trivia: date=February 2009

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 $O(\backslash infty)$ is the direct limit of the inclusions of real orthogonal groups $O(1)\backslash hookrightarrow\; O(2)\backslash hookrightarrow\backslash ldots\backslash hookrightarrow\; O(k)\backslash hookrightarrow\backslash ldots$ then $\backslash pi\_\{k+8\}(O(\backslash infty))\backslash cong\backslash pi\_\{k\}(O(\backslash infty))$. 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.