8 (number)

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789
−1 0 1 2 3 4 5 6 7 8 9
Cardinaleight
Ordinal8th
(eighth)
Factorization23
Divisors1, 2, 4, 8
Roman numeralVIII
Roman numeral (unicode)Ⅷ, ⅷ
Greek prefixocta-/oct-
Latin prefixocto-/oct-
Binary10002
Ternary223
Quaternary204
Quinary135
Senary126
Octal108
Duodecimal812
Hexadecimal816
Vigesimal820
Base 36836
Greekη (or Η)
Arabic٨,8
Urdu۸
Amharic
Bengali
Chinese numeral八,捌
Devanāgarī
Kannada
Telugu
Tamil
Hebrewח (Het)
Hebrewשמונה (shmoneh)
Khmer
Korean
Thai
 
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"8th", "Eight" and "Eighth" redirect here. For other uses see 8 (disambiguation)
789
−1 0 1 2 3 4 5 6 7 8 9
Cardinaleight
Ordinal8th
(eighth)
Factorization23
Divisors1, 2, 4, 8
Roman numeralVIII
Roman numeral (unicode)Ⅷ, ⅷ
Greek prefixocta-/oct-
Latin prefixocto-/oct-
Binary10002
Ternary223
Quaternary204
Quinary135
Senary126
Octal108
Duodecimal812
Hexadecimal816
Vigesimal820
Base 36836
Greekη (or Η)
Arabic٨,8
Urdu۸
Amharic
Bengali
Chinese numeral八,捌
Devanāgarī
Kannada
Telugu
Tamil
Hebrewח (Het)
Hebrewשמונה (shmoneh)
Khmer
Korean
Thai

8 (eight /ˈt/) is the natural number following 7 and preceding 9. It is the root word of two other numbers: eighteen (eight and ten) and eighty (eight tens). The word is derived from Middle English eighte.

In mathematics[edit]

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 2^3 (two cubed), and is the first number of the form p^3, 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 ;(2^x), 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.[1]

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.

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.

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 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.

In numeral systems[edit]

BaseNumeral systemRepresentation
2binary1000
3ternary22
4quaternary20
5quinary13
6senary12
7septenary11
8octal10
over 8 (decimal, hexadecimal)8

In culture[edit]

Evolution of the glyph[edit]

Evo8glyph.svg

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.[3]

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in TextFigs148.svg.

In science[edit]

Physics[edit]

Astronomy[edit]

Chemistry[edit]

Geology[edit]

Biology[edit]

Architecture and engineering[edit]

In religion[edit]

Buddhism
The 8-spoked Dharmacakra represents the Noble Eightfold Path
Judaism
Christianity
Islam
Other

In superstition and divination[edit]

As a lucky number[edit]

In astrology[edit]

In music and dance[edit]

In film and television[edit]

8 Guys is a 2003 short film written and directed by Dane Cook

In sports and other games[edit]

8 ball icon.svg

In technology[edit]

Seven-segment 8.svg

In measurement[edit]

In foods[edit]

In literature[edit]

In slang[edit]

In other fields[edit]

Four playing cards showing the "8" of all four suits

See also[edit]

References[edit]

  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 88
  2. ^ Ang, Swee Hoon (1997). "Chinese consumers’ perception of alpha-numeric brand names". Journal of Consumer Marketing 14 (3): 220–233. doi:10.1108/07363769710166800. 
  3. ^ 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
  4. ^ "Life Application New Testament Commentary", Bruce B. Barton. Tyndale House Publishers, Inc., 2001. ISBN 0-8423-7066-8, ISBN 978-0-8423-7066-0. p. 1257
  5. ^ Steven C. Bourassa, Vincent S. Peng (1999). "Hedonic Prices and House Numbers: The Influence of Feng Shui". International Real Estate Review 2 (1): 79–93. 
  6. ^ "Patriot games: China makes its point with greatest show" by Richard Williams, The Guardian, published 9 August 2008
  7. ^ Barney's burp song
  8. ^ A to Z Encyclopaedia of Ice Hockey
  9. ^ urban dictionary
  10. ^ psilocybin mushrooms
  11. ^ http://www.thegooddrugsguide.com/cocaine/faq.htm
  12. ^ , Targ8 your search engine

External links[edit]