This same principle is found in Finnic *kakte-ksa, which conveys a meaning of "two before (ten)". The Turkic words for "eight" are from a Proto-Turkic stem *sekiz, which has been suggested as originating as a negation of eki "two", as in "without two fingers" (i.e., "two short of ten two fingers are not being held up") It has been argued that, as the cardinal number 7 is the highest number of item that can universally be cognitively processed as a single set, the etymology of the numeral eight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar. The Chinese numeral, written 八 ( Mandarin: bā Cantonese: baat), is from Old Chinese *priāt-, ultimately from Sino-Tibetan b-r-gyat or b-g-ryat which also yielded Tibetan brgyat. The Semitic numeral is based on a root *θmn-, whence Akkadian smn-, Arabic ṯmn-, Hebrew šmn- etc. 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 eight siblings delivered in one birth. 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. List of basic calculations MultiplicationĮnglish eight, from Old English eahta, æhta, Proto-Germanic *ahto Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something. Even positive definite unimodular lattices exist only in dimensions divisible by 8.Ī figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating. The lowest-dimensional even unimodular lattice is the 8-dimensional E 8 lattice. 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.
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