8 (number) Information & 8 (number) Links at HealthHaven.com

8
	−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	8; eight
Ordinal	8th; eighth
Numeral system	octal
Factorization	23
Divisors	1, 2, 4, 8
Roman numeral	VIII
Roman numeral (Unicode)	Ⅷ, ⅷ
Arabic	٨
Amharic	፰
Bengali	৮
Chinese numeral	八，捌
Devanāgarī	८
Hebrew	ח (Het)
Hebrew	שמונה (shmoneh)
Khmer	៨
Korean	팔
Thai	๘
prefixes	octa-/oct- (from Greek) octo-/oct- (from Latin)
Binary	1000
Octal	10
Duodecimal	8
Hexadecimal	8

For other uses, see 8 (disambiguation).

Look up eight in Wiktionary, the free dictionary.

8 (eight) 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 of two other numbers: eighteen (eight and ten) and eighty (eight tens). Linguistically, it is derived from Middle English eighte.

[edit] In 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 $23$ (two cubed), and is the first number of the form $p 3$ . 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) 8.

All powers of 2 ;( $2 x$ ), have an aliquot sum of one less than themselves.

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 Fibonacci number that is a perfect cube.^[1]

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 verticies.

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 $O(\infty)$ is the direct limit of the inclusions of real orthogonal groups $O(1)\hookrightarrow O(2)\hookrightarrow\ldots\hookrightarrow O(k)\hookrightarrow\ldots$ then $\pi_{k+8}(O(\infty))\cong\pi_{k}(O(\infty))$ . Clifford algebras also display a periodicity of 8. For example the algebra $C l (p + 8, q)$ is isomorphic to the algebra of 16 by 16 matrices with entries in $C l (p, q)$ . 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 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.

[edit] In numeral systems

Base	Numeral system
2	binary	1000 (number)
3	ternary	22 (number)
4	quaternary	20 (number)
5	quinary	13 (number)
6	senary	12 (number)
7	septenary	11 (number)
8	octal	10 (number)
over 8 (decimal, hexadecimal)		8 (number)

[edit] 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.^[2]

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in . The "1" and "4" are old-style figures; the "8" is the same height in both old-style and modern figures. 1234567890 are all the same height; they are modern figures.

[edit] See also

Mathematics portal

[edit] References

^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88
^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.68

[edit] External links

My Favorite Numbers: 8, John C Baez
The Octonions, John C Baez
8by8, an art community based on the geometry of 8

[0] Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88

[1] Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.68

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