ผลต่างระหว่างรุ่นของ "ค่าคงตัวทางคณิตศาสตร์"
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บรรทัด 12:
: R - [[จำนวนตรรกยะ]], A - [[จำนวนพีชคณิต|จำนวนอตรรกยะ (พีชคณิต)]], T - [[จำนวนอดิศัย|จำนวนอตรรกยะ (อดิศัย)]]
: Gen - [[คณิตศาสตร์|ทั่วไป]], NuT - [[ทฤษฎีจำนวน]], ChT - [[ทฤษฎีความอลวน]], Com - [[คณิตศาสตร์เชิงการจัด]], Inf - [[ทฤษฎีสารสนเทศ]], Ana - [[คณิตวิเคราะห์]]
{| class="wikitable"
|- bgcolor=#a0e0a0
! Symbol || Approximate Value || Name || Field|| N || First Described || # of Known Digits
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">0</div>
|| 0
|| [[0_(number)|Zero]]
|| '''[[Mathematics|Gen]]'''
| align="center" | ''[[rational number|R]]''
| align=right | c. [[7th_century_BC|7th]]-[[5th_century_BC|5th century BC]]
| align=right | N/A
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">1</div>
|| 1
|| [[1_(number)|One]], Unity
|| '''[[Mathematics|Gen]]'''
| align="center" | ''[[rational number|R]]''
| align=right |
| align=right | N/A
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">''i''</div>
|| √−1
|| [[Imaginary unit]]
|| '''[[Mathematics|Gen]]''', '''[[Mathematical analysis|Ana]]'''
| align="center" | ''[[algebraic number|A]]''
| align=right | [[16th century]]
| align=right | N/A
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">π</div>
|| ≈ 3.14159 26535 89793 23846 26433 83279 50288
|| [[Pi]], [[Archimedes]]' constant or [[Ludolph van Ceulen|Ludolph]]'s number
|| '''[[Mathematics|Gen]]''', '''[[Mathematical analysis|Ana]]'''
| align="center" | ''[[transcendental number|T]]''
| align=right | by c. [[2000 BC|2000 BC]]
| align=right | 1,241,100,000,000
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">''e''</div>
|| ≈ 2.71828 18284 59045 23536 02874 71352 66249
||[[e (mathematical constant)|Napier's constant]], base of [[Natural logarithm]]
|| '''[[Mathematics|Gen]]''', '''[[Mathematical analysis|Ana]]'''
| align="center" | ''[[transcendental number|T]]''
| align=right | [[1618]]
| align=right | 50,100,000,000
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">√2</div>
|| ≈ 1.41421 35623 73095 04880 16887 24209 69807
|| [[Pythagoras]]' constant, [[square root of two]]
|| '''[[Mathematics|Gen]]'''
| align="center" | ''[[algebraic number|A]]''
| align=right | by c. [[800 BC|800 BC]]
| align="right" | 137,438,953,444
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">√3</div>
|| ≈ 1.73205 08075 68877 29352 74463 41505
|| [[Theodorus of Cyrene|Theodorus]]' constant, [[square root]] of three
|| '''[[Mathematics|Gen]]'''
| align="center" | ''[[algebraic number|A]]''
| align=right | by c. [[800 BC|800 BC]]
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">γ</div>
|| ≈ 0.57721 56649 01532 86060 65120 90082 40243
|| [[Euler-Mascheroni constant]]
||'''[[Mathematics|Gen]]''', '''[[Number theory|NuT]]'''
||
| align=right | [[1735]]
| align="right" | 108,000,000
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">φ</div>
|| ≈ 1.61803 39887 49894 84820 45868 34365 63811
|| [[Golden ratio]]
|| '''[[Mathematics|Gen]]'''
| align="center" | ''[[algebraic number|A]]''
| align=right | by [[3rd century BC]]
| align="right" | 3,141,000,000
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">β<sup>*</sup></div>
|| ≈ 0.70258
|| [[Embree-Trefethen constant]]
||'''[[Number theory|NuT]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">δ</div>
|| ≈ 4.66920 16091 02990 67185 32038 20466 20161
|| [[Feigenbaum constant]]
|| '''[[chaos theory|ChT]]'''
||
|align=right | [[1975]]
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">α</div>
|| ≈ 2.50290 78750 95892 82228 39028 73218 21578
|| [[Feigenbaum constant]]
|| '''[[chaos theory|ChT]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">C<sub>2</sub></div>
|| ≈ 0.66016 18158 46869 57392 78121 10014 55577
|| [[Twin prime conjecture|Twin prime constant]]
|| '''[[Number theory|NuT]]'''
||
||
| align="right" | 5,020
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">M<sub>1</sub></div>
|| ≈ 0.26149 72128 47642 78375 54268 38608 69585
|| [[Meissel-Mertens constant]]
|| '''[[Number theory|NuT]]'''
||
| align="right" | [[1866]]<br>[[1874]]
| align="right" | 8,010
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">B<sub>2</sub></div>
|| ≈ 1.90216 05823
|| [[Brun's constant]] for twin prime
|| '''[[Number theory|NuT]]'''
||
| align="right" | [[1919]]
| align="right" | 10
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">B<sub>4</sub></div>
|| ≈ 0.87058 83800
|| [[Brun's constant]] for prime quadruplets
|| '''[[Number theory|NuT]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">Λ</div>
|| > – 2.7 · 10<sup>-9</sup>
|| [[de Bruijn-Newman constant]]
|| '''[[Number theory|NuT]]'''
||
| align="right" | [[1950]]?
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">K</div>
|| ≈ 0.91596 55941 77219 01505 46035 14932 38411 </td>
|| [[Catalan's constant]]
|| '''[[combinatorics|Com]]'''
||
||
| align="right" | 201,000,000
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">K</div>
|| ≈ 0.76422 36535 89220 66
|| [[Landau-Ramanujan constant]]
|| '''[[Number theory|NuT]]'''
||
||
| align="right" | 30,010
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">K</div>
|| ≈ 1.13198 824
|| [[Viswanath's constant]]
|| '''[[Number theory|NuT]]'''
||
||
| align="right" | 8
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">B´<sub>L</sub></div>
|| = 1
|| [[Legendre's constant]]
|| '''[[Number theory|NuT]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">μ</div>
|| ≈ 1.45136 92348 83381 05028 39684 85892 027
|| [[Ramanujan-Soldner constant]]
|| '''[[Number theory|NuT]]'''
||
||
| align="right" | 75,500
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">E<sub>B</sub></div>
|| ≈ 1.60669 51524 15291 763
|| [[Erdős–Borwein constant]]
|| '''[[Number theory|NuT]]'''
| align="center" | ''[[algebraic number|A]]''
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">Ω</div>
|| depends on [[Turing machine|computation model]]
|| [[Chaitin's constant]]
|| '''[[Algorithmic information theory|Inf]]'''
| align="center" | ''[[transcendental number|T]]''
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">β</div>
|| ≈ 0.28016 94990
|| [[Bernstein's constant]][http://mathworld.wolfram.com/BernsteinsConstant.html ]
|| '''[[Mathematical analysis|Ana]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">λ</div>
|| ≈ 0.30366 30029
|| [[Gauss-Kuzmin-Wirsing constant]][http://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html ]
|| '''[[combinatorics|Com]]'''
||
| align=right | [[1974]]
| align=right | 385
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">''D''(1)</div>
|| ≈ 0.35323 63719
|| [[Hafner-Sarnak-McCurley constant]][http://mathworld.wolfram.com/Hafner-Sarnak-McCurleyConstant.html ]
|| '''[[Number theory|NuT]]'''
||
| align=right |[[1993]]
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">λ, μ</div>
|| ≈ 0.62432 99885
|| [[Golomb-Dickman constant]][http://mathworld.wolfram.com/Golomb-DickmanConstant.html ]
|| '''[[combinatorics|Com]] [[Number theory|NuT]]'''
||
| align=right | [[1930]]<br> [[1964]]
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 0.62946 50204
|| [[Cahen's constant]][http://www.tcaep.co.uk/science/constant/ctod.htm ]
||
||
||
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 0.66274 34193
||[[Laplace limit]][http://mathworld.wolfram.com/LaplaceLimit.html ]
||
||
||
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 0.80939 40205
|| [[Alladi-Grinstead constant]][http://mathworld.wolfram.com/Alladi-GrinsteadConstant.html ]
|| '''[[Number theory|NuT]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">Λ</div>
|| ≈ 1.09868 58055
|| [[Lengyel's constant]][http://mathworld.wolfram.com/LengyelsConstant.html ]
|| '''[[combinatorics|Com]]'''
||
| align=right | [[1992]]
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 1.18656 91104
|| [[Khinchin-Lévy constant]][http://mathworld.wolfram.com/Khinchin-LevyConstant.html ]
|| '''[[Number theory|NuT]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">ζ(3)</div>
|| ≈ 1.20205 69031 59594 28539 97381
|| [[Apéry's constant]][http://mathworld.wolfram.com/AperysConstant.html ]
||
||
| align=right | [[1979]]
| align=right | 1,000,000,000
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">θ</div>
|| ≈ 1.30637 78838 63080 69046
|| [[Mills' constant]][http://mathworld.wolfram.com/MillsConstant.html ]
||'''[[Number theory|NuT]]'''
||
| align=right | [[1947]]
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 1.45607 49485 82689 67139 95953 51116 54356
|| [[Backhouse's constant]][http://mathworld.wolfram.com/BackhousesConstant.html ]
||
||
||
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 1.46707 80794
|| [[Porter's constant]][http://mathworld.wolfram.com/PortersConstant.html ]
|| '''[[Number theory|NuT]]'''
||
| align=right | [[1975]]
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 1.53960 07178
|| [[Lieb's square ice constant]][http://www.mathsoft.com/mathresources/constants/discretestructures/article/0,,2265,00.html ]
|| '''[[combinatorics|Com]]'''
||
| align=right | [[1967]]
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 1.70521 11401 05367
|| [[Niven's constant]][http://mathworld.wolfram.com/NivensConstant.html ]
||'''[[Number theory|NuT]]'''
||
| align=right | [[1969]]
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">''K''</div>
|| ≈ 2.58498 17596
|| [[Sierpiński's constant]][http://www.tcaep.co.uk/science/constant/detail/sierpinskisconstant.htm ]
||
||
||
||
|-
| bgcolor=#d0f0d0 align=center|
|| ≈ 2.68545 2001
|| [[Khinchin's constant]][http://mathworld.wolfram.com/KhinchinsConstant.html ]
||'''[[Number theory|NuT]]'''
||
| align=right | [[1934]]
| align=right | 7350
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">''F''</div>
|| ≈ 2.80777 02420
|| [[Fransén-Robinson constant]][http://mathworld.wolfram.com/Fransen-RobinsonConstant.html ]
|| '''[[Mathematical analysis|Ana]]'''
||
||
||
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">''L''</div>
|| ≈ .5
|| [[Landau's constant]]
|| '''[[Mathematical analysis|Ana]]'''
||
||
| align=right | 1
|}
| |||