VIII 

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 八，捌
Devanāgarī ८
Hebrew ח (Het)
Hebrew שמונה (shmoneh)
Khmer ៨
Korean 팔
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). It is the root of two other numbers: eighteen (eight and ten) and eighty (eight tens). Linguistically, it is derived from Middle English eighte.

Contents

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 23 (two cubed), and is the first number of the form p3. 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 ;(2x), 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.1

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
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} \

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.2

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in Image:TextFigs148.svg. 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

Astronomy

Chemistry

Geology

Biology

Architecture and engineering

In religion

Buddhism
Judeo-Christianity
Other

In superstition and divination

As a lucky or unlucky number

In astrology

In music and dance

In sports and other games

In football, the number 8 has historically been the number of the Central Midfielder. 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.

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.

It is the retired jersey number of NHL player Cam Neely.citation needed

In technology

In measurement

In foods

In literature

In slang

In other fields

International maritime signal flag for 8
Four playing cards showing the "8" of all four suits

See also

Mathematics portal

References

  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88
  2. ^ 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
  3. ^ [1]
  4. ^ [2]
  5. ^ [3]

External links