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When rolling two standard six-sided dice, seven has a 6 in 36 (or 1/6) probability of being rolled (1–6, 6–1, 2–5, 5–2, 3–4, or 4–3), the greatest of any number.
, p being an integer greater than 1. 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)
All powers of 2 ;(
), have an aliquot sum of one less than themselves.
A number is divisible by 8 if its last 3 digits are also divisible by 8.
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 3bits. 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 positive Fibonacci number, aside from 1, that is a perfect cube.[1]
The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example if
is the direct limit of the inclusions of real orthogonal groups
then
. Clifford algebras also display a periodicity of 8. For example the algebra
is isomorphic to the algebra of 16 by 16 matrices with entries in
. 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.
is the unique such group that exhibits the phenomenon of triality.
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 geometricshape, 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.
It also is a number in the Fibonacci sequence 1,1,2,3,5,8,13,21