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| {{about|the number|the year|3|other uses|3 (disambiguation)}}
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| {{Example farm|date=July 2012}}
| |
| {{Infobox number
| |
| | number = 3
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| | numeral = [[Ternary numeral system|ternary]]
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| | factorization = [[prime number|prime]]
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| | divisor = 1, 3
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| | roman unicode = Ⅲ, ⅲ
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| | greek prefix = [[wikt:tri-|tri-]]
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| | latin prefix = [[wikt:tre-|tre-]]/[[wikt:ter-|ter-]]
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| | lang1 = [[Arabic (language)|Arabic]]
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| | lang1 symbol = {{resize|150%|٣,3}}
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| | lang2 = [[Urdu]]
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| | lang2 symbol = {{Urdu numeral|3|20}}
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| | lang3 = [[Bengali language|Bengali]]
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| | lang3 symbol = {{resize|150%|৩}}
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| | lang4 = [[Chinese numeral|Chinese]]
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| | lang4 symbol = 三，弎，叁
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| | lang5 = [[Devanāgarī]]
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| | lang5 symbol = {{resize|150%|३}} (tin)
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| | lang6 = [[Ge'ez alphabet|Ge'ez]]
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| | lang6 symbol = ፫
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| | lang7 = [[Greek numerals|Greek]]
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| | lang7 symbol = γ (or Γ)
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| | lang8 = [[Hebrew (language)|Hebrew]]
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| | lang8 symbol = {{resize|150%|ג}}
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| | lang9 = [[Japanese numerals|Japanese]]
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| | lang9 symbol = {{resize|150%|三}}
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| | lang10 = [[Khmer numerals|Khmer]]
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| | lang10 symbol = {{resize|150%|៣}}
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| | lang11 = [[Korean numerals|Korean]]
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| | lang11 symbol = 셋,삼
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| | lang12 = [[Malayalam language|Malayalam]]
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| | lang12 symbol = {{resize|150%|൩}}
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| | lang13 = [[Tamil language|Tamil]]
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| | lang13 symbol = {{resize|150%|௩}}
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| | lang14 = [[Telugu language|Telugu]]
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| | lang14 symbol = {{resize|150%|౩}}
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| | lang15 = [[Thai language|Thai]]
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| | lang15 symbol = {{resize|150%|๓}}
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| }}
| |
| '''3''' ('''three'''; {{IPAc-en|ˈ|θ|r|iː}}) is a [[number]], [[Numeral system|numeral]], and [[glyph]]. It is the [[natural number]] following [[2 (number)|2]] and preceding [[4 (number)|4]].
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| | |
| ==In mathematics==
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| * Three is approximately [[pi|π]] (actually closer to 3.14159) when doing rapid engineering guesses or estimates. The same is true if one wants a rough-and-ready estimate of [[E (mathematical constant)|''e'']], which is actually approximately 2.71828.
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| * Three is the first odd [[prime number]],<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 39</ref> and the second smallest prime. It is both the first [[Fermat prime]] (2<sup>2<sup>''n''</sup></sup> + 1) and the first [[Mersenne prime]] (2<sup>''n''</sup> − 1), the only number that is both, as well as the first [[lucky prime]]. However, it is the second [[Sophie Germain prime]], the second Mersenne prime exponent, the second [[factorial prime]] (2! + 1), the second [[Lucas prime]], the second [[Stern prime]].
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| * Three is the first [[unique prime]] due to the properties of its reciprocal.
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| * Three is the [[aliquot sum]] of [[4 (number)|4]].
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| * Three is the third [[Heegner number]].
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| * According to [[Pythagoras]] and the [[Pythagoreanism|Pythagorean]] school, the number 3, which they called ''triad'', is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.<ref>{{citation |author=Priya Hemenway |title=Divine Proportion: Phi In Art, Nature, and Science |publisher=Sterling Publishing Company Inc. |year=2005 |isbn=1-4027-3522-7 |pages=53–54}}</ref>
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| * Three is the second [[triangular number]] and it is the only prime triangular number. Three is the only prime which is one less than a [[square number|perfect square]]. Any other number which is ''n''<sup>2</sup> − 1 for some integer ''n'' is not prime, since it is (''n'' − 1)(''n'' + 1). This is true for 3 as well, but in its case one of the factors is 1.
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| * Three non-collinear points determine a [[Plane (mathematics)|plane]] and a [[circle]].
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| * Three is the fourth [[Fibonacci number]]. In the [[Perrin sequence]], however, 3 is both the zeroth and third [[Perrin number]]s.
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| * Three is the fourth [[open meandric number]].
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| * [[Vulgar fraction]]s with 3 in the [[denominator]] have a single [[numerical digit|digit]] repeating sequences in their [[decimal]] expansions, (.000..., .333..., .666...)
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| * A [[natural number]] is [[divisible]] by three if the sum of its digits in [[base 10]] is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any [[permutation]] of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc.). See also [[Divisibility rule]]. This works in [[base 10]] and in any [[positional notation|positional numeral system]] whose [[radix|base]] divided by three leaves a remainder of one (bases 4, 7, 10, etc.).
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| * A [[triangle]] is the only figure which, if all endpoints have hinges, will never change its shape unless the sides themselves are bent.
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| * 3 is the smallest prime of a [[Mersenne prime]] power tower 3, 7, 127, 170141183460469231731687303715884105727. It is not known whether any more of the terms are prime.
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| * Three of the five [[regular polyhedra]] have triangular faces — the [[tetrahedron]], the [[octahedron]], and the [[icosahedron]]. Also, three of the five [[regular polyhedra]] have [[vertex (geometry)|vertices]] where three faces meet — the [[tetrahedron]], the [[hexahedron]] ([[cube]]), and the [[dodecahedron]]. Furthermore, only three different types of [[polygons]] comprise the faces of the five [[regular polyhedra]] — the [[triangle]], the [[quadrilateral]], and the [[pentagon]].
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| * There are only three distinct 4×4 [[panmagic square]]s.
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| * Only three [[tetrahedral number]]s are also perfect squares.
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| * The first number, according to the [[Pythagoreans]], and the first male number.
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| * The first number, according to [[Proclus]], being the first number such that ''n''<sup>2</sup> is greater than 2''n''.
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| * The [[trisection of the angle]] was one of the three famous problems of antiquity.
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| * 3 is the second [[triangular number]].
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| * [[Gauss]] proved that every integer is the sum of at most 3 [[triangular numbers]].
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| * Gauss proved that for any prime number p (with the sole exception of 3) the product of its [[Primitive root modulo n|primitive roots]] is ≡ 1 (mod p).
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| * Any number not in the form of 4<sup>''n''</sup>(8''m''+7) is the sum of 3 squares.
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| | |
| ===In numeral systems===
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| It is frequently noted by historians of numbers that early counting systems often
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| relied on the three-patterned concept of "One- Two- Many" to describe counting limits.
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| In other words, in their own language equivalent way, early peoples had a word to
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| describe the quantities of one and two, but any quantity beyond this point was
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| simply denoted as "Many". As an extension to this insight, it can also be noted that
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| early counting systems appear to have had limits at the numerals 2, 3, and 4. References
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| to counting limits beyond these three indices do not appear to prevail as consistently
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| in the historical record.
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| | |
| ===List of basic calculations===
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| {|class="wikitable" style="text-align: center; background: white"
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| |-
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| !width="105px"|[[Multiplication]]
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| !1
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| !2
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| !3
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| !4
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| !5
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| !6
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| !7
| |
| !8
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| !9
| |
| !10
| |
| !11
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| !12
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| !13
| |
| !14
| |
| !15
| |
| !16
| |
| !17
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| !18
| |
| !19
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| !20
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| !21
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| !22
| |
| !23
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| !24
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| !25
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| !50
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| !100
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| !1000
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| |-
| |
| |<math>3 \times x</math>
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| |'''3'''
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| |[[6 (number)|6]]
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| |[[9 (number)|9]]
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| |[[12 (number)|12]]
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| |[[15 (number)|15]]
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| |[[18 (number)|18]]
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| |[[21 (number)|21]]
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| |[[24 (number)|24]]
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| |[[27 (number)|27]]
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| |[[30 (number)|30]]
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| |[[33 (number)|33]]
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| |[[36 (number)|36]]
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| |[[39 (number)|39]]
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| |[[42 (number)|42]]
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| |[[45 (number)|45]]
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| |[[48 (number)|48]]
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| |[[51 (number)|51]]
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| |[[54 (number)|54]]
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| |[[57 (number)|57]]
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| |[[60 (number)|60]]
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| |[[63 (number)|63]]
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| |[[66 (number)|66]]
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| |[[69 (number)|69]]
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| |[[72 (number)|72]]
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| |[[75 (number)|75]]
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| |[[150 (number)|150]]
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| |[[300 (number)|300]]
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| |[[3000 (number)|3000]]
| |
| |}
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| | |
| {|class="wikitable" style="text-align: center; background: white"
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| |-
| |
| !width="105px"|[[Division (mathematics)|Division]]
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| !1
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| !2
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| !3
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| !4
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| !5
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| !6
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| !7
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| !8
| |
| !9
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| !10
| |
| !width="5px"|
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| !11
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| !12
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| !13
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| !14
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| !15
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| |-
| |
| |<math>3 \div x</math>
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| |'''3'''
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| |[[1 (number)|1]].[[5 (number)|5]]
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| |1
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| |[[0 (number)|0]].75
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| |0.6
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| |0.5
| |
| |<math>0.\overline{428571}</math>
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| |0.[[375 (number)|375]]
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| |<math>0.\overline{3}</math>
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| |0.3
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| !
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| |<math>0.\overline{27}</math>
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| |0.[[25 (number)|25]]
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| |<math>0.\overline{230769}</math>
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| |<math>0.2\overline{142857}</math>
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| |0.2
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| |-
| |
| |<math>x \div 3</math>
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| |<math>0.\overline{3}</math>
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| |<math>0.\overline{6}</math>
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| |1
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| |<math>1.\overline{3}</math>
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| |<math>1.\overline{6}</math>
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| |2
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| |<math>2.\overline{3}</math>
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| |<math>2.\overline{6}</math>
| |
| |'''3'''
| |
| |<math>3.\overline{3}</math>
| |
| !
| |
| |<math>3.\overline{6}</math>
| |
| |4
| |
| |<math>4.\overline{3}</math>
| |
| |<math>4.\overline{6}</math>
| |
| |5
| |
| |}
| |
| | |
| {|class="wikitable" style="text-align: center; background: white"
| |
| |-
| |
| !width="105px"|[[Exponentiation]]
| |
| !1
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| !2
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| !3
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| !4
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| !5
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| !6
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| !7
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| !8
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| !9
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| !10
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| !width="5px"|
| |
| !11
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| !12
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| !13
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| |-
| |
| |<math>3 ^ x\,</math>
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| |'''3'''
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| |9
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| |27
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| |[[81 (number)|81]]
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| |[[243 (number)|243]]
| |
| |729
| |
| |2187
| |
| |6561
| |
| |19683
| |
| |59049
| |
| !
| |
| |177147
| |
| |531441
| |
| |1594323
| |
| |-
| |
| |<math>x ^ 3\,</math>
| |
| |1
| |
| |[[8 (number)|8]]
| |
| |[[27 (number)|27]]
| |
| |[[64 (number)|64]]
| |
| |[[125 (number)|125]]
| |
| |[[216 (number)|216]]
| |
| |[[343 (number)|343]]
| |
| |[[512 (number)|512]]
| |
| |729
| |
| |[[1000 (number)|1000]]
| |
| !
| |
| |1331
| |
| |1728
| |
| |2197
| |
| |}
| |
| | |
| ==Evolution of the glyph==
| |
| [[File:Evolution3glyph.png|x50px|right]]
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| Three is the largest number still written with as many lines as the number represents. (The [[Ancient Rome|Ancient Romans]] usually wrote 4 as IIII, but this was almost entirely replaced by the [[subtractive notation]] IV in the Middle Ages.) To this day 3 is written as three lines in Roman and [[Chinese numerals]]. This was the way the [[Brahmin]] Indians wrote it, and the [[Gupta Empire|Gupta]] made the three lines more curved. The Nagari started rotating the lines clockwise and ending each line with a slight downward stroke on the right. Eventually they made these strokes connect with the lines below, and evolved it to a character that looks very much like a modern 3 with an extra stroke at the bottom. It was the Western Ghubar [[Arab]]s who finally eliminated the extra stroke and created our modern 3. (The "extra" stroke, however, was very important to the Eastern Arabs, and they made it much larger, while rotating the strokes above to lie along a horizontal axis, and to this day Eastern Arabs write a 3 that looks like a mirrored 7 with ridges on its top line):
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| <span style="font-size:200%;">٣</span><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): 393, Fig. 24.63</ref>
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| | |
| While the shape of the 3 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:Text figures 036.svg|52px]].
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| In some [[French language|French]] text-figure typefaces, though, it has an ascender instead of a descender.
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| | |
| A common variant of the digit 3 has a flat top, similar to the character {{unicode|Ʒ}} ([[ezh (letter)|ezh]]). Since this form is sometimes used to prevent people from fraudulently changing a 3 into an 8, it is sometimes called a ''banker's 3''.
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| | |
| ==In science==
| |
| | |
| * The Roman numeral III stands for [[giant star]] in the [[stellar classification|Yerkes spectral classification scheme]].
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| * Three is the [[atomic number]] of [[lithium]].
| |
| * We perceive our [[universe]] to have [[Three-dimensional space|three spatial]] [[dimensions]], but some theories suggest there are more that we're not able to detect, such as [[string theory]].
| |
| | |
| ==In religion==
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| {{Main|Triple deity}}
| |
| Many world religions contain triple deities or concepts of trinity, including:
| |
| * the [[Christianity|Christian]] [[Trinity|Holy Trinity]]
| |
| * the [[Hindu]] [[Trimurti]]
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| * the Hindu [[Tridevi]]
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| * the [[Three Jewels]] of [[Buddhism]]
| |
| * the [[Three Pure Ones]] of [[Taoism]]
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| * the [[Triple Goddess (Neopaganism)|Triple Goddess]] of [[Wicca]]
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| | |
| [[File:Shield-Trinity-Scutum-Fidei-English.svg|thumb|The [[Shield of the Trinity]] is a diagram of the Christian doctrine of the Trinity]]
| |
| | |
| ===Christianity===
| |
| * The [[threefold office]] of Christ is a Christian doctrine that Christ performs the functions of [[prophet]], [[priest]], and [[Christ the king|king]].
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| ===In Buddhism===
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| * The Triple [[Bodhi]] (ways to understand the end of birth) are Budhu, Pasebudhu, and Mahaarahath.
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| | |
| ===In Hinduism===
| |
| [[Image:Om.svg|thumb|150px|right|The "[[Om]]" symbol, in [[Devanagari]] is also written ओ३म् (''ō̄m'' {{IPA-sa|õːːm|}}), where ३ is दीर्घ (''dirgha'', "'''three''' times as long")]]
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| * The [[Trimurti]]: [[Brahma]] the Creator, [[Vishnu]] the Preserver, and [[Shiva]] the Destroyer.
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| * The three [[Gunas]] underlie action, in the [[Historical Vedic religion|Vedic]] system of knowledge.
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| | |
| ===In Norse mythology===
| |
| Three is a very significant number in [[Norse mythology]], along with its powers 9 and 27.
| |
| * Prior to [[Ragnarök]], there will be three hard winters without an intervening summer, the [[Fimbulwinter]].
| |
| * Odin endured three hardships upon the World Tree in his quest for the [[runic alphabet|runes]]: he hanged himself, wounded himself with a spear, and suffered from hunger and thirst.
| |
| * [[Borr|Bor]] had three sons, [[Odin]], [[Vili]], and [[Vé]].
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| | |
| ===Other religions===
| |
| * The [[Wicca]]n [[Rule of Three (Wiccan)|Rule of Three]].
| |
| * The [[Triple Goddess (Neopaganism)|Triple Goddess]]: Maiden, Mother, Crone; the three fates.
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| | |
| ===In esoteric tradition===
| |
| * The [[Theosophical Society]] has [[Theosophy#The three objects|three conditions of membership]].
| |
| * [[Gurdjieff]]'s [[Three Centres|Three Centers]] and the [[Fourth Way|Law of Three]].
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| | |
| ===As a lucky or unlucky number===
| |
| {{Unreferenced section|date=April 2009}}
| |
| Three (三, formal writing: 叁, [[pinyin]] ''sān'', [[Cantonese]]: ''saam''<sup>1</sup>) is considered a [[numerology|good number]] in [[Chinese culture]] because it sounds like the word "alive" (生 pinyin ''shēng'', Cantonese: ''saang''<sup>1</sup>), compared to [[4 (number)|four]] (四, pinyin: ''sì'', Cantonese: ''sei''<sup>1</sup>), which sounds like the word "death" (死 pinyin ''sǐ'', Cantonese: ''sei''<sup>2</sup>).
| |
| | |
| Counting to three is common in situations where a group of people wish to perform an action in [[synchrony]]: ''Now, on the count of three, everybody pull!'' Assuming the counter is proceeding at a uniform rate, the first two counts are necessary to establish the rate, and the count of "three" is predicted based on the timing of the "one" and "two" before it. Three is likely used instead of some other number because it requires the minimal amount counts while setting a rate.
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| | |
| In [[Vietnam]], there is a superstition that considers it bad luck to take a photo with three people in it; it is professed that the person in the middle will die soon.
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| | |
| There is another superstition that it is unlucky to take a [[Three on a match (superstition)|third light]], that is, to be the third person to light a cigarette from the same match or lighter. This superstition is sometimes asserted to have originated among soldiers in the trenches of the First World War when a sniper might see the first light, take aim on the second and fire on the third.
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| | |
| The phrase "Third time's the charm" refers to the superstition that after two failures in any endeavor, a third attempt is more likely to succeed. This is also sometimes seen in reverse, as in "third man [to do something, presumably forbidden] gets caught".
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| | |
| [[Luck]], especially bad luck, is often said to "come in threes".<ref>See "[http://www.encyclopedia.com/doc/1O214-bad.html bad]" in the ''Oxford Dictionary of Phrase and Fable'', 2006, via Encyclopedia.com.</ref>
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| | |
| ==In philosophy== | |
| {{Main|Trichotomy (philosophy)}}
| |
| * The three [[Doshas]] (weaknesses) and their [[antidote]]s are the basis of [[Ayurvedic medicine]] in India.
| |
| * Philosophers such as [[Aquinas]], [[Immanuel Kant|Kant]], [[Hegel]], and [[Charles Sanders Peirce|C. S. Peirce]] have made threefold divisions, or trichotomies, which have been important in their work.
| |
| * [[Hegel]]'s [[Dialectic#Hegelian dialectics|dialectic]] of [[Thesis, antithesis, synthesis|Thesis + Antithesis = Synthesis]] creates three-ness from two-ness.
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| | |
| ==In sports== | |
| * In [[association football]]<nowiki/>in almost all leagues, and in the group phases of most international competitions, [[Three points for a win|3 competition points]] are awarded for a win.
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| * In [[Gaelic football]], [[hurling]] and [[camogie]], a "goal", with a scoring value of 3, is awarded when the attacking team legally sends the ball into the opponent's goal.
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| * In [[baseball]], 3 is the number of strikes before the batter is [[strikeout|out]] and the number of outs per side per inning.
| |
| * In [[basketball]]:
| |
| ** A shot made from [[three-point field goal|behind the three-point arc]] is worth 3 points (except in the [[3x3 (basketball)|3x3 variant]], in which it is worth 2 points).
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| ** A potential "three-point play" exists when a player is fouled while successfully completing a two-point [[Field goal (basketball)|field goal]], thus being awarded one additional [[free throw]] attempt.
| |
| ** On offense, the "[[Three seconds rule|3-second rule]]" states that an offensive player cannot remain in the opponent's free throw lane for more than 3 seconds while his team is in possession of the ball and the clock is running.
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| ** In the NBA only, the [[Defensive three-second violation|defensive 3-second violation]], also known as "illegal defense", states that a defensive player cannot remain in his own free throw lane for more than 3 seconds unless he is actively guarding an offensive player.
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| * A [[hat-trick]] in sports is associated with succeeding at anything three times in three consecutive attempts, as well as when any player in ice hockey or soccer scores three goals in one game (whether or not in succession). In [[cricket]], if a bowler takes 3 wickets in a row it is called a hat trick.
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| * A [[threepeat]] is a term for a team that wins three consecutive championships.
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| * A [[triathlon]] consists of three events: swimming, bicycling, and running.
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| ==See also==
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| {{Portal|Mathematics}}
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| * [[Cube (algebra)]] – (3 [[superscript]])
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| * [[Third]]
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| ==References==
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| {{refimprove|date=May 2013}}
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| {{Reflist}}
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| * Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 46–48
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| ==External links==
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| {{Wiktionary|three}}
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| {{Commons category|3}}
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| * [http://threes.com/ Tricyclopedic Book of Threes] by Michael Eck
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| * [http://www.meddean.luc.edu/lumen/MedEd/GrossAnatomy/Threes.html Threes in Human Anatomy] by Dr. John A. McNulty
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| * {{cite web|last=Grime|first=James|title=3 is everywhere|url=http://www.numberphile.com/videos/three.html|work=Numberphile|publisher=[[Brady Haran]]}}
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| * [http://www.numdic.com/3 The Number 3]
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| * [http://www.positiveintegers.org/3 The Positive Integer 3]
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| * [http://primes.utm.edu/curios/page.php/3.html Prime curiosities: 3]
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| {{Integers|zero}}
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| {{DEFAULTSORT:3 (Number)}}
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| [[Category:Integers|03]]
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