Difference between revisions of "8 (number)" - New World Encyclopedia

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:''This article is about the number eight.''
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{| class="infobox" style="width: 20em;"
 
{| class="infobox" style="width: 20em;"
 
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|-
 
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| [[numerical prefix|prefixes]]
 
| [[numerical prefix|prefixes]]
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| [[Wiktionary:octa-|octa-]]/[[Wiktionary:oct-|oct-]] (from [[Greek language|Greek]])
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| octa-/oct- (from [[Greek language|Greek]])
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[[Wiktionary:octo-|octo-]]/[[Wiktionary:oct-|oct-]] (from [[Latin]])
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octo-/oct- (from [[Latin]])
 
|-
 
|-
 
| [[Binary numeral system|Binary]]
 
| [[Binary numeral system|Binary]]
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|}
 
|}
  
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'''8''' ('''eight''') is the [[natural number]] following [[7 (number)|7]] and preceding [[9 (number)|9]]. The [[SI prefix]] for 1000<sup>8</sup> is yotta (Y), and for its reciprocal yocto (y).  
+
'''8''' '''(eight)''' is a [[number]], [[numeral]], and [[glyph]] that represents the number. It is the [[natural number]]<ref>A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.</ref> that follows [[7 (number)|7]] and precedes [[9 (number)|9]]. It is an [[integer]] and a [[cardinal number]], that is, a number that is used for counting.<ref>A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a series.</ref> In addition, it is classified as a [[real number]],<ref>A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real numbers includes rational and irrational numbers, which can be positive, negative, or zero.</ref> distinguishing it from [[imaginary number]]s.
 +
{{toc}}
 +
==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 the modern five. With the western Ghubar Arabs, the similarity of the glyph to five was banished by connecting the beginning and end of the stroke together. After that, the Europeans simply rounded the glyph, leading to the modern eight.<ref>Georges Ifrah, ''The Universal History of Numbers: From Prehistory to the Invention of the Computer'' (New York: Wiley, 2000, ISBN 0471393401), 395.</ref>
 +
 
 +
[[Image:Evo8glyph.svg|400px|left]]
 +
As in most modern [[typeface]]s, in typefaces with [[text figures]] the 8 character usually has an [[ascender]], for example, in [[Image:TextFigs148.svg]]. 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.
  
 
==In mathematics==
 
==In mathematics==
−
8 is a [[composite number]], its [[proper divisor]]s being [[1 (number)|1]], [[2 (number)|2]], and [[4 (number)|4]].
+
Eight is a [[composite number]], its [[proper divisor]]s being [[1 (number)|1]], [[2 (number)|2]], and [[4 (number)|4]].
 
Eight is a [[power of two]], being <math>2^3</math>, or two cubed. It has an [[aliquot sum]] of [[7 (number)|7]]. All powers of 2 have an aliquot sum of one less than themselves.
 
Eight is a [[power of two]], being <math>2^3</math>, or two cubed. It has an [[aliquot sum]] of [[7 (number)|7]]. All powers of 2 have an aliquot sum of one less than themselves.
  
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The number 8 is a [[Fibonacci number]], being [[3 (number)|3]] plus [[5 (number)|5]]. The next Fibonacci number is [[13 (number)|13]].
 
The number 8 is a [[Fibonacci number]], being [[3 (number)|3]] plus [[5 (number)|5]]. The next Fibonacci number is [[13 (number)|13]].
  
−
8 and 9 form a [[Ruth-Aaron pair]] under the second definition in which repeated prime factors are counted as often as they occur.
+
Eight and nine 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 number]]s. A [[polyhedron]] with eight faces is an [[octahedron]].
 
A [[polygon]] with eight sides is an [[octagon]]. [[Figurate numbers]] representing octagons (including eight) are called [[octagonal number]]s. A [[polyhedron]] with eight faces is an [[octahedron]].
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[[Sphenic number]]s always have exactly eight divisors.
 
[[Sphenic number]]s always have exactly eight divisors.
  
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8 is the dimension of the [[octonions]] and is the highest possible dimension of a [[normed division algebra]].
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Eight 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 <math>O(\infty)</math> is the direct limit of the inclusions of real orthogonal groups <math>O(1)\hookrightarrow O(2)\hookrightarrow\ldots\hookrightarrow O(k)\hookrightarrow\ldots</math> then <math>\pi_{k+8}(O(\infty))\cong\pi_{k}(O(\infty))</math>. Clifford algebras also display a periodicity of 8. For example the algebra <math>Cl(p+8,q)</math> is isomorphic to the algebra of 16 by 16 matrices with entries in <math>Cl(p,q)</math>. We also see a period of 8 in the [[K theory]] of spheres and in the [[group representation|representation theory]] of the [[rotation group]]s, 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 number 8 is involved with a number of interesting mathematical phenomena related to the notion of [[Bott periodicity]]. For example if <math>O(\infty)</math> is the direct limit of the inclusions of real orthogonal groups <math>O(1)\hookrightarrow O(2)\hookrightarrow\ldots\hookrightarrow O(k)\hookrightarrow\ldots</math> then <math>\pi_{k+8}(O(\infty))\cong\pi_{k}(O(\infty))</math>. Clifford algebras also display a periodicity of 8. For example the algebra <math>Cl(p+8,q)</math> is isomorphic to the algebra of 16 by 16 matrices with entries in <math>Cl(p,q)</math>. There is also a period of 8 in the [[K theory]] of spheres and in the [[group representation|representation theory]] of the [[rotation group]]s, 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 (Mathematics)|E<sub>8</sub>]] lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8.
 
The lowest dimensional even [[unimodular lattice]] is the 8-dimensional [[E8 (Mathematics)|E<sub>8</sub>]] lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8.
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===List of basic calculations===
 
===List of basic calculations===
  
 +
;Multiplication
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
 
|-
 
|-
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!9
 
!9
 
!10
 
!10
 +
|-
 +
|<math>8 \times x</math>
 +
|'''8'''
 +
|[[16 (number)|16]]
 +
|[[24 (number)|24]]
 +
|[[32 (number)|32]]
 +
|[[40 (number)|40]]
 +
|[[48 (number)|48]]
 +
|[[56 (number)|56]]
 +
|[[64 (number)|64]]
 +
|[[72 (number)|72]]
 +
|[[80 (number)|80]]
 +
|}
 +
{|class="wikitable" style="text-align: center; background: white"
 +
|-
 +
!width="105px"|[[Multiplication]]
 
!11
 
!11
 
!12
 
!12
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!19
 
!19
 
!20
 
!20
−
!width="5px"|
 
−
!21
 
−
!22
 
−
!23
 
−
!24
 
−
!25
 
−
!width="5px"|
 
−
!50
 
−
!100
 
−
!1000
 
 
|-
 
|-
 
|<math>8 \times x</math>
 
|<math>8 \times x</math>
−
|'''8'''
 
−
|[[16 (number)|16]]
 
−
|[[24 (number)|24]]
 
−
|[[32 (number)|32]]
 
−
|[[40 (number)|40]]
 
−
|[[48 (number)|48]]
 
−
|[[56 (number)|56]]
 
−
|[[64 (number)|64]]
 
−
|[[72 (number)|72]]
 
−
|[[80 (number)|80]]
 
 
|[[88 (number)|88]]
 
|[[88 (number)|88]]
 
|[[96 (number)|96]]
 
|[[96 (number)|96]]
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|[[152 (number)|152]]
 
|[[152 (number)|152]]
 
|[[160 (number)|160]]
 
|[[160 (number)|160]]
−
!
+
|}
 +
{|class="wikitable" style="text-align: center; background: white"
 +
|-
 +
!width="105px"|[[Multiplication]]
 +
!21
 +
!22
 +
!23
 +
!24
 +
!25
 +
!width="5px"|
 +
!50
 +
!100
 +
!1000
 +
|-
 +
|<math>8 \times x</math>
 
|[[168 (number)|168]]
 
|[[168 (number)|168]]
 
|[[176 (number)|176]]
 
|[[176 (number)|176]]
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|}
 
|}
  
 +
;Division
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
 
|-
 
|-
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!9
 
!9
 
!10
 
!10
−
!width="5px"|
 
−
!11
 
−
!12
 
−
!13
 
−
!14
 
−
!15
 
 
|-
 
|-
 
|<math>8 \div x</math>
 
|<math>8 \div x</math>
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|<math>0.\overline{8}</math>
 
|<math>0.\overline{8}</math>
 
|[[0 (number)|0]].8
 
|[[0 (number)|0]].8
−
!
 
−
|<math>0.\overline{72}</math>
 
−
|<math>0.\overline{6}</math>
 
−
|<math>0.\overline{615384}</math>
 
−
|<math>0.\overline{571428}</math>
 
−
|<math>0.5\overline{3}</math>
 
 
|-
 
|-
 
|<math>x \div 8</math>
 
|<math>x \div 8</math>
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|1.125
 
|1.125
 
|1.25
 
|1.25
−
!
+
|}
 +
{|class="wikitable" style="text-align: center; background: white"
 +
|-
 +
!width="105px"|[[Division (mathematics)|Division]]
 +
!11
 +
!12
 +
!13
 +
!14
 +
!15
 +
|-
 +
|<math>8 \div x</math>
 +
|<math>0.\overline{72}</math>
 +
|<math>0.\overline{6}</math>
 +
|<math>0.\overline{615384}</math>
 +
|<math>0.\overline{571428}</math>
 +
|<math>0.5\overline{3}</math>
 +
|-
 +
|<math>x \div 8</math>
 
|1.375
 
|1.375
 
|1.5
 
|1.5
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|}
 
|}
  
 +
;Exponentiation
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
 
|-
 
|-
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!9
 
!9
 
!10
 
!10
−
!width="5px"|
 
−
!11
 
−
!12
 
−
!13
 
 
|-
 
|-
 
|<math>8 ^ x\,</math>
 
|<math>8 ^ x\,</math>
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|134217728
 
|134217728
 
|1073741824
 
|1073741824
−
!
 
−
|8589934592
 
−
|68719476736
 
−
|549755813888
 
 
|-
 
|-
 
|<math>x ^ 8\,</math>
 
|<math>x ^ 8\,</math>
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|43046721
 
|43046721
 
|[[100000000 (number)|100000000]]
 
|[[100000000 (number)|100000000]]
−
!
 
−
|214358881
 
−
|429981696
 
−
|815730721
 
 
|}
 
|}
−
 
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
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!rowspan="2" width="105px"|[[Radix]]
 
−
!1
 
−
!5
 
−
!10
 
−
!15
 
−
!20
 
−
!25
 
−
!30
 
−
<!--
 
−
!35
 
−
—>
 
−
!40
 
−
<!--
 
−
!45
 
−
—>
 
−
!50
 
−
!60
 
−
!70
 
−
!80
 
−
!90
 
−
!100
 
 
|-
 
|-
−
!110
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!width="105px"|[[Exponentiation]]
−
!120
+
!11
−
!130
+
!12
−
!140
+
!13
−
!150
 
−
<!--
 
−
!160
 
−
!170
 
−
!180
 
−
!190
 
−
—>
 
−
!200
 
−
!250
 
−
!500
 
−
!1000
 
−
!10000
 
−
!100000
 
−
!1000000
 
−
|
 
−
|
 
 
|-
 
|-
−
|rowspan="2"|<math>x_{8} \ </math>
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|<math>8 ^ x\,</math>
−
|1
+
|8589934592
−
|5
+
|68719476736
−
|<math>12_{8} \ </math>
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|549755813888
−
|<math>17_{8} \ </math>
 
−
|<math>24_{8} \ </math>
 
−
|<math>31_{8} \ </math>
 
−
|<math>36_{8} \ </math>
 
−
<!--
 
−
|<math>32_{11} \ </math>
 
−
—>
 
−
|<math>50_{8} \ </math>
 
−
<!--
 
−
|<math>41_{11} \ </math>
 
−
—>
 
−
|<math>62_{8} \ </math>
 
−
|<math>74_{8} \ </math>
 
−
|<math>106_{8} \ </math>
 
−
|<math>120_{8} \ </math>
 
−
|<math>132_{8} \ </math>
 
−
|<math>144_{8} \ </math>
 
 
|-
 
|-
−
|<math>156_{8} \ </math>
+
|<math>x ^ 8\,</math>
−
|<math>170_{8} \ </math>
+
|214358881
−
|<math>202_{8} \ </math>
+
|429981696
−
|<math>214_{8} \ </math>
+
|815730721
−
|<math>226_{8} \ </math>
 
−
<!--
 
−
|<math>136_{11} \ </math>
 
−
|<math>145_{11} \ </math>
 
−
|<math>154_{11} \ </math>
 
−
|<math>163_{11} \ </math>
 
−
—>
 
−
|<math>310_{8} \ </math>
 
−
|<math>372_{8} \ </math>
 
−
|<math>764_{8} \ </math>
 
−
|<math>1750_{8} \ </math>
 
−
|<math>23420_{8} \ </math>
 
−
|<math>303240_{8} \ </math>
 
−
|<math>3641100_{8} \ </math>
 
 
|}
 
|}
−
 
−
==Evolution of the glyph==
 
−
 
−
[[Image:Evo8glyph.svg|200px]]
 
−
 
−
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.<ref>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</ref>
 
−
 
−
Just as in most modern [[typeface]]s, in typefaces with [[text figures]] the 8 character usually has an [[ascender]], as, for example, in [[Image:TextFigs148.svg]]. 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.
 
  
 
==In science==
 
==In science==
−
 
 
===Physics===
 
===Physics===
−
* In nuclear physics, the second [[Magic number (physics)|magic number]].
+
* In nuclear physics, 8 is the second [[Magic number (physics)|magic number]]; the first one being 2. A magic number (in this case) is the number of [[nucleon]]s ([[proton]]s and [[neutron]]s) in the atomic nucleus, such that they are arranged into complete shells in the nucleus.<ref>Xavier Borg, [http://www.mysearch.org.uk/website1/pdf/676.11.Borg.pdf Magic numbers derived from a variable phase nuclear model,] ''The General Science Journal.'' Retrieved October 7, 2022.</ref>
−
* In [[particle physics]], the [[eightfold way (physics)|eightfold way]] is used to classify sub-atomic particles.
+
* In [[particle physics]], the [[eightfold way (physics)|eightfold way]] is used to classify subatomic particles.
  
 
===Astronomy===
 
===Astronomy===
−
* [[Messier object]] [[Lagoon Nebula|M8]], a magnitude 5.0 [[nebula]] in the [[constellation]] of [[Sagittarius (constellation)|Sagittarius]].
+
* The [[Saros]] number of the [[solar eclipse]] series that began on March 7, 2579 B.C.E. and ended on April 26, 1281 B.C.E. The duration of Saros series 8 was 1298.17 years, and it contained 73 solar eclipses.<ref>NASA, [https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros008.html Saros Series 8] Saros Series Catalog of Solar Eclipses. Retrieved October 7, 2022.</ref>
−
* The [[New General Catalogue]] object<ref>[http://www.ngcic.org/ NGC/IC Project] Retrieved July 28, 2008.</ref> [[NGC 8]], a double star in the constellation [[Pegasus (constellation)|Pegasus]].
+
* The Saros number of the [[lunar eclipse]] series that began on August 8, 2494 B.C.E. and ended on February 13, 961 B.C.E. The duration of Saros series 8 was 1532.56 years, and it contained 86 lunar eclipses.<ref>NASA, [https://eclipse.gsfc.nasa.gov/LEsaros/LEsaros008.html Saros Series 8] Catalog of Lunar Eclipse Saros Series. Retrieved October 7, 2022.</ref>
−
* The [[Saros]] number<ref>[http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros0-180.html Solar Eclipses of Saros 0 to 180.] NASA Eclipse Web Site. Retrieved July 28, 2008.</ref> of the [[solar eclipse]] series which began on [[2579 B.C.E.|2579]] [[Common Era|BCE]] March 7 and ended on [[1281 B.C.E..|1281]] BCE April 26. The duration of Saros series 8 was 1298.1 years, and it contained 73 solar eclipses.
+
* Eight of the bodies orbiting the [[Sun]] are considered [[planet]]s in the [[Solar System]].
−
* The Saros number<ref>[http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html Lunar Eclipses of Saros Series 1 to 175.] NASA Eclipse Web Site. Retrieved July 28, 2008.</ref> of the [[lunar eclipse]] series which began on [[2512 B.C.E.|2512]] BCE July 27 and ended on [[961 B.C.E..|961]] BCE February 13. The duration of Saros series 7 was 1550.6 years, and it contained 87 lunar eclipses.
 
−
* As of 2006, in our [[solar system]], eight of the bodies orbiting the Sun are considered to be [[planet]]s.
 
  
 
===Chemistry===
 
===Chemistry===
−
* The [[atomic number]] of [[oxygen]].
+
* Eight is the [[atomic number]] of [[oxygen]].
−
* The number of [[allotropes of carbon]].
 
 
* The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.
 
* The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.
−
* The maximum number of electrons that can occupy a [[valence shell]].
+
* In the [[electronic configuration]]s of atoms, eight is usually the maximum number of electrons that can occupy a [[valence shell]].
−
* The red pigment [[Lycopene]] consits of eight [[isoprene]] units.
+
* The red pigment [[lycopene]] consists of eight [[isoprene]] units.
  
 
===Biology===
 
===Biology===
 
* There are eight known [[B vitamins]] that play important roles in [[Cell (biology)|cell]] [[metabolism]].
 
* There are eight known [[B vitamins]] that play important roles in [[Cell (biology)|cell]] [[metabolism]].
−
* All [[spider]]s, and more generally all [[arachnid]]s, have eight legs. An [[octopus]] has eight tentacles.
+
* All [[spider]]s, and more generally all [[arachnid]]s, have eight legs.
−
* [[Timothy Leary]] identified a [[8-Circuit Consciousness|hierarchy of eight levels of consciousness]]
+
* An [[octopus]] has eight tentacles.
−
* In the human adult dentition there are 8 teeth in each quadrant. The 8th tooth is the so called the wisdom tooth.
+
* In the adult human dentition, there are 8 teeth in each quadrant. The eighth tooth is the so-called [[wisdom tooth]].
  
−
==Architecture and engineering==
+
===Measurement===
−
* Various types of buildings are usually eight-sided (octagonal), such as single-roomed [[gazebo]]s and multi-roomed [[pagoda]]s (descended from stupas; see religion section below).
+
* The [[SI prefix]] for 1000<sup>8</sup> is yotta (Y), and that for its reciprocal is yocto (y).
 +
* In liquid measurement ([[US customary units]]), there are 8 [[fluid ounces]] in a [[Cup (unit)|cup]], 8 [[pint]]s in a [[gallon]], and 8 [[tablespoon]]s in a [[gill (unit)|gill]]
 +
* There are 8 [[furlongs]] in a mile.
  
−
==In religion==
+
==In technology==
−
* The [[Dharmachakra]], a [[Buddhism|Buddhist]] symbol, has eight spokes. The Buddha's principal teaching—the Four Noble Truths—ramifies as the [[Noble Eightfold Path]]. In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas (Manjushri, Vajrapani, Avalokiteshvara, Maitreya, Kshitigarbha, Nivaranavishkambhi, Akashagarbha, and Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogachara school of thought: consciousness in the five senses, thought-consciousness, self-consciousness and unconsciousness-'consciousness' (alaya-vijñana). The 'irreversible' state of enlightenment, at which point a Bodhisattva goes on 'autopilot', is the Eight Ground or ''bhūmi''. In general, 'eight' seems to be an auspicious number for Buddhists, e.g., the 'eight auspicious symbols' (the jewel-encrusted parasol; the goldfish (always shown as a pair, e.g., the glyph of Pisces); the self-replenishing amphora; the white ''kamala'' lotus-flower; the white conch; the eternal (Celtic-style, infinitely looping) knot; the banner of imperial victory; the eight-spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching). Similarly, [[Buddha's Birthday|Buddha's birthday]] falls on the 8th day of the 4th month of the [[Chinese calendar]].
+
[[Image:Seven-segment 8.svg|50px|right]]
−
* The [[Judaism|Jewish]] religious rite of [[brit milah]] is held on a baby boy's eighth day of life
 
−
* [[Hanukkah]] is an eight-day Jewish holiday that starts on the 25th day of [[Kislev]]
 
−
* [[Sukkot#Shemini Atzeret and Simchat Torah|Shemini Atzeret]] ([[Hebrew language|Hebrew]]: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of [[Sukkot]]
 
  
−
* The [[Eight Immortals]] are Chinese deities
+
* Many (mostly historic) computer architectures are eight-bit, among them the [[Nintendo Entertainment System]]
−
* Members of [[The Church of Jesus Christ of Latter-day Saints]] believe that humans are responsible for their actions by the age of 8. Before that age, children lack sufficient knowledge to commit sin and are therefore exempt from judgment for their actions.
+
* One [[byte]] is eight [[bits]].
 +
* A [[V8 engine]] is an [[internal combustion engine]] with 8 cylinders configured in two banks (rows) of 4 forming a "V" when seen from the end.
  
−
* In [[Christianity]], it is allegoric to:
+
==In religion==
−
** what is beyond time (because the number 7 refers to the days of the week which repeat themselves),
 
−
** and is the number of [[Beatitudes]].
 
−
* In [[Islam]], It is the number of [[Angels]] carrying The Holy [[Throne]] of [[Allah]] in heavens.
 
−
* In [[Neopaganism]], there are eight Sabbats, festivals, seasons, or spokes in the [[Wheel of the Year]].
 
−
* In [[Hinduism]] its the number of wealth , abundance. The Goddess Lakshmi has eightfold forms. There are eight nidhis - seats of wealth.
 
  
−
==In superstition and divination==
+
=== Judaism ===
 +
* The [[Judaism|Jewish]] religious rite of [[brit milah]] is held on a baby boy's eighth day of life.
 +
* [[Hanukkah]] is an eight-day Jewish holiday that starts on the twenty-fifth day of [[Kislev]].
 +
* [[Sukkot#Shemini Atzeret and Simchat Torah|Shemini Atzeret]] ([[Hebrew language|Hebrew]]: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of [[Sukkot]].
  
−
* If each of the [[classical element]]s is assigned a cosmic projection, the resulting number (8) represents them.
+
=== Christianity ===
 +
* Eight is the number of [[Beatitudes]] in Jesus' [[Sermon on the Mount]].
 +
* It is allegoric to what is beyond time (because the number 7 refers to the days of the week which repeat themselves).
 +
* Members of [[The Church of Jesus Christ of Latter-day Saints]] believe that humans are responsible for their actions by the age of 8. Before that age, children lack sufficient knowledge to commit sin and are therefore exempt from judgment for their actions.
  
 +
=== Buddhism ===
 +
* The [[Dharmachakra]], a [[Buddhism|Buddhist]] symbol, has eight spokes. The Buddha's principal teaching—the Four Noble Truths—ramifies as the [[Noble Eightfold Path]].
 +
* In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas (Manjushri, Vajrapani, Avalokiteshvara, Maitreya, Kshitigarbha, Nivaranavishkambhi, Akashagarbha, and Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogachara school of thought: Consciousness in the five senses, thought-consciousness, self-consciousness, and unconsciousness-"consciousness" (alaya-vijñana).
 +
* The "irreversible" state of enlightenment, at which point a Bodhisattva goes on "autopilot," is the Eight Ground or ''bhūmi''.
 +
* In general, "eight" seems to be an auspicious number for Buddhists, such as the "eight auspicious symbols" (the jewel-encrusted parasol; the goldfish (always shown as a pair, for example, the glyph of Pisces); the self-replenishing amphora; the white ''kamala'' lotus-flower; the white conch; the eternal (Celtic-style, infinitely looping) knot; the banner of imperial victory; the eight-spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching).
 +
* [[Buddha's Birthday|Buddha's birthday]] falls on the 8th day of the 4th month of the [[Chinese calendar]].
  
−
===As a lucky or unlucky number===<!-- This section is linked from [[2008 Summer Olympics]] —>
+
=== Other religions ===
−
* Eight ({{lang|zh-Hani|八}}; [[Chinese numbers#Numeral characters|accounting]] {{lang|zh-Hani|捌}}; [[pinyin]] ''bā'') is considered a [[Numbers in Chinese culture|lucky number in Asian culture]] because it sounds like the word "prosper" or "[[wealth]]" ({{lang|zh-Hant|发}}; Pinyin: ''fā''). Additionally, it is considered lucky in Japan because the Chinese numeral character resembles a mountain, specifically [[Fujisan]].
+
* In [[Islam]], eight is the number of [[Angels]] carrying The Holy [[Throne]] of [[Allah]] in heaven.
−
* In [[numerology]], 8 is the number of building, and in some theories, also the number of destruction.
+
* In [[Hinduism]], eight is the number of wealth and abundance. The Goddess Lakshmi has eightfold forms. There are eight nidhis, or seats of wealth.
−
 
+
* In [[Neopaganism]], there are eight Sabbats, festivals, seasons, or spokes in the [[Wheel of the Year]].
−
===In astrology===
+
* The [[Eight Immortals]] are Chinese deities.
−
* In [[Astrology]], [[Scorpius|Scorpio]] is the 8th [[astrological sign]] of the [[Zodiac]]
 
−
* In the [[middle ages]], 8 was the number of "unmoving" stars in the sky, and symbolized the perfectioning of incoming planetary energy
 
  
 
==In music==
 
==In music==
−
* A note played for one-eighth the duration of a whole note is called an eighth note, or [[quaver]]
+
* A note played for one-eighth the duration of a whole note is called an eighth note, or [[quaver]].
−
* An [[octave]], the interval between two [[notes]] with the same letter name (where one has double the frequency of the other), is so called because there are eight notes on a [[Musical scale#Scales in Western music|western scale]] between the two, including the notes themselves
+
* An [[octave]], the interval between two [[notes]] with the same letter name (where one has double the frequency of the other), is so called because there are eight notes on a [[Musical scale#Scales in Western music|western scale]] between the two, including the notes themselves.
−
* There are eight notes in an [[octatonic scale]]
+
* There are eight notes in an [[octatonic scale]].
−
* There are eight musicians in an [[octet]]
+
* There are eight musicians in an [[octet]].
−
* [[Album]]s with the number eight in their title include ''[[8 (Arvingarna album)|8]]'' by the Swedish band Arvingarna and ''The Meaning of 8'' by Minnesota indie rock band [[Cloud Cult]]
+
* The [[Stereo 8|8-track cartridge]] is a musical recording format
−
* [[Dream Theater]]'s eighth album ''[[Octavarium (album)|Octavarium]]'' contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork
 
−
* "Eight maids a-milking" is the gift on the eighth day of Christmas in the carol "[[The Twelve Days of Christmas (song)|The Twelve Days of Christmas]]"
 
−
* The [[Stereo 8|8-track cartridge]] is a musical recording format  
 
−
* "#8" is the stagename of [[Slipknot (band)|Slipknot]] vocalist [[Corey Taylor]]
 
−
* "Too Many Eights" is a song by Athens, Georgia's [[Supercluster (band)]].
 
−
* [[Eight Seconds]], a Canadian musical group popular in the 1980s with their most notable song "Kiss You (When It's Dangerous)"
 
−
* "[[Eight Days a Week (song)|Eight Days a Week]]" is #1 single for the music group [[The Beatles]].
 
  
 
==In sports==
 
==In sports==
  
−
In [[football (soccer)|football]], the number 8 has historically been the number of the Central Midfielder while in [[rugby union]] the number eight central [[Rugby union positions|back row position]] wears the 8 shirt. Similarly in [[baseball]], in its numbering system used to record defensive plays, eight represents the [[center fielder]]'s position. The [[Philadelphia Flyers]] once had a line called the [[Crazy Eights]] with [[Eric Lindros]] at center (88); [[Mark Recchi]] (8); and [[Brent Fedyk]] (18).
+
* In [[football (soccer)|football]], the number 8 has historically been the number of the Central Midfielder.
−
[[Kobe Bryant]] wore this number for most parts of his career.
+
* In [[rugby union]], the central [[Rugby union positions|back row position]] wears the 8 shirt.
−
49ers Quarterback Steve Young wore this number.
+
* In [[baseball]], in its numbering system used to record defensive plays, eight represents the [[center fielder]]'s position.
−
In [[chess]], each side has eight pawns and the board is made of 64 squares arranged in an eight by eight lattice. The [[eight queens puzzle]] is a challenge to arrange eight queens on the board so that none can capture any of the others.
+
* In [[chess]], each side has eight pawns and the board is made of 64 squares arranged in an eight by eight lattice.
 +
* The [[eight queens puzzle]] is a challenge to arrange eight queens on the board so that none can capture any of the others.
 +
* [[Eight ball]] [[billiards]] is played with 15 balls; the black ball numbered 8 being the middle and most important one. [[Magic 8 Ball]] is a randomized process of predicting the future or answering various questions, packaged to resemble this ball and often sold as a fortune-telling device.
 +
* In [[Rowing (sport)|rowing]], an "eight" refers to a sweep oar boat with eight rowers plus a [[coxswain]].
  
−
[[Eight ball]] [[billiards]] is played with 15 balls; the black ball numbered 8 being the middle and most important one. [[Magic 8 Ball]] is a randomized process of predicting the future or answering various questions, packaged to resemble this ball and often sold as a fortune-telling device.
+
==In slang==
−
 
+
* An Eighth is a common measurement of [[cannabis (drug)|marijuana]], meaning an eighth of an [[ounce]].
−
In [[Rowing (sport)|rowing]] an 'eight' refers to a sweep oar boat with eight rowers plus a [[coxswain]].
+
* Referring to the shape of the numeral, eight was represented in [[Bingo (US)|bingo]] slang, before [[political correctness]], as "One Fat Lady." Eighty-eight was "Two Fat Ladies."
−
 
+
* The numeral "8" is sometimes used in writing to represent the syllable "ate," as in writing "H8" for "hate," or "congratul8ions" for "congratulations." [[Avril Lavigne]]'s song "Sk8er Boi" uses this convention in the title. It is also often found on [[vanity plates]]
−
In [[rugby union]], the only position without a proper name is the [[Rugby union positions#8. Number eight|Number 8]], a forward position.
+
* "Section 8" is common U.S. slang for "crazy," based on the [[United States armed forces|U.S. military's]] [[Section 8 (military)|Section 8]] discharge for [[Mental illness|mentally unfit]] personnel.
−
 
+
* In China, "8" is used in chat speak as a term for parting. This is due to the closeness in pronunciation of "8" (bā) and the English word "bye."
−
It is the retired jersey number of [[Baseball Hall of Fame]]  players [[Cal Ripken, Jr.]], [[Joe Morgan]], [[Willie Stargell]], [[Carl Yastrzemski]], and [[Yogi Berra]].
 
−
 
 
−
Ray Fosse, an all-star catcher and gold glove winner in 1970 and 1971, wore '''number 8''' when he played for the Cleveland Indians (1967-1972). [Fosse also played for Cleveland in 1976 and 1977, but wore number 10 in those years.] His name "Ray Fosse" has '''8''' letters. His birthday is April 4 (4 + 4 = '''8'''). His playing height was 6' 2" (6 + 2 = '''8''') and playing weight was 215 lbs. (2 + 1 + 5 = '''8'''). He was drafted by the Cleveland Indians in 1965 as the seventh pick in the first round (7 + 1 = '''8'''). His major league debut was on the '''8th''' (of September, 1967); he batted '''8th''' in the lineup and had '''8''' put-outs as the catcher. In his first year with the Cleveland Indians (1967), the team finished in '''8th''' place. He played with the Cleveland Indians for '''8''' seasons (1967-72 and 1976-77). When Fosse won his second gold glove in 1971, it was the '''8th''' time that a Cleveland Indian won a gold glove. In his first two seasons with Cleveland, he played in '''8''' games. In 1970, he had the only 5 RBI game of his career on May 21 (5 + 2 + 1 = '''8'''). In 1977, he caught the only no hitter of his career (by Dennis Eckersley) on May 30 (5 + 3 + 0 = '''8'''). In 1977, he played in 11 games with the Seattle Mariners—his position was catcher for '''8''' of those games.
 
−
 
 
−
==In technology==
 
−
[[Image:Seven-segment 8.svg|25px|right]]
 
−
* Many (mostly historic) computer architectures are eight-bit, among them the [[Nintendo Entertainment System]]
 
−
* A [[byte]] is eight [[bits]]
 
−
* On most phones, the 8 key is associated with the letters [[T]], [[U]], and [[V]], but on the [[BlackBerry]] it is the key for [[B]] , [[N]], and [[X]].
 
−
* A [[V8 engine]] is an [[internal combustion engine]] with 8 cylinders configured in two banks (rows) of 4 forming a "V" when seen from the end.
 
−
* A figure eight is a type of [[knot]] frequently used by climbers.
 
−
 
 
−
==In measurement==
 
−
* In liquid measurement ([[US customary units]]), there are 8 [[fluid ounces]] in a [[Cup (unit)|cup]], 8 [[pint]]s in a [[gallon]], and 8 [[tablespoon]]s in a [[gill (unit)|gill]]
 
−
* There are 8 [[furlongs]] in a mile
 
−
 
 
−
==In foods==
 
−
* There is a brand of chocolates filled with peppermint-flavoured cream called "After Eight," referring to the time 8 p.m.
 
−
* There are eight vegetables in [[V8 (beverage)|V8]] juice
 
−
* In cooking recipes, there are approximately 8 pinches to a [[teaspoon]]
 
−
 
 
−
==In literature==
 
−
* In [[Terry Pratchett]]'s ''[[Discworld]]'' series, eight is a holy number and is considered taboo. Eight is not safe to be said by wizards on the [[Discworld (world)|Discworld]] and is the number of [[Discworld gods#Bel-Shamharoth|Bel-Shamharoth]]. Also, there are eight days in a Disc week and eight colours in a Disc spectrum, the eighth one being [[Minor Discworld concepts#Octarine|Octarine]]
 
−
* [[Lewis Carroll]]'s poem [[The Hunting of the Snark]] has 8 "fits" (cantos), which is noted in the full name "The Hunting of the Snark - ''An Agony, in Eight Fits''
 
−
* 8 apparitions appear to [[Macbeth]] in Act 4 scene 1 of Shakespeare's Macbeth as representations of the 8 descendants of [[Banquo]]
 
  
−
==In slang==
+
==Miscellany==
−
* An Eighth is a common measurement of [[cannabis (drug)|marijuana]], meaning an eighth of an [[ounce]]
+
[[Image:ICS Eight.svg|right|thumb|350px|[[International maritime signal flag]] for 8]]
−
* Referring to the shape of the numeral, eight was represented in [[Bingo (US)|bingo]] slang, before [[political correctness]], as "One Fat Lady." Eighty-eight was "Two Fat Ladies"
+
[[Image:8 playing cards.jpg|thumb|400px|Four [[playing card]]s showing the "8" of all four suits]]
−
* The numeral "8" is sometimes used in writing to represent the syllable "ate," as in writing "H8" for "hate," or "congratul8ions" for "congratulations." [[Avril Lavigne]]'s song "Sk8er Boi" uses this convention in the title. Often found on [[vanity plates]]
 
−
* "Section 8" is common U.S. slang for "crazy," based on the [[United States armed forces|U.S. military's]] [[Section 8 (military)|Section 8]] discharge for [[Mental illness|mentally unfit]] personnel
 
−
* In [[Colombia]] and [[Venezuela]], "volverse un ocho" (meaning to tie oneself in a figure 8) refers to getting in trouble or contradicting one's self.
 
−
* In China, '8' is used in chat speak as a term for parting. This is due to the closeness in pronunciation of '8' (bā) and the English word 'bye'.
 
−
* Eight is symbolic for lesbian sexual relations.
 
  
−
==In other fields==
 
−
[[Image:ICS Eight.svg|right|thumb|100px|[[International maritime signal flag]] for 8]]
 
−
[[Image:8 playing cards.jpg|thumb|250px|Four [[playing card]]s showing the "8" of all four suits]]
 
−
* 08/08/2008 - [[2008 Summer Olympics|Games of the XXIX Olympiad]] will be celebrated in Beijing, China. Also, it is the official birth date of Jao, whose founding figure will turn [[Number 33|33]].
 
−
* The number of tentacles on an octopus.
 
 
* The ordinal adjective is ''octaval'' or ''octavary''.
 
* The ordinal adjective is ''octaval'' or ''octavary''.
 
* The distributive adjective is ''octonary''.
 
* The distributive adjective is ''octonary''.
−
* Eight babies delivered in one birth are called [[octuplet]]s. The first set of eight surviving babies, the [[Chukwu octuplets]], were born in 1998
+
* In cooking recipes, there are approximately 8 pinches to a [[teaspoon]].
−
* October was the eighth month in the Roman calendar; currently August is the eighth month
+
* A figure-eight [[knot]] is a type of knot frequently used by climbers.
−
* [[I-8]] is the designation of the [[United States|US]] [[interstate highway]] that runs from [[San Diego, California]] to [[Casa Grande, Arizona]]
+
* Various types of buildings are usually eight-sided (octagonal), such as single-roomed [[gazebo]]s and multi-roomed [[pagoda]]s (descended from stupas).
−
* Eight is the number of categories the [[VALS system]] uses to classify consumer groups, and the number of categories used by [[Fallon-McElligott]]'s system for teen marketing
+
* Eight babies delivered in a single birth are called [[octuplet]]s. The first set of eight surviving babies, the [[Chukwu octuplets]], was born in 1998.
−
* [[War of the Eight Princes]], a war in Chinese history
+
* October was the eighth month in the Roman calendar; currently August is the eighth month.
 +
* [[War of the Eight Princes]] was a war in Chinese history
 
* "88" is the abbreviated terminology used by the [[Aryan Brotherhood]] for the [[Nazism|Nazi]] salute, [[Hitler salute|"Heil Hitler"]]—"H" being the eighth letter of the alphabet, twice
 
* "88" is the abbreviated terminology used by the [[Aryan Brotherhood]] for the [[Nazism|Nazi]] salute, [[Hitler salute|"Heil Hitler"]]—"H" being the eighth letter of the alphabet, twice
−
* The silver [[Spanish dollar|piece of eight]] was coined in the [[Spanish Empire]] and moved trade around the world
+
* The silver [[Spanish dollar|piece of eight]] was coined in the [[Spanish Empire]] and moved trade around the world.
−
* There are [[Eight Principles of Yong]] in Chinese calligraphy
+
* There are [[Eight Principles of Yong]] in Chinese calligraphy.
−
* 8 is the number of days one can expect to wait for approval on Devilshire.
+
* Eight ({{lang|zh-Hani|八}}; [[Chinese numbers#Numeral characters|accounting]] {{lang|zh-Hani|捌}}; [[pinyin]] ''bā'') is considered a [[Numbers in Chinese culture|lucky number in Asian culture]] because it sounds like the word "prosper" or "[[wealth]]" ({{lang|zh-Hant|发}}; Pinyin: ''fā''). Additionally, it is considered lucky in Japan because the Chinese numeral character resembles a mountain, specifically [[Fujisan]].
−
* 8 is one of [[Mythology of Lost#The Numbers|The Numbers]] - 4, 8, 15, 16, 23, and 42 - featured in [[Lost]].  
+
* In [[numerology]], 8 is the number of building, and in some theories, also the number of destruction.
−
* In ''[[Stargate SG-1]]'' and ''[[Stargate Atlantis]]'', dialing an 8-chevron address will open a wormhole to another galaxy.
+
* In the [[Middle Ages]], 8 was the number of "unmoving" stars in the sky.
 
* [[8vo]] is shorthand for "octavo," a book size.
 
* [[8vo]] is shorthand for "octavo," a book size.
−
* Eight is an often significant number in [[video games]], particularly older games (8 worlds in [[Super Mario Bros.]], 8 bosses in [[Mega Man]], etc). This is mostly due to logical constraints of the computer systems, and its use in most modern games is an arbitrary tradition.
+
* [[The Eight]]: Eight American painters who exhibited together only once in 1908 in New York City. They joined this exhibition to oppose traditions upheld by the National Academy and help advance modernism in the United States. Five of the eight painters were associated with the [[Ashcan School]]: Robert Henri (1865-1929), George Luks (1867-1933), William Glackens (1870-1938), John Sloan (1871-1951), and Everett Shinn (1876-1953). The others were Maurice Prendergast (1859-1924), Ernest Lawson (1873-1939), and Arthur Bowen Davies (1862-1928).
−
* [[The Eight]] - Eight American painters who exhibited together only once in 1908 in New York City. They joined this exhibition to oppose traditions upheld by the National Academy and help advance modernism in the United States. Five of the eight painters were associated with the [[Ashcan School]]: Robert Henri (1865-1929), George Luks (1867-1933), William Glackens (1870-1938), John Sloan (1871-1951), and Everett Shinn (1876-1953), along with Maurice Prendergast (1859-1924), Ernest Lawson (1873-1939), and Arthur Bowen Davies (1862-1928).
 
  
 
== See also ==
 
== See also ==
−
 
+
* [[Arithmetic]]
 +
* [[Integer]]
 
* [[Number]]
 
* [[Number]]
  
Line 538: Line 436:
  
 
==References==
 
==References==
−
 
+
* Flegg, Graham. ''Numbers: Their History and Meaning.'' Mineola, NY: Dover Publications, 2002. ISBN 0486421651
−
* Flegg, Graham. 2002. ''Numbers: Their History and Meaning.'' Mineola, NY: Dover Publications. ISBN 0486421651.
+
* Higgins, Peter M. ''Number Story: From Counting to Cryptography.'' London: Copernicus, 2008. ISBN 978-1848000001
−
 
+
* Ifrah, Georges. ''The Universal History of Numbers: From Prehistory to the Invention of the Computer.'' Translated by David Bellos et al. New York: Wiley, 2000. ISBN 0471393401
−
* Higgins, Peter M. 2008. ''Number Story: From Counting to Cryptography.'' London: Copernicus. ISBN 978-1848000001.
+
* McLeish, John. ''The Story of Numbers: How Mathematics Has Shaped Civilization.'' New York: Fawcett Columbine, 1994. ISBN 0449909387
−
 
+
* Menninger, Karl. ''Number Words and Number Symbols: A Cultural History of Numbers.'' New York: Dover Publications, 1992. ISBN 0486270963
−
* Ifrah, Georges. 2000. ''The Universal History of Numbers: From Prehistory to the Invention of the Computer.'' Translated by David Bellos et al. New York: Wiley. ISBN 0471393401.
+
* Wells, D. G. ''The Penguin Dictionary of Curious and Interesting Numbers.'' London: Penguin Books, 1998. ISBN 0140261494
−
 
 
−
* McLeish, John. 1994. ''The Story of Numbers: How Mathematics Has Shaped Civilization.'' New York: Fawcett Columbine. ISBN 0449909387.
 
−
 
 
−
* Menninger, Karl. 1992. ''Number Words and Number Symbols: A Cultural History of Numbers.'' New York: Dover Publications. ISBN 0486270963.
 
−
 
 
−
* Wells, D. G. 1998. ''The Penguin Dictionary of Curious and Interesting Numbers.'' Rev. ed. London, UK: Penguin Books. ISBN 0140261494.
 
  
 
==External links==
 
==External links==
 +
All links retrieved June 13, 2023.
  
−
* [http://math.ucr.edu/home/baez/octonions/octonions.html The Octonions] John C Baez
+
* [https://math.ucr.edu/home/baez/octonions/octonions.html The Octonions]. John C. Baez.  
−
* [http://www.flickr.com/groups/297659@N24/ Flickr] 8, the infinite beauty of - photo group
 
−
* [http://www.8by8.net/ 8by8] an art community based on the geometry of 8
 
  
 
[[Category:Physical sciences]]
 
[[Category:Physical sciences]]

Latest revision as of 06:48, 13 June 2023

8

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
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)
Khmer ៨
Thai ๘
prefixes octa-/oct- (from Greek)

octo-/oct- (from Latin)

Binary 1000
Octal 10
Duodecimal 8
Hexadecimal 8

8 (eight) is a number, numeral, and glyph that represents the number. It is the natural number[1] that follows 7 and precedes 9. It is an integer and a cardinal number, that is, a number that is used for counting.[2] In addition, it is classified as a real number,[3] distinguishing it from imaginary numbers.

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 the modern five. With the western Ghubar Arabs, the similarity of the glyph to five was banished by connecting the beginning and end of the stroke together. After that, the Europeans simply rounded the glyph, leading to the modern eight.[4]

Evo8glyph.svg

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

In mathematics

Eight is a composite number, its proper divisors being 1, 2, and 4. Eight is a power of two, being , or two cubed. It has an aliquot sum of 7. All powers of 2 have an aliquot sum of one less than themselves.

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.

Eight and nine 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.

Sphenic numbers always have exactly eight divisors.

Eight 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 . There is also 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

In binary code eight is 1000; in ternary code eight is 22; in quaternary numeral system code eight is 20; in quinary eight is 13; in senary eight is 12; in septenary eight is 11; in octal eight is 10; in novenary code and all codes above (such as decimal and hexadecimal) eight is 8.

A fallen or lying down 8 (∞, the lemniscate) is used to represent infinity in mathematics. This interpretation of 8 may be related to the representation of the caduceus (where two snakes form several figure eights) as stability or balance of opposing forces.

Eight is the number of Thurston model geometries. Eight is not a prime number

E8 has rank 8.

As of 2008, there are only eight known Stern primes.

In numeral systems

Base Numeral system
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

List of basic calculations

Multiplication
Multiplication 1 2 3 4 5 6 7 8 9 10
8 16 24 32 40 48 56 64 72 80
Multiplication 11 12 13 14 15 16 17 18 19 20
88 96 104 112 120 128 136 144 152 160
Multiplication 21 22 23 24 25 50 100 1000
168 176 184 192 200 400 800 8000
Division
Division 1 2 3 4 5 6 7 8 9 10
8 4 2 1.6 1 0.8
0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.125 1.25
Division 11 12 13 14 15
1.375 1.5 1.625 1.75 1.875
Exponentiation
Exponentiation 1 2 3 4 5 6 7 8 9 10
8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824
1 256 6561 65536 390625 1679616 5764801 16777216 43046721 100000000
Exponentiation 11 12 13
8589934592 68719476736 549755813888
214358881 429981696 815730721

In science

Physics

  • In nuclear physics, 8 is the second magic number; the first one being 2. A magic number (in this case) is the number of nucleons (protons and neutrons) in the atomic nucleus, such that they are arranged into complete shells in the nucleus.[5]
  • In particle physics, the eightfold way is used to classify subatomic particles.

Astronomy

  • The Saros number of the solar eclipse series that began on March 7, 2579 B.C.E. and ended on April 26, 1281 B.C.E. The duration of Saros series 8 was 1298.17 years, and it contained 73 solar eclipses.[6]
  • The Saros number of the lunar eclipse series that began on August 8, 2494 B.C.E. and ended on February 13, 961 B.C.E. The duration of Saros series 8 was 1532.56 years, and it contained 86 lunar eclipses.[7]
  • Eight of the bodies orbiting the Sun are considered planets in the Solar System.

Chemistry

  • Eight is the atomic number of oxygen.
  • The most stable allotrope of a sulfur molecule is made of eight sulfur atoms arranged in a rhombic form.
  • In the electronic configurations of atoms, eight is usually the maximum number of electrons that can occupy a valence shell.
  • The red pigment lycopene consists of eight isoprene units.

Biology

  • There are eight known B vitamins that play important roles in cell metabolism.
  • All spiders, and more generally all arachnids, have eight legs.
  • An octopus has eight tentacles.
  • In the adult human dentition, there are 8 teeth in each quadrant. The eighth tooth is the so-called wisdom tooth.

Measurement

  • The SI prefix for 10008 is yotta (Y), and that for its reciprocal is yocto (y).
  • In liquid measurement (US customary units), there are 8 fluid ounces in a cup, 8 pints in a gallon, and 8 tablespoons in a gill
  • There are 8 furlongs in a mile.

In technology

Seven-segment 8.svg
  • Many (mostly historic) computer architectures are eight-bit, among them the Nintendo Entertainment System
  • One byte is eight bits.
  • A V8 engine is an internal combustion engine with 8 cylinders configured in two banks (rows) of 4 forming a "V" when seen from the end.

In religion

Judaism

  • The Jewish religious rite of brit milah is held on a baby boy's eighth day of life.
  • Hanukkah is an eight-day Jewish holiday that starts on the twenty-fifth day of Kislev.
  • Shemini Atzeret (Hebrew: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of Sukkot.

Christianity

  • Eight is the number of Beatitudes in Jesus' Sermon on the Mount.
  • It is allegoric to what is beyond time (because the number 7 refers to the days of the week which repeat themselves).
  • Members of The Church of Jesus Christ of Latter-day Saints believe that humans are responsible for their actions by the age of 8. Before that age, children lack sufficient knowledge to commit sin and are therefore exempt from judgment for their actions.

Buddhism

  • The Dharmachakra, a Buddhist symbol, has eight spokes. The Buddha's principal teaching—the Four Noble Truths—ramifies as the Noble Eightfold Path.
  • In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas (Manjushri, Vajrapani, Avalokiteshvara, Maitreya, Kshitigarbha, Nivaranavishkambhi, Akashagarbha, and Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogachara school of thought: Consciousness in the five senses, thought-consciousness, self-consciousness, and unconsciousness-"consciousness" (alaya-vijñana).
  • The "irreversible" state of enlightenment, at which point a Bodhisattva goes on "autopilot," is the Eight Ground or bhūmi.
  • In general, "eight" seems to be an auspicious number for Buddhists, such as the "eight auspicious symbols" (the jewel-encrusted parasol; the goldfish (always shown as a pair, for example, the glyph of Pisces); the self-replenishing amphora; the white kamala lotus-flower; the white conch; the eternal (Celtic-style, infinitely looping) knot; the banner of imperial victory; the eight-spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching).
  • Buddha's birthday falls on the 8th day of the 4th month of the Chinese calendar.

Other religions

  • In Islam, eight is the number of Angels carrying The Holy Throne of Allah in heaven.
  • In Hinduism, eight is the number of wealth and abundance. The Goddess Lakshmi has eightfold forms. There are eight nidhis, or seats of wealth.
  • In Neopaganism, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year.
  • The Eight Immortals are Chinese deities.

In music

  • A note played for one-eighth the duration of a whole note is called an eighth note, or quaver.
  • An octave, the interval between two notes with the same letter name (where one has double the frequency of the other), is so called because there are eight notes on a western scale between the two, including the notes themselves.
  • There are eight notes in an octatonic scale.
  • There are eight musicians in an octet.
  • The 8-track cartridge is a musical recording format

In sports

  • In football, the number 8 has historically been the number of the Central Midfielder.
  • In rugby union, the central back row position wears the 8 shirt.
  • In baseball, in its numbering system used to record defensive plays, eight represents the center fielder's position.
  • In chess, each side has eight pawns and the board is made of 64 squares arranged in an eight by eight lattice.
  • The eight queens puzzle is a challenge to arrange eight queens on the board so that none can capture any of the others.
  • Eight ball billiards is played with 15 balls; the black ball numbered 8 being the middle and most important one. Magic 8 Ball is a randomized process of predicting the future or answering various questions, packaged to resemble this ball and often sold as a fortune-telling device.
  • In rowing, an "eight" refers to a sweep oar boat with eight rowers plus a coxswain.

In slang

  • An Eighth is a common measurement of marijuana, meaning an eighth of an ounce.
  • Referring to the shape of the numeral, eight was represented in bingo slang, before political correctness, as "One Fat Lady." Eighty-eight was "Two Fat Ladies."
  • The numeral "8" is sometimes used in writing to represent the syllable "ate," as in writing "H8" for "hate," or "congratul8ions" for "congratulations." Avril Lavigne's song "Sk8er Boi" uses this convention in the title. It is also often found on vanity plates
  • "Section 8" is common U.S. slang for "crazy," based on the U.S. military's Section 8 discharge for mentally unfit personnel.
  • In China, "8" is used in chat speak as a term for parting. This is due to the closeness in pronunciation of "8" (bā) and the English word "bye."

Miscellany

International maritime signal flag for 8
Four playing cards showing the "8" of all four suits
  • The ordinal adjective is octaval or octavary.
  • The distributive adjective is octonary.
  • In cooking recipes, there are approximately 8 pinches to a teaspoon.
  • A figure-eight knot is a type of knot frequently used by climbers.
  • Various types of buildings are usually eight-sided (octagonal), such as single-roomed gazebos and multi-roomed pagodas (descended from stupas).
  • Eight babies delivered in a single birth are called octuplets. The first set of eight surviving babies, the Chukwu octuplets, was born in 1998.
  • October was the eighth month in the Roman calendar; currently August is the eighth month.
  • War of the Eight Princes was a war in Chinese history
  • "88" is the abbreviated terminology used by the Aryan Brotherhood for the Nazi salute, "Heil Hitler"—"H" being the eighth letter of the alphabet, twice
  • The silver piece of eight was coined in the Spanish Empire and moved trade around the world.
  • There are Eight Principles of Yong in Chinese calligraphy.
  • Eight (八; accounting 捌; pinyin bā) is considered a lucky number in Asian culture because it sounds like the word "prosper" or "wealth" (发; Pinyin: fā). Additionally, it is considered lucky in Japan because the Chinese numeral character resembles a mountain, specifically Fujisan.
  • In numerology, 8 is the number of building, and in some theories, also the number of destruction.
  • In the Middle Ages, 8 was the number of "unmoving" stars in the sky.
  • 8vo is shorthand for "octavo," a book size.
  • The Eight: Eight American painters who exhibited together only once in 1908 in New York City. They joined this exhibition to oppose traditions upheld by the National Academy and help advance modernism in the United States. Five of the eight painters were associated with the Ashcan School: Robert Henri (1865-1929), George Luks (1867-1933), William Glackens (1870-1938), John Sloan (1871-1951), and Everett Shinn (1876-1953). The others were Maurice Prendergast (1859-1924), Ernest Lawson (1873-1939), and Arthur Bowen Davies (1862-1928).

See also

Notes

  1. ↑ A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.
  2. ↑ A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a series.
  3. ↑ A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real numbers includes rational and irrational numbers, which can be positive, negative, or zero.
  4. ↑ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer (New York: Wiley, 2000, ISBN 0471393401), 395.
  5. ↑ Xavier Borg, Magic numbers derived from a variable phase nuclear model, The General Science Journal. Retrieved October 7, 2022.
  6. ↑ NASA, Saros Series 8 Saros Series Catalog of Solar Eclipses. Retrieved October 7, 2022.
  7. ↑ NASA, Saros Series 8 Catalog of Lunar Eclipse Saros Series. Retrieved October 7, 2022.

References
ISBN links support NWE through referral fees

  • Flegg, Graham. Numbers: Their History and Meaning. Mineola, NY: Dover Publications, 2002. ISBN 0486421651
  • Higgins, Peter M. Number Story: From Counting to Cryptography. London: Copernicus, 2008. ISBN 978-1848000001
  • Ifrah, Georges. The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos et al. New York: Wiley, 2000. ISBN 0471393401
  • McLeish, John. The Story of Numbers: How Mathematics Has Shaped Civilization. New York: Fawcett Columbine, 1994. ISBN 0449909387
  • Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers. New York: Dover Publications, 1992. ISBN 0486270963
  • Wells, D. G. The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books, 1998. ISBN 0140261494

External links

All links retrieved June 13, 2023.

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