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Eight

هشت


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(Wikipedia) - 8 (number)   (Redirected from Eight) "8th", "Eight" and "Eighth" redirect here. For other uses see 8 (disambiguation)
This article may be in need of reorganization to comply with Wikipedia's layout guidelines. Please help by editing the article to make improvements to the overall structure. (April 2012)
← 7 8 9 →
−1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal eight Ordinal 8th (eighth) Factorization 23 Divisors 1, 2, 4, 8 Roman numeral VIII Roman numeral (unicode) Ⅷ, ⅷ Greek prefix octa-/oct- Latin prefix octo-/oct- Binary 10002 Ternary 223 Quaternary 204 Quinary 135 Senary 126 Octal 108 Duodecimal 812 Hexadecimal 816 Vigesimal 820 Base 36 836 Greek η (or Η) Arabic ٨,8 Urdu Amharic ፰ Bengali ৮ Chinese numeral 八,捌 Devanāgarī ८ Kannada ೮ Telugu ౮ Tamil ௮ Hebrew ח (Het) Hebrew שמונה (shmoneh) Khmer ៨ Korean 팔 Thai ๘

8 (eight /ˈeɪt/) is the natural number following 7 and preceding 9. The SI prefix for 10008 is yotta (Y), and for its reciprocal, yocto (y). It is the root word of two other numbers: eighteen (eight and ten) and eighty (eight tens). Linguistically, it is derived from Middle English eighte, and is presumably related to the French huit.

ContentsIn mathematics

8 is a composite number, its proper divisors being 1, 2, and 4. It is twice 4 or four times 2. Eight is a power of two, being (two cubed), and is the first number of the form , 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 3 bits. 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.

8 is the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem.

8 is the order of the smallest non-abelian group all of whose subgroups are normal.

8 and 9 form a Ruth–Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

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.

8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra.

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.

The spin group 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.

In numeral systems Base Numeral system Representation
2 binary 1000
3 ternary 22
4 quaternary 20
5 quinary 13
6 senary 12
7 septenary 11
8 octal 10
over 8 (decimal, hexadecimal) 8
In culture Evolution of the glyph

In the beginning, various groups in India wrote eight more or less in one stroke as a curve that looks like an uppercase H with the bottom half of the left line and the upper half of the right line removed. At one point this glyph came close to looking like our modern five. With the western Ghubar Arabs, the similarity of the glyph to five was banished by connecting the beginning and the end of stroke together, and it was only a matter of the Europeans rounding the glyph that led to our modern eight.

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in .

In science Physics Astronomy Chemistry Geology Biology Architecture and engineering In religionBuddhismThe 8-spoked Dharmacakra represents the Noble Eightfold Path JudaismChristianityIslamOther In superstition and divination As a lucky number In astrology In music and dance In books In film and television In sports and other games In technology In measurement In foods In literature In slang In other fieldsNATO signal flag for 8Four playing cards showing the "8" of all four suits

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