The spin group Spin(8) is the unique such group that exhibits the phenomenon of triality. All of these properties are closely related to the properties of the octonions. 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. For example, the algebra Cl( p + 8, q) is isomorphic to the algebra of 16 by 16 matrices with entries in Cl( p, q). Ĭlifford algebras also display a periodicity of 8. For example, if O(∞) is the direct limit of the inclusions of real orthogonal groups The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. Sphenic numbers always have exactly eight divisors. A cuboctahedron has as faces six equal squares and eight equal regular triangles. Figurate numbers representing octagons (including eight) are called octagonal numbers.Ī polyhedron with eight faces is an octahedron. Ī polygon with eight sides is an octagon. There are a total of eight convex deltahedra.
the first number to be the aliquot sum of two numbers other than itself the discrete biprime 10, and the square number 49.Ī number is divisible by 8 if its last three digits, when written in decimal, are also divisible by 8, or its last three digits are 0 when written in binary.the dimension of the octonions and is the highest possible dimension of a normed division algebra.the order of the smallest non-abelian group all of whose subgroups are normal.the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem.8 is the only positive Fibonacci number, aside from 1, that is a perfect cube. In modern computers, a byte is a grouping of eight bits, also called an octet. In octal, one digit represents three bits. the base of the octal number system, which is mostly used with computers.the first number which is neither prime nor semiprime.a power of two, being 2 3 (two cubed), and is the first number of the form p 3, p being an integer greater than 1.a composite number, its proper divisors being 1, 2, and 4.6.3 In religion, folk belief and divination.Orders placed after 5 PM PST require one additional day processing time. † Custom Design services will require additional processing time. Some licensed character products excluded.
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