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{{redirect|Four|other uses|4 (disambiguation)}}
{{About|the mathematical number|other uses|6 (disambiguation)}}
{{example farm|date=March 2010}}
{{Infobox number
{{Infobox number
| number = 4
| number = 6
| numeral = [[Quaternary numeral system|quaternary]]
| numeral = [[senary]]
| divisor = 1, 2, 4
| divisor = 1, 2, 3, 6
| roman unicode = ,
| roman unicode = , ⅵ, ↅ
| greek prefix = [[wikt:tetra-|tetra-]]
| greek prefix = [[Wiktionary:hexa-|hexa-]]/[[Wiktionary:hex-|hex-]]
| latin prefix = [[wikt:quadri-|quadri-]]/[[wikt:quadr-|quadr-]]
| latin prefix = [[Wiktionary:sexa-|sexa-]]/[[Wiktionary:sex-|sex-]]
| lang1 = [[Greek numerals|Greek]]  
| lang1 = [[Greek numerals|Greek]]  
| lang1 symbol = δ (or Δ)
| lang1 symbol = στ (or ΣΤ or ς)
| lang2 = [[Arabic language|Arabic]]  
| lang2 = [[Arabic language|Arabic]]  
| lang2 symbol = {{resize|150%|٤,4}}
| lang2 symbol = {{resize|150%|٦}}
| lang3 = [[Persian language|Persian]]
| lang3 = [[Persian language|Persian]]  
| lang3 symbol = {{resize|150%|۴}}
| lang3 symbol = {{resize|150%|۶}}
| lang4 = [[Urdu]]
|lang4 = [[Urdu]]
| lang4 symbol= {{Urdu numeral|4|20}}
|lang4 symbol = {{Urdu numeral|6|20}}
| lang5 = [[Ge'ez alphabet|Ge'ez]]  
| lang5 = [[Amharic language|Amharic]]
| lang5 symbol =
| lang5 symbol =
| lang6 = [[Bengali language|Bengali]]  
| lang6 = [[Bengali language|Bengali]]
| lang6 symbol = {{resize|150%|}}
| lang6 symbol = {{resize|150%|}}
| lang7 = [[Chinese numeral]]  
| lang7 = [[Chinese numeral]]
| lang7 symbol = 四,亖,肆
| lang7 symbol = 六,陆
| lang8 = [[Korean numerals|Korean]]  
| lang8 = [[Devanāgarī]]
| lang8 symbol = 넷,사
| lang8 symbol = {{resize|150%|६}}
| lang9 = [[Devanāgarī|Devanagari]]  
| lang9 = [[Hebrew (language)|Hebrew]]
| lang9 symbol = {{resize|150%|}} (char)
| lang9 symbol = {{resize|150%|ו}} (Vav)
| lang10 = [[Telugu language|Telugu]]  
| lang10 = [[Khmer numerals|Khmer]]
| lang10 symbol = {{resize|150%|౪}}
| lang10 symbol =
| lang11 = [[Malayalam Language|Malayalam]]  
| lang11 = [[Thai numerals|Thai]]
| lang11 symbol = {{resize|150%|൪}}
| lang11 symbol =
| lang12 = [[Tamil language|Tamil]]  
| lang12 = [[Telugu language|Telugu]]
| lang12 symbol = {{resize|150%|௪}}
| lang12 symbol =
| lang13 = [[Hebrew (language)|Hebrew]]  
| lang13 = [[Tamil numerals|Tamil]]
| lang13 symbol = ארבע (Arba, pronounced AR-bah) or {{resize|150%|ד}} ([[Dalet]], 4th letter of the Hebrew alphabet)
| lang13 symbol =
| lang14 = [[Khmer numerals|Khmer]]  
| lang14 = [[Saraiki language|Saraiki]]  
| lang14 symbol = 
| lang14 symbol =  {{resize|200%|٦}}
| lang15 = [[Thai numerals|Thai]]
| lang15 symbol =  ๔
| lang16 = [[Kannada language|Kannada]]
| lang16 symbol =  ४
}}
}}
'''4''' ('''four'''; {{IPAc-en|'|f|oUr}}) is a [[number]], [[numeral system|numeral]], and [[glyph]]. It is the [[natural number]] following {{num|3}} and preceding {{num|5}}. Four is the only number that has the same number of characters as its value in the English language.<ref>{{cite web|url=http://www.omg-facts.com/view/Facts/3109|title=Four facts about 4|publisher=Omg facts}}</ref>
{{Wiktionary|six}}
'''6''' ('''six'''{{IPAc-en|ˈ|s|ɪ|k|s|}}) is the [[natural number]] following [[5 (number)|5]] and preceding [[7 (number)|7]].
 
The [[SI prefix]] for 1000<sup>6</sup> is [[exa]] (E), and for its reciprocal [[atto-]] (a).


==In mathematics==
==In mathematics==
Four is the smallest [[composite number]], its proper [[divisor]]s being {{num|1}} and {{num|2}}. Four is also a [[highly composite number]]. The next highly composite number is {{num|6}}.
6 is the smallest positive integer which is neither a square number nor a [[prime number]].
Six is the second smallest [[composite number]]; its proper [[divisor]]s are [[1 (number)|1]], [[2 (number)|2]] and [[3 (number)|3]].


Four is the second [[square number]], the second [[centered triangular number]].
Since six equals the sum of its proper divisors, six is the smallest [[perfect number]], [[Granville number]], and <math>\mathcal{S}</math>-perfect number.<ref>{{cite book |title=Number Story: From Counting to Cryptography |last=Higgins |first=Peter |year=2008 |publisher=Copernicus |location=New York |isbn=978-1-84800-000-1 |page=11 |pages= }}</ref><ref name=OEIS>{{cite web|title=Granville number|url=http://oeis.org/|work=OeisWiki|publisher=The Online Encyclopedia of Integer Sequences|accessdate=27 March 2011| archiveurl= http://web.archive.org/web/20110329130407/http://oeis.org/| archivedate= 29 March 2011 <!--DASHBot-->| deadurl= no}}</ref>


4 is the smallest squared prime (''p''<sup>2</sup>) and the only even number in this form. It has an [[aliquot sum]] of 3 which is itself prime. The [[aliquot sequence]] of 4 has 4 members (4, {{num|3}}, 1, 0) and is accordingly the first member of the 3-aliquot tree.
As a perfect number:
*6 is related to the [[Mersenne prime]] 3, since 2<sup>1</sup>(2<sup>2</sup> - 1) = 6. (The next perfect number is [[28 (number)|28]].)
*6 is the only even perfect number that is not the sum of successive odd cubes.<ref>David Wells, ''[[The Penguin Dictionary of Curious and Interesting Numbers]]''. London: Penguin Books (1987): 67</ref>
*As a perfect number, 6 is the root of the 6-aliquot tree, and is itself the [[aliquot sum]] of only one number; the [[square number]], [[25 (number)|25]].


A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because 92 = 4×23.
Six is the only number that is both the sum and the product of three consecutive positive numbers.<ref>Peter Higgins, ''Number Story''. London: Copernicus Books (2008): 12</ref>


Only one number has an aliquot sum of 4 and that is squared prime {{num|9}}.
Unrelated to 6 being a perfect number, a [[Golomb ruler]] of length 6 is a "perfect ruler."<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 72</ref> Six is a [[congruent number]].


The prime factorization of four is two times two.
Six is the first discrete biprime (2.3) and the first member of the (2.q) discrete biprime family.


Four is the smallest composite number that is equal to the sum of its prime factors. (As a consequence of this, it is the smallest [[Smith number]]). However, it is the only composite number ''n'' for which <math>(n - 1)!\ \equiv\ 0 \ ({\rm mod}\ n)</math> is false.
Six is a [[unitary perfect number]], a [[harmonic divisor number]] and a [[superior highly composite number]], the last to also be a [[primorial]]. The next superior highly composite number is [[12 (number)|12]].  The next primorial is [[30 (number)|30]].


It is also a [[Motzkin number]].
5 and 6 form a [[Ruth-Aaron pair]] under either definition.


In bases 6 and 12, 4 is a 1-[[automorphic number]].
The smallest non-[[abelian group|abelian]] [[group (mathematics)|group]] is the [[symmetric group]] ''S''<sub>3</sub> which has [[factorial|3!]] = 6 elements.


In addition, 2 + 2 = 2 × 2 = 2<sup>2</sup> = 4. Continuing the pattern in [[Knuth's up-arrow notation]], <math>2 \uparrow\uparrow 2 = 2 \uparrow\uparrow\uparrow 2 = 4</math>, and so on, for any number of up arrows.
''S''<sub>6</sub>, with 720 elements, is the only finite symmetric group which has an [[outer automorphism]]. This automorphism allows us to construct a number of exceptional mathematical objects such as the S(5,6,12) [[Steiner system]], the [[projective plane]] of order 4 and the [[Hoffman-Singleton graph]]. A closely related result is the following theorem: 6 is the only natural number ''n'' for which there is a construction of ''n'' [[isomorphic]] objects on an ''n''-set ''A'', invariant under all permutations of ''A'', but not naturally in 1-1 correspondence with the elements of ''A''. This can also be expressed category theoretically: consider the [[category (mathematics)|category]] whose objects are the ''n'' element sets and whose arrows are the [[bijection]]s between the sets. This category has a non-trivial [[functor]] to itself only for ''n''=6.


A four-sided plane figure is a [[quadrilateral]] (quadrangle) or [[square (geometry)|square]], sometimes also called a ''tetragon''. A [[circle]] divided by 4 makes [[right angle]]s. Because of it, four (4) is the base number of [[plane (mathematics)]]. Four [[cardinal directions]], [[Season|four seasons]], [[duodecimal]] system, and [[vigesimal]] system are based on four.
6 similar coins can be arranged around a central coin of the same radius so that each coin makes contact with the central one (and touches both its neighbors without a gap), but seven cannot be so arranged. This makes 6 the answer to the two-dimensional [[kissing number problem]]. The densest [[sphere packing]] of the plane is obtained by extending this pattern to the [[hexagon]]al [[lattice (group)|lattice]] in which each circle touches just six others.


A solid figure with four faces is a [[tetrahedron]]. The regular tetrahedron is the simplest [[Platonic solid]]. A [[tetrahedron]], which can also be called a 3-[[simplex]], has four triangular faces and four vertices. It is the only self-dual [[regular polyhedron]].
[[File:120px-Hexahedron-slowturn.gif|frame|left|A [[cube]] has 6 [[Face (geometry)|faces]]]]
6 is the largest of the four [[Harshad number|all-Harshad number]]s.


[[Four-dimensional space|Four-dimensional]] space is the highest-dimensional space featuring more than three convex regular figures:
A six-sided [[polygon]] is a hexagon, one of the three regular polygons capable of [[tessellation|tiling the plane]]. [[Figurate number]]s representing hexagons (including six) are called [[hexagonal number]]s. Because 6 is the product of a power of 2 (namely 2<sup>1</sup>) with nothing but distinct [[Fermat prime]]s (specifically 3), a regular hexagon is a [[constructible polygon]].
* Two-dimensional: infinitely many convex [[regular polygon]]s.
* Three-dimensional: five convex [[Regular polyhedron|regular polyhedra]] (the five [[Platonic Solid]]s).
* Four-dimensional: six [[Convex regular 4-polytope|convex regular polychora]].
* Five-dimensional and every higher-dimensional: three regular convex [[polytope]]s ([[simplex|regular simplexes]], [[hypercube]]s, [[cross-polytope]]s).


Four-dimensional [[differential manifold]]s have some unique properties. There is only one [[differential structure]] on <math>\mathbb{R}^{n}</math> except when ''n'' = 4, in which case there are uncountably many.
Six is also an [[octahedral number]]. It is a [[triangular number]] and so is its square ([[36 (number)|36]]).


The smallest non-[[cyclic group|cyclic]] [[group (mathematics)|group]] has four elements; it is the [[Klein four-group]]. Four is also the order of the smallest non-trivial groups that are not [[simple group|simple]].
There are six basic [[trigonometric functions]].


Four is the maximum number of dimensions of a real [[division algebra]] (the [[quaternions]]), by a theorem of [[Ferdinand Georg Frobenius]].
There are six [[Convex regular 4-polytope|convex regular polytopes]] in four [[dimensions]].


The [[four-color theorem]] states that a [[planar graph]] (or, equivalently, a flat [[map]] of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 48</ref> Three colors are not, in general, sufficient to guarantee this. The largest planar [[complete graph]] has four vertices.
Six is the four-bit [[binary numeral system|binary]] complement of number [[9 (number)|nine]] (6 = 0110<sub>2</sub> and 9 = 1001<sub>2</sub>).


[[Lagrange's four-square theorem]] states that every positive integer can be written as the sum of at most four [[square number]]s. Three are not always sufficient; {{num|7}} for instance cannot be written as the sum of three squares.
The [[six exponentials theorem]] guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.


Four is the first positive non-[[Fibonacci number]].
All primes above 3 are of the form 6n±1 for n≥1.


Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4''x'' = ''y''<sup>2</sup> − ''z''<sup>2</sup>.
===In numeral systems===
{| class=wikitable
|-
! [[Radix|Base]] !! [[Numeral system]] !! Representation
|-
| 2 || [[Binary numeral system|binary]] || 110
|-
| 3 || [[Ternary numeral system|ternary]] || 20
|-
| 4 || [[quaternary numeral system|quaternary]] || 12
|-
| 5 || [[quinary]] || 11
|-
| 6 || [[senary]] || 10
|-
| colspan=2 | over 6 ([[decimal]], [[hexadecimal]]) || 6
|}


Four is an [[Harshad number|all-Harshad number]] and a [[semi-meandric number]].
In bases 10, 15 and 30, 6 is a 1-[[automorphic number]].


===List of basic calculations===
===List of basic calculations===
{|class="wikitable" style="text-align: center; background: white"
{|class="wikitable" style="text-align: center; background: white"
|-
|-
!width="105px"|[[Multiplication]]
! style="width:105px;"|[[Multiplication]]
!1
!1
!2
!2
Line 104: Line 120:
!9
!9
!10
!10
!width="5px"|
! style="width:5px;"|
!11
!11
!12
!12
Line 115: Line 131:
!19
!19
!20
!20
!width="5px"|
! style="width:5px;"|
!21
!21
!22
!22
Line 121: Line 137:
!24
!24
!25
!25
!width="5px"|
! style="width:5px;"|
!50
!50
!100
!100
!1000
!1000
|-
|-
|<math>4 \times x</math>
|<math>6 \times x</math>
|'''4'''
|'''6'''
|{{num|8}}
|[[12 (number)|12]]
|{{num|12}}
|[[18 (number)|18]]
|{{num|16}}
|[[24 (number)|24]]
|{{num|20}}
|[[30 (number)|30]]
|{{num|24}}
|[[36 (number)|36]]
|{{num|28}}
|[[42 (number)|42]]
|{{num|32}}
|[[48 (number)|48]]
|{{num|36}}
|[[54 (number)|54]]
|{{num|40}}
|[[60 (number)|60]]
!
!
|{{num|44}}
|[[66 (number)|66]]
|{{num|48}}
|[[72 (number)|72]]
|{{num|52}}
|[[78 (number)|78]]
|{{num|56}}
|[[84 (number)|84]]
|{{num|60}}
|[[90 (number)|90]]
|{{num|64}}
|[[96 (number)|96]]
|{{num|68}}
|[[102 (number)|102]]
|{{num|72}}
|[[108 (number)|108]]
|{{num|76}}
|[[114 (number)|114]]
|{{num|80}}
|[[120 (number)|120]]
!
!
|{{num|84}}
|[[126 (number)|126]]
|{{num|88}}
|[[132 (number)|132]]
|{{num|92}}
|[[138 (number)|138]]
|{{num|96}}
|[[144 (number)|144]]
|{{num|100}}
|[[150 (number)|150]]
!
!
|{{num|200}}
|[[300 (number)|300]]
|{{num|400}}
|[[600 (number)|600]]
|{{num|4000}}
|[[6000 (number)|6000]]
|}
|}


{|class="wikitable" style="text-align: center; background: white"
{|class="wikitable" style="text-align: center; background: white"
|-
|-
!width="105px"|[[Division (mathematics)|Division]]
! style="width:105px;"|[[Division (mathematics)|Division]]
!1
!1
!2
!2
Line 173: Line 189:
!9
!9
!10
!10
!width="5px"|
! style="width:5px;"|
!11
!11
!12
!12
Line 179: Line 195:
!14
!14
!15
!15
!16
|-
|-
|<math>4 \div x</math>
|<math>6 \div x</math>
|'''4'''
|'''6'''
|3
|2
|2
|<math>1.\overline{3}</math>
|1.5
|1.2
|1
|1
|0.8
|<math>0.\overline{85714}\overline{2}</math>
|0.75
|<math>0.\overline{6}</math>
|<math>0.\overline{6}</math>
|<math>0.\overline{571428}</math>
|0.6
!
|<math>0.\overline{5}\overline{4}</math>
|0.5
|0.5
|<math>0.\overline{4}</math>
|<math>0.\overline{46153}\overline{8}</math>
|<math>0.\overline{42857}\overline{1}</math>
|0.4
|0.4
!
|-
|<math>0.\overline{36}</math>
|<math>x \div 6</math>
|<math>0.1\overline{6}</math>
|<math>0.\overline{3}</math>
|<math>0.\overline{3}</math>
|<math>0.\overline{307692}</math>
|<math>0.\overline{285714}</math>
|<math>0.2\overline{6}</math>
|0.25
|-
|<math>x \div 4</math>
|0.25
|0.5
|0.5
|0.75
|<math>0.\overline{6}</math>
|<math>0.8\overline{3}</math>
|1
|1
|1.25
|<math>1.1\overline{6}</math>
|<math>1.\overline{3}</math>
|1.5
|1.5
|1.75
|<math>1.\overline{6}</math>
!
|<math>1.8\overline{3}</math>
|2
|2
|2.25
|<math>2.1\overline{6}</math>
|<math>2.\overline{3}</math>
|2.5
|2.5
!
|2.75
|3
|3.25
|3.5
|3.75
|4
|}
|}


{|class="wikitable" style="text-align: center; background: white"
{|class="wikitable" style="text-align: center; background: white"
|-
|-
!width="105px"|[[Exponentiation]]
! style="width:105px;"|[[Exponentiation]]
!1
!1
!2
!2
Line 233: Line 246:
!9
!9
!10
!10
!width="5px"|
! style="width:5px;"|
!11
!11
!12
!12
!13
!13
|-
|-
|<math>4 ^ x\,</math>
|<math>6 ^ x\,</math>
|4
|'''6'''
|16
|36
|64
|[[216 (number)|216]]
|256
|1296
|1024
|7776
|4096
|46656
|16384
|279936
|65536
|1679616
|262144
|10077696
|1048576
|60466176
!
!
|4194304
|362797056
|16777216
|2176782336
|67108864
|13060694016
|-
|-
|<math>x ^ 4\,</math>
|<math>x ^ 6\,</math>
|1
|1
|16
|[[64 (number)|64]]
|81
|729
|256
|625
|1296
|2401
|4096
|4096
|6561
|15625
|10000
|46656
|117649
|262144
|531441
|[[1000000 (number)|1000000]]
!
!
|14641
|1771561
|20736
|2985984
|28561
|4826809
|}
|}


==Evolution of the glyph==
==Greek and Latin word parts==
[[File:Evolution4glyph.png|x50px|right]]
 
Representing 1, 2 and 3 in as many lines as the number represented worked well. The [[Brahmin]] Indians simplified 4 by joining its four lines into a cross that looks like our modern plus sign. The [[Sunga empire|Sunga]] would add a horizontal line on top of the numeral, and the Kshatrapa and Pallava evolved the numeral to a point where speed of writing was a secondary concern. The [[Arab]]s' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the numeral less cursive, ending up with a glyph very close to the original Brahmin cross.<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): 394, Fig. 24.64</ref>
===''Hexa''===
'''''Hexa''''' is classical [[Greek language|Greek]] for "six". Thus:
* "[[Hexadecimal]]" combines ''hexa-'' with the Latinate ''decimal'' to name a [[number base]] of 16
* A [[hexagon]] is a [[regular polygon]] with six sides
** ''L’Hexagone'' is a French nickname for the continental part of [[Metropolitan France]]
* A [[hexahedron]] is a [[polyhedron]] with six faces, with a [[cube (geometry)|cube]] being a special case
* [[Hexameter]] is a poetic form consisting of six feet per line
*A "hex nut" is a [[Nut (hardware)|nut]] with six sides, and a hex [[Screw|bolt]] has a six-sided head
*The prefix "hexa-" also occurs in the [[systematic name]] of many [[chemical compound]]s, such as "[[hexamethyl]]"
 
===The prefix ''sex-''===
'''''Sex-''''' is a [[Latin]] [[Prefix (linguistics)|prefix]] meaning "six". Thus:
*''Senary'' is the ordinal adjective meaning "sixth"
*People with [[sexdactyly]] have six fingers on each hand (see above photo)
*The measuring instrument called a [[sextant]] got its name because its shape forms one-sixth of a whole [[circle]]
*A group of six musicians is called a [[sextet]]
*Six babies delivered in one birth are [[sextuplet]]s
 
== Evolution of the glyph ==
[[File:Evolution6glyph.png|x50px|right]]
The evolution of our modern glyph for 6 appears rather simple when compared with that for the other numerals. Our modern 6 can be traced back to the [[Brahmin]]s of [[India]], who wrote it in one stroke like a cursive lowercase e rotated 90 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Ghubar Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.<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. 24.66</ref>
 
On the [[seven-segment display]]s of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a 'b' is not practical.


While the shape of the 4 character has an [[ascender (typography)|ascender]] in most modern [[typeface]]s, in typefaces with [[text figures]] the character usually has a [[descender]], as, for example, in [[File:TextFigs148.svg|40px]].
Just as in most modern [[typeface]]s, in typefaces with [[text figures]] the 6 character usually has an [[Ascender (typography)|ascender]], as, for example, in [[File:Text figures 036.svg|52px]].


[[File:Seven-segment 4.svg|x50px|left]]
This numeral resembles an inverted ''9''. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.
On the [[seven-segment display]]s of pocket calculators and digital watches, as well as certain [[optical character recognition]] fonts, 4 is seen with an open top.


[[Television station]]s that operate on [[channel 4 (disambiguation)|channel 4]] have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the [[Canadian Aboriginal syllabics]] letter ᔦ. The [[magnetic ink character recognition]] "CMC-7" font also uses this variety of "4".
==In music==
[[File:Guitar 1.jpg|thumb|200px|A standard [[guitar]] has 6 [[String instrument|strings]]]]


==In religion==
===In artists===
;Buddhism
*[[Les Six]] ("The Six" in English) was a group consisting of the French composers [[Georges Auric]], [[Louis Durey]], [[Arthur Honegger]], [[Darius Milhaud]], [[Francis Poulenc]] and [[Germaine Tailleferre]] in the 1920s
* [[Four Noble Truths]]
*Bands with the number six in their name include [[Six Organs of Admittance]], 6 O'clock Saints, [[Electric Six]], [[Eve 6]], [[Los Xey]] (''sei'' is Basque for "six"), Out On Blue Six, Six In Six, [[Sixpence None the Richer]], [[Slant 6]], Vanity 6, and [[You Me At Six]]
** [[Dukkha]] – The Noble Truth of Suffering
* #6 is the pseudonym of [[United States|American]] musician [[Shawn Crahan]], when performing with the band [[Slipknot (band)|Slipknot]]
** [[Pratītyasamutpāda|Samudaya]] – The Noble Truth of the Cause of Suffering
** [[Nirvana|Nirodha]] – The Noble Truth of the Cessation of Suffering
** [[Noble Eightfold Path|Magga]] – The Noble Truth of the Path leading to the Cessation of Suffering
* [[Four sights]] – observations which affected Prince Siddhartha deeply and made him realize the sufferings of all beings, and compelled him to begin his spiritual journey—an [[old age|old]] man, a [[illness|sick]] man, a [[death|dead]] man, and an [[ascetic]]
* [[Mahābhūta|Four Great Elements]] [[earth (classical element)|earth]], [[water (classical element)|water]], [[fire (classical element)|fire]], and [[air (classical element)|wind]]
* [[Four Heavenly Kings]]
* [[Satipatthana|Four Foundations of Mindfulness]] – contemplation of the body, contemplation of feelings, contemplation of mind, contemplation of mental objects
* [[Four Right Exertions]]
* [[Iddhipada|Four Bases of Power]]
* [[Jhāna|Four jhānas]]
* [[Arūpajhāna|Four arūpajhānas]]
* [[Brahmavihara|Four Divine Abidings]] – [[Mettā|loving-kindness]], [[Karuṇā|compassion]], [[Mudita|sympathetic joy]], and [[Upekkha|equanimity]]
* [[Four stages of enlightenment]] – [[Sotāpanna|stream-enterer]], [[Sakadagami|once-returner]], [[Anagami|non-returner]], and [[Arahant (Buddhism)|arahant]]
* [[Buddhist pilgrimage|Four main pilgrimage sites]] – [[Lumbini]], [[Bodh Gaya]], [[Sarnath]], and [[Kusinara]]


;Judeo-Christian symbolism
===In instruments===
* The [[Tetragrammaton]] is the four-letter name of [[God]].
*A standard [[guitar]] has 6 strings
* The four Matriarchs (foremothers) of [[Judaism]] are [[Sarah]], [[Rebekah]], [[Leah]], and [[Rachel]].
*Most [[woodwind]] instruments have 6 basic holes or keys (e.g., bassoon, clarinet, pennywhistle, saxophone); these holes or keys are usually not given numbers or letters in the fingering charts
* The [[Four Species]] ([[lulav]], [[hadass]], [[Aravah (Sukkot)|aravah]] and [[etrog]]) are taken as one of the [[mitzvah|mitzvot]] on the [[Jewish]] holiday of [[Sukkot]]. ([[Judaism]])
* The Four Cups of Wine to drink on the [[Jewish]] holiday of [[Passover]]. ([[Judaism]])
* The Four Questions to be asked on the [[Jewish]] holiday of [[Passover]]. ([[Judaism]])
* The Four Sons to be dealt with on the [[Jewish]] holiday of [[Passover]]. ([[Judaism]])
* The Four Expressions of Redemption to be said on the [[Jewish]] holiday of [[Passover]]. ([[Judaism]])
* The [[Four Horsemen of the Apocalypse]] ride in the [[Book of Revelation]].
* The four [[Gospel]]s: [[Gospel of Matthew|Matthew]], [[Gospel of Mark|Mark]], [[Gospel of Luke|Luke]], and [[Gospel of John|John]].


;Hinduism
===In music theory===
* In [[Puruṣārtha]] there are 4 aims of human life [[Dharma]], [[Artha]], [[Kāma]], [[Moksha]].
*There are 6 semitones in a tritone
* The four stages of life [[Brahmacharya]] (student life), [[Grihastha]] (household life), [[Vanaprastha]] (retired life) and [[Sannyasa]] (renunciation).
* The four primary castes or strata of society  [[Brahmana]] (priest/teacher), [[Kshatriya]] (warrior/politician), [[Vaishya]] (landowner/entrepreneur) and [[Shudra]] (servant/manual laborer).


;Islam
===In works===
* [[Eid al-Adha]] lasts for four days, from the 10th to the 14th of [[Dhul Hijja]].
*"Six geese a-laying" were given as a present on the sixth day in the popular [[Christmas carol]], "[[The Twelve Days of Christmas (song)|The Twelve Days of Christmas]]."
* There are four The Rightly Guided Caliphs or [[Rashidun]]: [[Abu Bakr]], [[Umar ibn al-Khattab]], [[Uthman ibn Affan]] and [[Ali ibn Abi Talib]].
*Divided in six arias, [[Hexachordum Apollinis]] is generally regarded as one of the pinnacles of [[Johann Pachelbel]]'s oeuvre.  
* The Four Arch Angels in Islam are: Jibraeel (Gabriel), Mikaeel (Michael), Izraeel (Azrael), and Israfil (Raphael)
*The  concerti grossi Opus 3, organ concertos Opus 4 and Opus 7 (each) by [[Georg Frideric Handel]].
* There are four Sacred Months in Islam: [[Muharram]], [[Rajab]], [[Dhu al-Qi'dah]] and [[Dhu al-Hijjah]].
*The sixth album by Dream Theater, ''Six Degrees Of Inner Turbulence'', was based around the number six: the album has six songs, and the sixth song&nbsp;— that is, the complete second disc&nbsp;— explores the stories of six individuals suffering from various mental illnesses.
* There are four [[Sunni]] schools of [[fiqh]]: [[Hanafi]], [[Shafi`i]], [[Maliki]] and [[Hanbali]].
* There are four major sunni Imams: [[Abū Ḥanīfa]], [[Muhammad ibn Idris ash-Shafi`i]], [[Malik ibn Anas]] and [[Ahmad ibn Hanbal]].
* There are four books in Islam: Torah, Zaboor, Injeel, Quran.
* Waiting for four months is ordained for those who take an oath for abstention from their wives.
* The waiting period of the woman whose husband dies, is four months and ten days.
* When Abraham said: “My Lord, show me how You give life to the dead,” Allah said: “Why! Do you have no faith?” Abraham replied: “Yes, but in order that my heart be at rest.” He said: “Then take four birds, and tame them to yourself, then put a part of them on every hill, and summon them; they will come to you flying.
* The respite of four months was granted to give time to the mushriks in Surah Taubah so that they should consider their position carefully and decide whether to make preparation for war or to emigrate from the country or to accept Islam.
* Those who accuse honourable women (of unchastity) but do not produce four witnesses, flog them with eighty lashes, and do not admit their testimony ever after. They are indeed transgressors.


;Other
==In religion==
* Four is the sacred number of the [[Zia (New Mexico)|Zia]], an indigenous tribe located in the [[U.S.]] State of [[New Mexico]].
[[File:Black Star of David.svg|100px|right]]
* The Chinese, Vietnamese, the Korean and the Japanese are [[tetraphobia|superstitious about the number four]] because it is a homonym for "death" in their languages.
*There are 6:
**Points on a [[Star of David]]
**Orders of the [[Mishnah]]
**Symbolic foods placed on the [[Passover Seder Plate]]
*[[Yahweh]] took 6 days to create the world in the [[Old Testament]] [[Book of Genesis]]; humankind was created on day 6. In the [[City of God (book)|''City of God'']], [[Augustine of Hippo]] suggested ([http://www.newadvent.org/fathers/120111.htm book 11, chapter 30]) that God's creation of the world took six days because 6 is a [[perfect number]].
*The [[Judaism|Jewish]] holiday of [[Shavuot]] starts on the sixth day of the [[Hebrew calendar|Hebrew]] month of [[Sivan]]
*In Islam:
**There are [[Six articles of belief]]
**Fasting six days of [[Shawwal]], together with the month of [[Ramadan]], is equivalent to fasting the whole year
*In [[Āstika and nāstika|Hindu theology]], a ''[[Hindu_units_of_measurement#Small units of time used in the Vedas|trasarenu]]'' is the combination of 6 celestial ''paramānus'' ([[Vaisheshika#The_atomic_theory|atoms]])
See also [[666 (number)|666]].


==In science==
==In science==
* A [[tetramer]] is a thing formed out of four sub-units.


===In astronomy===
===Astronomy===
* Four terrestrial (or rocky) planets in the [[Solar system]]: [[Mercury (planet)|Mercury]], [[Venus]], [[Earth]], [[Mars]].
*[[Messier object]] [[Messier Object 6|M6]], a magnitude 4.5 [[open cluster]] in the constellation [[Scorpius]], also known as the [[Butterfly Cluster]]
* Four giant gas planets in the [[Solar system]]: [[Jupiter]], [[Saturn]], [[Uranus]], [[Neptune]].
*The [[New General Catalogue]] [http://www.ngcic.org/ object] [[NGC 6]], [[spiral galaxy]] in the [[constellation]] [[Andromeda constellation|Andromeda]]
* Four of Jupiter's moons (the [[Galilean moons]]) are readily visible from Earth.
*The [[Saros number|Saros]] [http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html number] of the [[solar eclipse]] series which began on [[-2691]] March 16 and ended on [[-1393]] May 3. The duration of Saros series 6 was 1298.1 years, and it contained 73 solar eclipses
* [[Messier object]] [[Messier 4|M4]], a magnitude 7.5 [[globular cluster]] in the constellation [[Scorpius]].
*The Saros [http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html number] of the [[lunar eclipse]] series which began on [[-2642]] July 25 and ended on [[-1091]] February 10. The duration of Saros series 6 was 1550.6 years, and it contained 87 lunar eclipses
* The [[New General Catalogue]] [http://www.ngcic.org/ object] [[NGC 4]], a faint [[galaxy]] in the [[constellation]] [[Pisces (constellation)|Pisces]]
* The Roman numeral VI:
* The Roman numeral IV stands for [[subgiant]] in the [[stellar classification|Yerkes spectral classification scheme]].
**Stands for [[subdwarf]]s in the [[stellar classification|Yerkes spectral classification scheme]]
* The Roman numeral IV (usually) stands for the fourth-discovered satellite of a planet or minor planet (e.g. [[Jupiter IV]])
**(Usually) stands for the sixth-discovered satellite of a planet or minor planet (e.g. [[Jupiter VI]])


===In biology===
===Biology===
* Four is the number of [[nucleobase]] types in [[DNA]] and [[RNA]] – [[adenine]], [[guanine]], [[cytosine]], [[thymine]] ([[uracil]] in [[RNA]]).
*The cells of a [[beehive]] are [[hexagon|6-sided]]
* Many [[chordate]]s have four feet, legs or leglike appendages ([[Tetrapods]]).
*[[Insects]] have 6 [[leg]]s
* The [[mammal]]ian [[heart]] consists of four chambers.
* Many [[mammal]]s ([[Carnivora]], [[Ungulata]]) use four fingers for movement.
* The fourth finger of a human hand (on the left hand – ring-finger) is moved when the little finger moves.
* All [[insect]]s with wings except [[fly|flies]] have four [[wing]]s.
* Insects of the superorder [[Endopterygota]], also known as Holometabola, such as butterflies, ants, bees, beetles, fleas, flies, moths, and wasps, undergo [[holometabolism]] – complete metamorphism in four stages – from (1) embryo (ovum, egg), to (2) larva (such as grub, caterpillar), then (3) pupa (such as the chrysalis), and finally (4) the imago.
* There are four human [[blood]] groups (A, B, O, AB).
* [[Humans]] have four [[canine tooth|canines]], four [[incisor]]s and four [[wisdom teeth]].
* The cow's stomach is divided in four digestive compartments: reticulum, rumen, omasum and abomasum.


===In chemistry===
===Chemistry===
* [[Valence (chemistry)|Valency]] of [[carbon]] (that is basis of life on the Earth) is four. Also because of its tetrahedral crystal bond structure, [[diamond]] (one of the natural allotropes of carbon) is the hardest known naturally occurring material. It is also the valence of [[silicon]], whose compounds form the majority of the mass of the Earth's crust.
[[File:Benzene structure.png|right|A [[molecule]] of [[benzene]] has a [[Aromaticity|ring]] of 6 [[carbon]] [[atom]]s]]
* The [[atomic number]] of [[beryllium]]
*A benzene molecule has a ring of 6 carbon atoms
* There are four basic states of [[matter]]: [[solid]], [[liquid]], [[gas]], and [[plasma (physics)|plasma]].
*6 is the [[atomic number]] of carbon
* The four elements of [[alchemy]] are [[earth]], [[water]], [[air]] and [[fire]].
*The sixfold [[symmetry]] of [[snowflake]]s arises from the [[hexagon]]al [[crystal structure]] of [[Ice|ordinary ice]]
*A [[hexamer]] is an oligomer made of six subunits
[[File:Bienenwabe mit Eiern und Brut 5.jpg|thumb|200px|The cells of a [[beehive]] are 6-sided]]


===In physics===
===Medicine===
* [[Special relativity]] and [[general relativity]] treat nature as four-[[dimension]]al – [[time]] and three-dimensional [[space]] are treated together and called [[spacetime]]. Also, any event ''E'' has a [[light cone]] composed of four zones of possible communication and cause and effect (outside the light cone is strictly incommunicado).
*There are 6 tastes in traditional Indian Medicine called [[Ayurveda]]: sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body
* An [[alpha particle]] (helium nucleus, also called a helion) consists of four [[hadron]]s.
*Phase 6 is one of six [[WHO pandemic phases|pandemic influenza phases]]
* There are four [[fundamental forces]] ([[electromagnetism]], [[gravitation]], the [[weak nuclear force]], and the [[strong nuclear force]]).
* In [[statistical mechanics]], the [[four functions inequality]] is an inequality for four functions on a finite [[distributive lattice]].


==In logic and philosophy==
===Physics===
* The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns"..."lord of the four quarters of the earth"...<ref><span lang=fr>Chevalier, Jean</span> and <span lang=fr>Gheerbrant, Alain</span> (1994), ''The Dictionary of Symbols''. The quote beginning "Almost from prehistoric times..." is on p. 402.</ref> by which is understood to the extent of their powers both territorially and in terms of total control of their subjects' doings.
[[File:Standard Model of Elementary Particles.svg|thumb|right|200px|In the [[Standard Model]] of [[particle physics]], there are 6 [[Flavour (particle physics)|types]] of [[quark]] and 6 types of [[lepton]]]]
* The [[Square of Opposition]], in both its Aristotelian version and its [[Square of Opposition#Modern squares of opposition|Boolean version]], consists of four forms: A ("All ''S'' is ''R''"), I ("Some ''S'' is ''R''"), E ("No ''S'' is ''R''"), and O ("Some ''S'' is not ''R''").
*In the Standard Model of particle physics, there are 6 types of [[quarks]] and 6 types of [[leptons]]
* In regard to whether two given propositions can have the same [[truth value]], there are four separate logical possibilities: the propositions are ''subalterns'' (possibly both are true, and possibly both are false); ''subcontraries'' (it is possible that both are true, but not that both are false); ''contraries'' (it is possible that both are false, but not that both are true); or ''contradictories'' (it is not possible that both are true, and it is not possible that both are false).
*In [[statistical mechanics]], the [[Ice-type model|six-vertex model]] has 6 possible configurations of arrows at each vertex
* [[Aristotle]] held that there are basically [[Aristotle#Causality, the four causes|four causes]] in nature: the [[Four causes#Efficient cause|efficient cause]], the [[Four causes#Material cause|matter]], the [[Four causes#Final cause|end]], and the [[Four causes#Formal cause|form]].
 
* The [[Stoicism|Stoics]] held with four basic [[categories (Stoic)|categories]], all viewed as bodies (substantial and insubstantial): (1) ''substance'' in the sense of substrate, primary formless matter; (2) ''quality'', matter's organization to differentiate and individualize something, and coming down to a physical ingredient such as ''pneuma'', breath; (3) ''somehow holding'' (or ''disposed''), as in a posture, state, shape, size, action, and (4) ''somehow holding'' (or ''disposed'') ''toward something,'' as in relative location, familial relation, and so forth.
==In sports==
* [[Immanuel Kant]] expounded a [[Category (Kant)#The table of judgments|table of judgments]] involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a [[Category (Kant)#The table of categories|table of four categories]], named by the terms just listed, and each with three subcategories.
* 6 entities in a grouping:
* [[Arthur Schopenhauer]]'s doctoral thesis was ''[[On the Fourfold Root of the Principle of Sufficient Reason]]''.
**The National Basketball Association has six divisions (the National Hockey League had six divisions until realigning into four divisions for the 2013-14 season)
* [[Franz Brentano]] held that any major philosophical period has four phases: (1) Creative and rapidly progressing with scientific interest and results; then declining through the remaining phases, (2) practical, (3) increasingly skeptical, and (4) literary, mystical, and scientifically worthless – until philosophy is renewed through a new period's first phase. (See Brentano's essay "The Four Phases of Philosophy and Its Current State" 1895, tr. by Mezei and Smith 1998.)
**The [[Original Six]] teams in the National Hockey League are Toronto, [[Chicago Blackhawks|Chicago]], [[Montreal Canadiens|Montreal]], [[New York Rangers|New York]], [[Boston Bruins|Boston]], and Detroit. They are the oldest remaining teams in the league, though not necessarily the first six; they comprised the entire league from [[1942–43 NHL season|1942]] to [[1967 NHL expansion|1967]]
* [[Charles Sanders Peirce|C. S. Peirce]], usually a [[trichotomy (philosophy)|trichotomist]], discussed four methods for overcoming troublesome uncertainties and achieving secure beliefs: (1) the method of tenacity (policy of sticking to initial belief), (2) the method of authority, (3) the method of congruity (following a fashionable [[paradigm]]), and (4) the [[Fallibilism|fallibilistic]], self-correcting method of science (see "[[s:The Fixation of Belief|The Fixation of Belief]]", 1877); and four barriers to inquiry, barriers refused by the fallibilist: (1) assertion of absolute certainty; (2) maintaining that something is absolutely unknowable; (3) maintaining that something is absolutely inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (see "[http://www.princeton.edu/~batke/peirce/frl_99.htm F.R.L.]" [First Rule of Logic], 1899).
**In American [[college football]], there are [[BCS conference#Popular usage|six conferences]] that automatically qualify for [[Bowl Championship Series]] games
* [[Paul Weiss (philosopher)|Paul Weiss]] built a system involving four modes of being: Actualities (substances in the sense of substantial, spatio-temporally finite beings), Ideality or Possibility (pure normative form), Existence (the dynamic field), and God (unity). (See Weiss's ''Modes of Being'', 1958).
*Number of players:
* [[Karl Popper]] outlined a tetradic schema to describe the growth of theories and, via generalization, also the emergence of new behaviors and living organisms: (1) problem, (2) tentative theory, (3) (attempted) error-elimination (especially by way of critical discussion), and (4) new problem(s). (See Popper's ''Objective Knowledge'', 1972, revised 1979.)
**[[Six-man football]] is a variant of American or Canadian football, played by smaller schools with insufficient enrollment to field the traditional 11-man (American) or 12-man (Canadian) squad
* [[John Boyd (military strategist)]] made his key concept the decision cycle or [[John Boyd (military strategist)#The OODA Loop|OODA loop]], consisting of four stages: (1) observation (data intake through the senses), (2) orientation (analysis and synthesis of data), (3) decision, and (4) action. Boyd held that his decision cycle has philosophical generality, though for strategists the point remains that, through swift decisions, one can disrupt an opponent's decision cycle.
**In football (soccer), the number of substitutes combined by both teams, that are allowed in the game.
* [[Richard McKeon]] outlined four classes (each with four subclasses) of modes of philosophical inquiry: (1) Modes of Being (Being); (2) Modes of Thought (That which is); (3) Modes of Fact (Existence); (4) Modes of Simplicity (Experience) – and, corresponding to them, four classes (each with four subclasses) of philosophical semantics: Principles, Methods, Interpretations, and Selections. (See McKeon's "Philosophic Semantics and Philosophic Inquiry" in ''Freedom and History and Other Essays'', 1989.)
**In [[ice hockey]], the number of players per team, including the goaltender, that are on the ice at any one time, excluding penalty situations.
* [[Jonathan Lowe]] (E.J. Lowe) argues in ''The Four-Category Ontology,'' 2006, for four categories: ''kinds'' (substantial universals), ''attributes'' (relational universals and property-universals), ''objects'' (substantial particulars), and ''modes'' (relational particulars and property-particulars, also known as "[[trope (philosophy)|tropes]]"). (See Lowe's "Recent Advances in Metaphysics," 2001, [http://www.cs.vassar.edu/~weltyc/fois/fois-2001/keynote/ Eprint])
**In [[volleyball]], 6 players from each team on each side play against each other
*Scoring and related terminology:
**In some [[sports]], 6 goals is known as a double-hat-trick, but is very hard to accomplish
**In [[American football|American]] and [[Canadian football]], a [[touchdown]] earns 6 points
**In Australian Rules football, six points are received for a goal
**In [[baseball scorekeeping]], the number 6 represents the [[shortstop]]'s position.
**In [[cricket]] (See [[cricket terminology#S|cricket terminology]]):
***a "six" or "sixer" is a shot in which the ball clears the [[boundary (cricket)|boundary]] without bouncing, scoring six runs
***there are six balls to an [[over (cricket)|over]]
*Jersey number 6 and car number 6:
**In [[football (soccer)|football/soccer]]:
***Is the number of AC Milan's centre back and captain [[Franco Baresi]]; the shirt was retired in 1997
**In [[NASCAR]]:
***The number 6 is currently owned by [[Roush Fenway Racing]]. Since the 2007 season, the first year in which Roush Racing was merged with the [[Fenway Sports Group]] that owns the Boston Red Sox, the [[Sprint Cup Series|Cup Series]] version of the car has been driven by [[David Ragan]]. From 1988 to 2006, [[Mark Martin]] drove the #6 in the Cup Series for what was then Roush Racing.
**In rugby:
***In most [[rugby league]] competitions (but not the European [[Super League]], which uses static squad numbering), the jersey number 6 is worn by the starting [[five-eighth]] (Southern Hemisphere term) or [[stand-off half]] (Northern Hemisphere term).
***In [[rugby union]], the starting blindside flanker wears jersey number 6. (Some teams use "left" and "right" flankers instead of "openside" and "blindside", with 6 being worn by the starting left flanker.)
** The jersey number 6 has been retired by several [[Major professional sports leagues in the United States and Canada|North American sports]] teams in honor of past playing greats or other key figures (or, in two cases, a team's fans):
*** In [[Major League Baseball]]:
**** The [[Atlanta Braves]], for [[manager (baseball)|manager]] [[Bobby Cox]]
**** The [[Boston Red Sox]], for [[Johnny Pesky]]
**** The [[Detroit Tigers]], for [[National Baseball Hall of Fame and Museum|Hall of Famer]] [[Al Kaline]]
**** The [[Minnesota Twins]], for [[Tony Oliva]]
**** The [[St. Louis Cardinals]], for Hall of Famer [[Stan Musial]]
**** The [[San Diego Padres]], for [[Steve Garvey]]
*** In the [[National Basketball Association|NBA]]:
**** The [[Boston Celtics]], for [[Naismith Memorial Basketball Hall of Fame|Hall of Famer]] [[Bill Russell]]
**** The [[Orlando Magic]], for their fans (the "sixth man")
**** The [[Philadelphia 76ers]], for Hall of Famer [[Julius Erving]]
**** The [[Phoenix Suns]], for [[Walter Davis (basketball)|Walter Davis]]
**** The [[Sacramento Kings]], also for their fans
*** In the [[National Football League|NFL]]:
**** The [[Kansas City Chiefs]], for [[Warren McVea]]
*** In the [[National Hockey League|NHL]]:
**** The [[Detroit Red Wings]], for [[Larry Aurie]]
**** The [[Pittsburgh Penguins]], for [[Ian Ackerman]]
**** The [[Toronto Maple Leafs]], for [[Hockey Hall of Fame|Hall of Famer]] [[Ace Bailey]]. The Leafs have a unique policy of not retiring numbers unless the player honoured either died or suffered a career-ending incident while a member of the team. Bailey suffered a fractured skull during a game in 1933; while he recovered and lived for nearly 60 years after the incident, he never played again. The Leafs would issue the number to [[Ron Ellis]] in 1968 at Bailey's personal request, and Ellis wore it until his own retirement in 1981.


==In technology==
==In technology==
[[File:U+2676 DejaVu Sans.svg|50px|right|4 as a resin identification code, used in recycling.]]
[[File:U+2678 DejaVu Sans.svg|80px|right|6 as a resin identification code, used in recycling.]]
* The [[resin identification code]] used in recycling to identify [[low-density polyethylene]].
*On most phones, the 6 key is associated with the letters [[M]], [[N]], and [[O]], but on the [[BlackBerry]] it is the key for [[J]] and [[K]], and on the BlackBerry 8700 series and [[BlackBerry Curve 8900|Curve 8900]] with full keyboard, it is the key for [[F]]
* Most [[furniture]] has four legs – tables, chairs, etc.
*The "[[6-meter band]]" in [[amateur radio]] includes the frequencies from 50 to 54&nbsp;MHz
* Four [[horse]]s (quadriga) is the maximal number of horses in one row for carriage.
*6 is the [[resin identification code]] used in recycling to identify [[polystyrene]]
* The [[four color process]] ([[CMYK]]) is used for [[printing]].
* Wide use of [[rectangle]]s (with four angles and four sides) because they have effective form and capability for close adjacency to each other (houses, rooms, tables, bricks, sheets of paper, screens, film frames).
* In the [[Rich Text Format]] specification, language code 4 is for the [[Chinese language]]. Codes for regional variants of Chinese are congruent to 4 mod 256.
* [[Credit card]] machines have four-twelve function keys.
* On most phones, the 4 key is associated with the letters [[G]], [[H]], and [[I]], but on the [[BlackBerry]] cellular phone, it is the key for [[D]] and [[F]].
* On many [[computer keyboard]]s, the "4" key may also be used to type the [[dollar sign]] ($) if the [[shift key]] is held down.
* It is the number of [[bit]]s in a [[nibble]], equivalent to half a [[byte]]
* In [[internet slang]], "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you".
* In [[Leet]]speak, "4" may be used to replace the letter "A".


==In transport==
==In calendars==
[[File:BKV m 4 jms.svg|100px|right]]
*In the ancient [[Roman calendar]], [[Sextilis]] was the sixth month. After the [[Julian calendar|Julian reform]], June became the sixth month and Sextilis was renamed August
* Most [[vehicle]]s, including [[motor vehicle]]s, and particularly [[automobile|cars/automobiles]] and light [[commercial vehicle]]s have four road [[wheel]]s.
*[[Sextidi]] was the sixth day of the [[decade]] in the [[French Revolutionary calendar]]
* "[[quattro (four wheel drive system)|quattro]]", meaning four in the Italian language, is used by [[Audi]] as a trademark to indicate that [[four-wheel drive]] (4WD) technologies are used on Audi-branded cars. The word "Quattro" was initially used by Audi in 1980 in its original 4WD coupé, the [[Audi Quattro]]. Audi also has a privately held subsidiary company called [[quattro GmbH]].
* [[List of highways numbered 4]]


==In sports==
==In the arts and entertainment==
* In [[cricket]], a four is a specific type of scoring event, whereby the ball crosses the [[boundary (cricket)|boundary]] after touching the ground at least one time, scoring four runs. Taking four wickets in four consecutive balls is typically referred to as a double hat trick (two consecutive, overlapping hat tricks).
*''[[The Super 6]]'' - 1966 animated cartoon series featuring six different super-powered heroes.
* In [[basketball]], the number four is used to designate the [[Power Forward (basketball)|Power Forward]] position, often referred to as "The four spot".
*The [[Bionic Six]] are the heroes of the eponymous animated series
* Also in [[basketball]], there is a term called the [[four point play]], when a fouled player attempts a [[3-point field goal]] and makes it, and makes the resulting [[free throw]].
*The number of sides on a cube, hence the highest number on a standard [[dice|die]]
* The number of quarters in an [[NBA]] or [[NFL]] game.
*The highest number on one end of a standard [[Dominoes|domino]]
* The basketball term [[Final Four]] refers to:
*[[The Power of Six]] is a book written by Pittacus Lore, and the second in the [[Lorien Legacies]] series.
** in the United States, the last four teams remaining in the NCAA playoff tournament, each of which is the winner of its respective region (for collegiate hockey the term [[Frozen Four]] is used).
*[[Number Six (Battlestar Galactica)|Number Six]] ([[Tricia Helfer]]), is a family of fictional characters from the reimagined science fiction television series, [[Battlestar Galactica (2004 TV series)|Battlestar Galactica]]
** In Europe, the last four teams remaining in many national and transnational club competitions, most notably the [[Euroleague Basketball|Euroleague]].
*Number 6 is a character in the book series [[Lorien Legacies]]
* In [[rowing (sport)|rowing]], a four refers to a [[boat]] for four rowers, with or without [[coxswain]]. In rowing nomenclature 4− represents a coxless four and 4+ represents a coxed four.
*Number 6 ([[Teresa Palmer]]) is a character in the movie ''[[I Am Number Four (film)|I Am Number Four]]'' (2011)
* There are four bases in the game of [[baseball]]: [[first base]], [[second base]], [[third base]], and [[home plate]]; to score a run, an offensive player must complete, in the sequence shown, a circuit of those four bases.
*Number 6, the main protagonist in ''[[The Prisoner]]'' played by [[Patrick McGoohan]], portrayed by [[Jim Caviezel]] in [[The Prisoner (2009 miniseries)|the remake.]]
* In [[baseball]] scoring, number 4 is assigned to the [[second baseman]]. Also, four is the most number of runs that can be scored on any single at bat, whereby all three baserunners and the batter score (the most common being via a [[grand slam (baseball)|grand slam]]).
* In [[gridiron football]] codes,
** In [[American football]], the offensive team has four downs (plays) to advance the ball 10 yards otherwise loss of possession occurs.
** four points are awarded in a handful of leagues for rarely attempted types of [[field goal (American football)|field goals]]; an example is in [[six-man football]]. Because of the difficulties of getting a successful kick due to the few players on the field, a field goal is worth four points. Also, in [[Arena Football]], a successful [[dropkick]]ed field goal attempt scores four points.
** the "four hole" in offense terminology is the space between the right guard and the right tackle on the offensive line
** the "four back" is an extra [[running back]] (outside the [[fullback (American football)|fullback]] and [[halfback (American football)|halfback]], often referred to as an [[H-back]]) in the backfield; e.g. a play call for a "44 lead" indicates the H-back will follow the fullback into the hole between the right guard and the right tackle.
* In [[rugby union]]:
** One of the two starting [[Lock (rugby union)|locks]] wears the jersey number 4.
** At several points in the history of the sport, 4 points were awarded for the following scores:
*** A [[goal from mark]] from 1891 to 1904 (3 points after that time; abolished in 1977).
*** A [[drop goal]] from 1891 to 1947 (now 3 points).
*** A [[try]] from 1971 to 1991 (now 5 points).
** In most league competitions, as well as the pool phases of the [[Rugby World Cup]] and many other worldwide championships, 4 competition points are awarded for a win (see [[rugby union bonus points system]]).
* In [[rugby league]]:
** A try is worth 4 points.
** In most competitions (though not the European [[Super League]], which uses static squad numbering), the starting [[Rugby league positions#Centres|left centre]] wears jersey number 4.
* The jersey number 4 has been retired by several [[Major professional sports leagues in the United States and Canada|North American sports]] teams in honor of past playing greats or other key figures:
** In [[Major League Baseball]]:
*** The [[Baltimore Orioles]], for [[National Baseball Hall of Fame and Museum|Hall of Fame]] [[manager (baseball)|manager]] [[Earl Weaver]].
*** The [[Boston Red Sox]], for Hall of Famer [[Joe Cronin]].
*** The [[Chicago White Sox]], for Hall of Famer [[Luke Appling]].
*** The [[Los Angeles Dodgers]], for Hall of Famer [[Duke Snider]].
*** The [[Milwaukee Brewers]], for Hall of Famer [[Paul Molitor]].
*** The [[History of the New York Giants (NL)|New York Giants]], for Hall of Famer [[Mel Ott]]; the team has continued to honor the number in its current home of [[San Francisco Giants|San Francisco]].
*** The [[New York Yankees]], for Hall of Famer [[Lou Gehrig]]. Notably, he was the first player in major North American sports to be so honored by a U.S.-based team (he was preceded in this honor by [[Ace Bailey]], whose [[6 (number)#In sports|#6]] was retired by the Toronto Maple Leafs five years earlier).
*** The [[Pittsburgh Pirates]], for Hall of Famer [[Ralph Kiner]].
** In the [[National Basketball Association|NBA]]:
*** The [[Chicago Bulls]], for [[Jerry Sloan]], who later served as the team's head coach and went on to a [[Naismith Memorial Basketball Hall of Fame|Hall of Fame]] career [[List of coaches in the Naismith Memorial Basketball Hall of Fame|in that role]] (mainly with the [[Utah Jazz]]).
*** The [[Detroit Pistons]], for [[List of players in the Naismith Memorial Basketball Hall of Fame|Hall of Fame player]] [[Joe Dumars]], who later served as team president.
*** The [[Milwaukee Bucks]], for [[Sidney Moncrief]].
*** The [[Brooklyn Nets#1967–1976: The ABA years|New York Nets]], for [[Wendell Ladner]], who died in [[Eastern Air Lines Flight 66|a 1975 plane crash]].
*** The [[Sacramento Kings]], for [[Chris Webber]].
*** The [[Utah Jazz]], for Hall of Fame player [[Adrian Dantley]].
** In the [[National Hockey League|NHL]]:
*** The [[Boston Bruins]], for [[Hockey Hall of Fame|Hall of Famer]] [[Bobby Orr]].
*** The [[Montreal Canadiens]], for Hall of Famer [[Jean Beliveau]].
*** The [[New Jersey Devils]], for Hall of Famer [[Scott Stevens]].
*** The [[Philadelphia Flyers]], for [[Barry Ashbee]].
*** The [[Toronto Maple Leafs]] have a policy of not retiring numbers unless the player honoured either died or suffered a career-ending incident while a member of the team. Other players whose numbers would otherwise be retired instead have their numbers enshrined by the team as "Honoured Numbers", which remain in circulation for future players. The number 4 is currently honoured for Hall of Famer [[Red Kelly]].
** In the [[National Football League|NFL]]:
*** The [[New York Giants]], for [[Pro Football Hall of Fame|Hall of Famer]] [[Tuffy Leemans]].


==In other fields==
==In other fields==
[[File:ICS Four.svg|right|thumb|100px|[[International maritime signal flag]] for 4]]
[[File:ICS Six.svg|right|thumb|66px|[[International maritime signal flags|International maritime signal flag]] for 6]]
''See also [[4 (disambiguation)]].''
[[File:Polydactyly 01 Lhand AP.jpg|right|thumb|200px|[[Radiography|X-ray]] of a [[Polydactyly|polydactyl]] [[human]] [[hand]] with six [[finger]]s]]
* The phrase "[[four-letter word]]" is used to describe most [[profanity|swear]] words in the [[English language]], as most swear words do indeed possess four letters.
* Four (四, formal writing: 肆, [[pinyin]] sì) is considered an [[unlucky number]] in [[Chinese culture|Chinese]], [[Korean culture|Korean]], [[Culture of Vietnam|Vietnamese]] and [[Culture of Japan|Japanese]] cultures because it sounds like the word "death" (死, [[pinyin]] sǐ). Due to that, many numbered product lines skip the "four": e.g. [[Nokia]] [[cell phones]] (there is no series beginning with a 4), [[Microsoft Windows]] (which switched to "Windows 95" for version 4<ref>http://windowsteamblog.com/blogs/windowsvista/archive/2008/10/14/why-7.aspx</ref>{{Failed verification|date=December 2012}}), [[PalmOne, Inc.|Palm]] [[Personal digital assistant|PDAs]], the [[Leisure Suit Larry (series)|Leisure Suit Larry]] games, etc. Some buildings skip floor 4 or replace the number with the letter "F", particularly in heavily Asian areas. ''See [[tetraphobia]]'' and ''[[Numbers in Chinese culture]]''.
* The number of characters in a canonical [[four-character idiom]].
* In the [[ICAO spelling alphabet|NATO phonetic alphabet]], the digit 4 is called "fower".
* In [[Astrology]], [[Cancer (constellation)|Cancer]] is the 4th [[astrological sign]] of the [[Zodiac]].
* In [[Tarot]], [[The Emperor (Tarot card)|The Emperor]] is the fourth [[trump]] or [[Major Arcana]] card.
* In [[Nintendo]]'s ''[[Mario Kart]]'' series, four is the number of courses that each cup holds.
* In ''[[Tetris]]'', a game named for the Greek word for 4, every shape in the game is formed of 4 blocks each.
* 4 represents the number of Justices on the [[Supreme Court of the United States]] necessary to grant a writ of [[certiorari]] (i.e., agree to hear a case; it is one less than the number necessary to render a majority decision).


==In music==
*The standard term in office for a [[United States senate|United States senator]] is six years
* In [[classical music]], [[Time signature|common time]] is constructed of four beats.
*The name of the smallest group of [[Cub Scout]]s, traditionally consisting of six people and is led by a 'sixer'.
* The number of movements in a [[symphony]].
*[[Six pack]] is a common form of packaging for six bottles or cans of drink (especially beer), and by extension, other assemblages of six items.
* The number of completed, numbered symphonies by [[Johannes Brahms]].
*The number of fundamental [[flight instruments]] lumped together on a cockpit display, called the [[Basic Six|six-pack]].
* The number of strings on a [[violin]], a [[viola]], a [[cello]], [[double bass]], a [[cuatro (instrument)|cuatro]] and a [[ukulele]], and the number of string pairs on a [[mandolin]].
*The number of [[Foot (length)|feet]] below ground level a [[coffin]] is traditionally buried; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead
* "Four colly birds" is the gift on the fourth day of Christmas in the carol "[[The Twelve Days of Christmas (song)|The Twelve Days of Christmas]]
*In [[Astrology]], [[Virgo (astrology)|Virgo]] is the 6th [[astrological sign]] of the [[Zodiac]]
* [[Four (Bloc Party album)|Four]], british rock album [[Bloc Party]]'s fourth full-length album.
*The number of dots in a [[Braille]] cell.
 
*The number of Royal Stickers that [[Mario]] must collect in the [[Nintendo 3DS]] game ''[[Paper Mario: Sticker Star]]''
==Groups of four==
*There are said to be no more than [[six degrees of separation]] between any two people on Earth. See also [[Six degrees (disambiguation)]].
* Four rules: [[addition]], [[subtraction]], [[multiplication]], [[division (mathematics)|division]].
*[[Extra-sensory perception]] is sometimes called the "sixth sense"
* [[Classical element#Classical elements in Greece|Greek classical elements]] ([[fire]], [[air]], [[water]], [[earth]]).
*Six [[Cardinal Directions]]: [[north]], [[south]], [[east]], [[west]], [[wikt:up|up]], and [[wikt:down|down]]
* [[Season|Four seasons]]: [[spring (season)|spring]], [[summer]], [[autumn]], [[winter]].
*The [[Six Dynasties]] form part of [[Chinese history]]
* Four [[Terrestrial planet|rocky planets]] in Earth's [[Solar System]]: [[Mercury (planet)|Mercury]], [[Venus]], [[Earth]], [[Mars]].
*6 is a lucky [[number in Chinese culture]]
* Four is the minimal number of contemporary [[continent]]s: [[Americas]], [[Afro-Eurasia|Eurafrasia]], [[Australia (continent)|Sahul]], [[Antarctica]].
*The [[Birmingham Six]] were held in prison for 16 years
* Approximately four weeks (4 times 7 days) to a lunar month ([[synodic month]] = 29.53 days). Thus the number four is universally an integral part of primitive sacred calendars.
*"Six" is used as an informal slang term for the British Secret Intelligence Service, [[MI6]]
* Four [[cardinal directions]]: [[north]], [[south]], [[east]], [[west]].
*[[Six Flags]] amusement parks and theme parks
* [[Four Temperaments]]: [[sanguine]], [[choleric]], [[melancholic]], [[phlegmatic]].
* [[Humorism|Four Humors]]: [[blood]], [[yellow bile]], [[black bile]], [[phlegm]].
* [[Four Great Ancient Capitals of China]]
* [[Four corner method]]
* [[Four cardinal principles|Cardinal principles]]
* [[Four cardinal virtues]]: justice, prudence, temperance, fortitude.
* Four canonical [[Christianity|Christian]] [[Gospels]], attributed to the [[Four Evangelists]] ([[Matthew the Evangelist|Matthew]], [[Mark the Evangelist|Mark]], [[Luke the Evangelist|Luke]], and [[John the Evangelist|John]])
* [[Four horsemen of the Apocalypse]]: [[war]], [[famine]], [[infectious disease|pestilence]], [[death]].
* Four [[suit (cards)|suits]] of [[playing card]]s: hearts, diamonds, clubs, spades.
* Four [[nation]]s of the [[United Kingdom]]: England, [[Wales]], [[Scotland]], [[Northern Ireland]].
* [[Four Noble Truths]] in the [[Buddhist]] religion.
* Four estates: [[politics]], [[public administration|administration]], [[judiciary]], [[journalism]]. Especially in the expression "[[Fourth Estate]]", which means journalism.
* [[Four Corners Monument|Four Corners]] is the only location in the United States where four [[U.S. state|states]] come together at a single point: [[Colorado]], [[Utah]], [[New Mexico]], and [[Arizona]].
* The [[Fantastic Four]]: Mr. Fantastic, The Invisible Woman, The Human Torch, The Thing.
* [[The Beatles]] were also known as the "Fab Four": John Lennon, Ringo Starr, George Harrison, Paul McCartney.
* [[Gang of Four (band)|Gang of Four]] is a British [[post-punk]] [[rock and roll|rock]] band formed in the late 1970s.
* Typically there are four string players in a classical [[string quartet]], usually two [[violin]]ists, a [[viola|violist]], and a [[cello|cellist]].
* Four rivers in the [[Garden of Eden]] ([[Book of Genesis|Genesis]] 2:10–14): [[Pishon]] (perhaps the Jaxartes or [[Syr Darya]]), [[Gihon]] (perhaps the Oxus or [[Amu Darya]]), Hiddekel ([[Tigris]]), and P'rat ([[Euphrates]])
* There are also four years in a single [[Olympiad]] (duration between the [[Olympic Games]]). Many major international sports competitions follow this cycle, among them the [[FIFA World Cup]] and its [[FIFA Women's World Cup|women's version]], the FIBA World Championships for [[FIBA World Championship|men]] and [[FIBA World Championship for Women|women]], and the [[Rugby World Cup]].
* Four opposed camps of the morality and nature of evil: [[moral absolutism]], [[amoralism]], [[moral relativism]], and [[moral universalism]].
* There are four limbs on the [[human]] body.


==References==
==References==
{{Reflist}}
{{Reflist}}
* Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 55 - 58
 
* ''The Odd Number 6'', JA Todd, Math. Proc. Camb. Phil. Soc. 41 (1945) 66—68
* ''A Property of the Number Six'', Chapter 6, P Cameron, JH v. Lint, ''Designs, Graphs, Codes and their Links'' ISBN 0-521-42385-6
* Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 67 - 69


==External links==
==External links==
{{wiktionary|four}}
* [http://www.numdic.com/6 The Number 6]
{{Commons category|4 (number)}}
* [http://www.positiveintegers.org/6 The Positive Integer 6]
* [http://www.marijn.org/everything-is-4 Marijn.Org on Why is everything four?]
* [http://primes.utm.edu/curios/page.php/6.html Prime curiosities: 6]
* [http://www.samuel-beckett.net/Penelope/four_symbolism.html A few thoughts on the number four], by Penelope Merritt at samuel-beckett.net
* [http://www.numdic.com/4 The Number 4]
* [http://www.positiveintegers.org/4 The Positive Integer 4]
* [http://primes.utm.edu/curios/page.php/4.html Prime curiosities: 4]


{{Integers|zero}}
{{Integers|zero}}


{{Superstitions}}
{{DEFAULTSORT:6 (Number)}}
 
[[Category:Integers|06]]
[[Category:Integers|04]]
[[Category:Superstitions about numbers]]

Revision as of 17:57, 10 August 2014

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The SI prefix for 10006 is exa (E), and for its reciprocal atto- (a).

In mathematics

6 is the smallest positive integer which is neither a square number nor a prime number. Six is the second smallest composite number; its proper divisors are 1, 2 and 3.

Since six equals the sum of its proper divisors, six is the smallest perfect number, Granville number, and 𝒮-perfect number.[1][2]

As a perfect number:

  • 6 is related to the Mersenne prime 3, since 21(22 - 1) = 6. (The next perfect number is 28.)
  • 6 is the only even perfect number that is not the sum of successive odd cubes.[3]
  • As a perfect number, 6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one number; the square number, 25.

Six is the only number that is both the sum and the product of three consecutive positive numbers.[4]

Unrelated to 6 being a perfect number, a Golomb ruler of length 6 is a "perfect ruler."[5] Six is a congruent number.

Six is the first discrete biprime (2.3) and the first member of the (2.q) discrete biprime family.

Six is a unitary perfect number, a harmonic divisor number and a superior highly composite number, the last to also be a primorial. The next superior highly composite number is 12. The next primorial is 30.

5 and 6 form a Ruth-Aaron pair under either definition.

The smallest non-abelian group is the symmetric group S3 which has 3! = 6 elements.

S6, with 720 elements, is the only finite symmetric group which has an outer automorphism. This automorphism allows us to construct a number of exceptional mathematical objects such as the S(5,6,12) Steiner system, the projective plane of order 4 and the Hoffman-Singleton graph. A closely related result is the following theorem: 6 is the only natural number n for which there is a construction of n isomorphic objects on an n-set A, invariant under all permutations of A, but not naturally in 1-1 correspondence with the elements of A. This can also be expressed category theoretically: consider the category whose objects are the n element sets and whose arrows are the bijections between the sets. This category has a non-trivial functor to itself only for n=6.

6 similar coins can be arranged around a central coin of the same radius so that each coin makes contact with the central one (and touches both its neighbors without a gap), but seven cannot be so arranged. This makes 6 the answer to the two-dimensional kissing number problem. The densest sphere packing of the plane is obtained by extending this pattern to the hexagonal lattice in which each circle touches just six others.

A cube has 6 faces

6 is the largest of the four all-Harshad numbers.

A six-sided polygon is a hexagon, one of the three regular polygons capable of tiling the plane. Figurate numbers representing hexagons (including six) are called hexagonal numbers. Because 6 is the product of a power of 2 (namely 21) with nothing but distinct Fermat primes (specifically 3), a regular hexagon is a constructible polygon.

Six is also an octahedral number. It is a triangular number and so is its square (36).

There are six basic trigonometric functions.

There are six convex regular polytopes in four dimensions.

Six is the four-bit binary complement of number nine (6 = 01102 and 9 = 10012).

The six exponentials theorem guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.

All primes above 3 are of the form 6n±1 for n≥1.

In numeral systems

Base Numeral system Representation
2 binary 110
3 ternary 20
4 quaternary 12
5 quinary 11
6 senary 10
over 6 (decimal, hexadecimal) 6

In bases 10, 15 and 30, 6 is a 1-automorphic number.

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
6×x 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 300 600 6000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
6÷x 6 3 2 1.5 1.2 1 0.857142 0.75 0.6 0.6 0.54 0.5 0.461538 0.428571 0.4
x÷6 0.16 0.3 0.5 0.6 0.83 1 1.16 1.3 1.5 1.6 1.83 2 2.16 2.3 2.5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
6x 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
x6 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809

Greek and Latin word parts

Hexa

Hexa is classical Greek for "six". Thus:

The prefix sex-

Sex- is a Latin prefix meaning "six". Thus:

  • Senary is the ordinal adjective meaning "sixth"
  • People with sexdactyly have six fingers on each hand (see above photo)
  • The measuring instrument called a sextant got its name because its shape forms one-sixth of a whole circle
  • A group of six musicians is called a sextet
  • Six babies delivered in one birth are sextuplets

Evolution of the glyph

The evolution of our modern glyph for 6 appears rather simple when compared with that for the other numerals. Our modern 6 can be traced back to the Brahmins of India, who wrote it in one stroke like a cursive lowercase e rotated 90 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Ghubar Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.[6]

On the seven-segment displays of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a 'b' is not practical.

Just as in most modern typefaces, in typefaces with text figures the 6 character usually has an ascender, as, for example, in .

This numeral resembles an inverted 9. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.

In music

A standard guitar has 6 strings

In artists

In instruments

  • A standard guitar has 6 strings
  • Most woodwind instruments have 6 basic holes or keys (e.g., bassoon, clarinet, pennywhistle, saxophone); these holes or keys are usually not given numbers or letters in the fingering charts

In music theory

  • There are 6 semitones in a tritone

In works

  • "Six geese a-laying" were given as a present on the sixth day in the popular Christmas carol, "The Twelve Days of Christmas."
  • Divided in six arias, Hexachordum Apollinis is generally regarded as one of the pinnacles of Johann Pachelbel's oeuvre.
  • The concerti grossi Opus 3, organ concertos Opus 4 and Opus 7 (each) by Georg Frideric Handel.
  • The sixth album by Dream Theater, Six Degrees Of Inner Turbulence, was based around the number six: the album has six songs, and the sixth song — that is, the complete second disc — explores the stories of six individuals suffering from various mental illnesses.

In religion

See also 666.

In science

Astronomy

Biology

Chemistry

A molecule of benzene has a ring of 6 carbon atoms
A molecule of benzene has a ring of 6 carbon atoms
The cells of a beehive are 6-sided

Medicine

  • There are 6 tastes in traditional Indian Medicine called Ayurveda: sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body
  • Phase 6 is one of six pandemic influenza phases

Physics

In the Standard Model of particle physics, there are 6 types of quark and 6 types of lepton

In sports

In technology

6 as a resin identification code, used in recycling.
6 as a resin identification code, used in recycling.

In calendars

In the arts and entertainment

In other fields

International maritime signal flag for 6
X-ray of a polydactyl human hand with six fingers

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  • The Odd Number 6, JA Todd, Math. Proc. Camb. Phil. Soc. 41 (1945) 66—68
  • A Property of the Number Six, Chapter 6, P Cameron, JH v. Lint, Designs, Graphs, Codes and their Links ISBN 0-521-42385-6
  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 67 - 69

Template:Integers

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  2. Template:Cite web
  3. David Wells, The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books (1987): 67
  4. Peter Higgins, Number Story. London: Copernicus Books (2008): 12
  5. Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 72
  6. 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. 24.66