is the number of building, and in some theories, also the number of destruction

[edit] 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

[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 musicians in an octet
Songs with the number eight in their title include the Byrds's Eight Miles High and the Beatles' Eight Days a Week
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 "Twelve Days of Christmas" carol
Using hyperbole, the Beatles sang about loving their addressee "Eight Days a Week". Also from music is the 8-track cartridge
8 (Arvingarna album) - An album by Swedish "dansband" Arvingarna
"8," a song by Sunny Day Real Estate from their 1995 album Sunny Day Real Estate

[edit] In sports

In chess, each side has eight pawns; see also Eight queens puzzle
In rugby union the number eight central back row position wears the 8 shirt
In the Nextel Cup series, 8 is Dale Earnhardt Jr.'s car number
In baseball, eight represents the center fielder's position
Eight ball billiards is played with 15 balls; the black ball numbered 8 being the 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
The retired numbers of former baseball players Yogi Berra, Willie Stargell, Carl Yastrzemski, Joe Morgan, Gary Carter, and Cal Ripken, Jr.
The number of Russian hockey player and current member of the NHL's Washington Capitals, Alexander Ovechkin
In Rowing an eight refers to a sweep oar boat with eight rowers plus a coxswain.
The shirt number of Steven Gerrard who plays for Liverpool FC
The shirt number of Frank Lampard when playing for the England National Football Team and Chelsea FC, his club.
The jersey number of Hall of Fame quarterbacks Troy Aikman and Steve Young
The shirt number of Hristo Stoitchkov who played for FC Barcelona
The jersey number of Kobe Bryant from 1996-2006 (now is #24).
The record number of goals that Brighton & Hove Albion FC have scored at the Withdean Stadium - beating Northwich Victoria in the First Round of the FA Cup on 11 November 2006.

[edit] In technology

Many (mostly historic) computer architectures are eight-bit, among them the Nintendo Entertainment System
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 and N
There are eight bits in a byte

[edit] In measurement

In liquid measurement (U.S. customary units), there are 8 fluid ounces in a cup, 8 pints in a gallon, and 8 tablespoons in a gill
There are 8 furlongs in a mile

[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 who will be king

[edit] In slang

An Eighth is a common measurement of high grade 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 "congratul8ons" 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.

[edit] In other fields

International maritime signal flag for 8

The ordinal adjective is octonary
Eight babies delivered in one birth are called octuplets. The first set of eight surviving babies, the Louis-Chukwu Octuplets, were born in 1998
October was the eighth month in the Roman calendar; currently August is the eighth month

The number 8

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, repeated 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 one of the "Lost Numbers" on the television show, Lost, along with 4, 15, 16, 23, and 42

[edit] Historical years

8 A.D., 8 B.C., 1908, 2008, etc.

[edit] Reference

The Octonions John C Baez

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Category: Integers

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