8


8 is the natural number following 7 and preceding 9.

In mathematics

8 is:
A 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.
There are a total of eight convex deltahedra.
A polygon with eight sides is an octagon. Figurate numbers representing octagons 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
then
Clifford algebras also display a periodicity of 8. For example, the algebra Cl is isomorphic to the algebra of 16 by 16 matrices with entries in Cl. 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 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 lattices 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.

List of basic calculations

Division123456789101112131415
8 ÷ x842.21.61.1.10.0.80.0.0.0.0.5
x ÷ 80.1250.250.3750.50.6250.750.87511.1251.251.3751.51.6251.751.875

Exponentiation12345678910111213
88645124096327682621442097152167772161342177281073741824858993459268719476736549755813888
x1256656165536390625167961657648011677721643046721100000000214358881429981696815730721

Etymology

English eight, from Old English eahta, æhta, Proto-Germanic *ahto
is a direct continuation of Proto-Indo-European :wikt:Appendix:Proto-Indo-European/oḱtṓw|*oḱtṓ-, and as such cognate with Greek ὀκτώ and Latin octo-, both of which stems are reflected by the English prefix :wikt:oct-|oct-, as in the ordinal adjective octaval or octavary, the distributive adjective is octonary.
The adjective octuple 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.
The Semitic numeral is based on a root *θmn-, whence Akkadian smn-, Arabic ṯmn-, Hebrew šmn- etc.
The Chinese numeral, written 八, is from Old Chinese *priāt-, ultimately from Sino-Tibetan :wikt:Appendix:Proto-Sino-Tibetan/b-r-gjat ~ b-g-rjat|b-r-gyat or b-g-ryat which also yielded Tibetan :wikt:བརྒྱད|brgyat.
It has been argued that, as the cardinal number 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 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" ;
this same principle is found in Finnic :wikt:Appendix:Proto-Finnic/kakteksa|*kakte-ksa, which conveys a meaning of "two before ". The Proto-Indo-European reconstruction :wikt:Appendix:Proto-Indo-European/oḱtṓw|*oḱtṓ- itself has been argued as representing an old dual, which would correspond to an original meaning of "twice four".
Proponents of this "quaternary hypothesis" adduce the numeral , which might be built on the stem new-, meaning "new".

Glyph

The modern 8 glyph, like all modern Arabic numerals originates with the Brahmi numerals.
The Brahmi numeral for eight by the 1st century was written in one stroke as a curve └┐ looking like an uppercase H with the bottom half of the left line and the upper half of the right line removed.
However the eight glyph used in India in the early centuries of the Common Era developed considerable variation, and in some cases took the shape of a single wedge, which was adopted into the Perso-Arabic tradition as :wikt:٨|٨ ; the alternative curved glyph also existed as a variant in Perso-Arabic tradition, where it came to look similar to our glyph 5.
The numerals as used in Al-Andalus by the 10th century were a distinctive western variant of the glyphs used in the Arabic-speaking world, known as ghubār numerals. In these numerals, the line of the 5-like glyph used in Indian manuscripts for eight came to be formed in ghubār as a closed loop, which was the 8-shape that became adopted into European use in the 10th century.
Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in.
The infinity symbol ∞, described as a "sideways figure eight" is unrelated to the 8 glyph in origin; it is first used in the 17th century, and it may be derived from the Roman numeral for "one thousand" CIƆ, or alternatively from the final Greek letter, ω.
The numeral eight in Greek numerals, developed in Classical Greece by the 5th century BC, was written as Η, the eighth letter of the Greek alphabet.
The Chinese numeral eight is written in two strokes, :wikt:八; the glyph is also the 12th Kangxi radical.

In science

Physics

Architecture

Hinduism

"Maha-lakshmi, Dhana-lakshmi, Dhanya-lakshmi, Gaja-lakshmi,
Santana-lakshmi, Veera-lakshmi, Vijaya-lakshmi and Vidhya-lakshmi"