Proto-Germanic *ahto is a direct continuation of Proto-Indo-European *oḱtṓ(w)-, and as such cognate with Greek ὀκτώ and Latin octo-, both of which stems are reflected by the English prefix oct(o)-, as in the ordinal adjective octaval or octavary, the distributive adjective is octonary)
(the adjective octuple (Latin octu-plus) may also be used as a noun, meaning “a set of eight items”
(the diminutive octuplet is mostly used to refer to 8 sibling delivered in one birth)
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(8 is a composite number, its proper divisors being 1, 2, and 4)
(it is twice 4 or four times 2)
(a power of two, being 23 (two cubed), and is the first number of the form p3, p being an integer greater than 1)
the first number which is neither prime nor semiprime.
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.
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.
the only nonzero perfect power that is one less than another perfect power, by Mihăilescu’s Theorem.
the order of the smallest non-abelian group all of whose subgroups are normal.
the dimension of the octonions and is the highest possible dimension of a normed division algebra.
the first number to be the aliquot sum of two numbers other than itself; the discrete biprime 10, and the square number 49.
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. All powers of 2 (2x), have an aliquot sum of one less than themselves.
A number is divisible by 8 if its last 3 digits, when written in decimal, are also divisible by 8, or its last 3 digits are 0 when written in binary.
8 and 9 form a Ruth–Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.
There are a total of eight convex deltahedra.
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.
A cube has eight vertices.
Sphenic numbers always have exactly eight divisors.
The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example, if O(∞) is the direct limit of the inclusions of real orthogonal groups
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 spin group Spin(8) 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 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)
