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A mathematical constant is a quantity, usually a real number or a complex number , that arises naturally in mathematics and does not change. Unlike physical constants , mathematical constants are defined independently of any physical measurement.
f with f' = f . Therefore, f (1)/f (0) is a mathematical constant, the constant e. f is also a periodic function , and the absolute value of its period is another mathematical constant, 2π.
real numbers or complex numbers . Mathematical constants that one can talk about are definable numbers (and almost always also computable ).
Table of selected mathematical constants
Abbreviations used:
I - irrational number , A - algebraic number , T - transcendental number , ? - unknown Gen - General , NuT - Number theory , ChT - Chaos theory , Com - Combinatorics , Inf - Information theory , Ana - Mathematical analysis Symbol Approximate Value Name Field N First described # of known digits π ≈ 3.14159 26535 89793 23846 26433 83279 50288 Pi , Archimedes ' constant or Ludoph 's numberGen Ana T ? 1,241,100,000,000 e ≈ 2.71828 18284 59045 23536 02874 71352 66249 Napier's constant, base of Natural logarithm Gen Ana T 50,100,000,000 √2 ≈ 1.41421 35623 73095 04880 16887 24209 69807 Pythagoras ' constant, square root of two Gen I ,A 137,438,953,444 √3 ≈ 1.73205 08075 68877 29352 74463 41505 Theodorus' constant, square root of three Gen I ,A γ ≈ 0.57721 56649 01532 86060 65120 90082 40243 Euler-Mascheroni constant Gen NuT ? 108,000,000 φ ≈ 1.61803 39887 49894 84820 45868 34365 63811 Golden ratio Gen A 3,141,000,000 β* ≈ 0.70258 Embree-Trefethen constant NuT δ ≈ 4.66920 16091 02990 67185 32038 20466 20161 Feigenbaum constant ChT α ≈ 2.50290 78750 95892 82228 39028 73218 21578 Feigenbaum constant ChT C2 ≈ 0.66016 18158 46869 57392 78121 10014 55577 Twin prime constant NuT 5,020 M1 ≈ 0.26149 72128 47642 78375 54268 38608 69585 Meissel-Mertens constant NuT 1866 1874 8,010 B2 ≈ 1.90216 05823 Brun's constant for twin prime NuT 1919 10 B4 ≈ 0.87058 83800 Brun's constant for prime quadruplets NuT Λ > – 2.7 ˇ 10-9 de Bruijn-Newman constant NuT 1950 ? K ≈ 0.91596 55941 77219 01505 46035 14932 38411 Catalan's constant Com 201,000,000 K ≈ 0.76422 36535 89220 66 Landau-Ramanujan constant NuT I ? ) 30,010 K ≈ 1.13198 824 Viswanath's constant 1 NuT 8 B´L ≈ 1.08366 Legendre's constant NuT μ ≈ 1.45136 92348 83381 05028 39684 85892 027 Ramanujan-Soldner constant NuT 75,500 EB ≈ 1.60669 51524 15291 763 Erdös-Borwein constant NuT I Ω ? Chaitin's constant Inf T β ≈ 0.28016 94990 Bernstein's constant[1] (http://mathworld.wolfram.com/BernsteinsConstant.html ) Ana λ ≈ 0.30366 30029 Gauss-Kuzmin-Wirsing constant[2] (http://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html ) Com 1974 385 D (1)≈ 0.35323 63719 Hafner-Sarnak-McCurley constant[3] (http://mathworld.wolfram.com/Hafner-Sarnak-McCurleyConstant.html ) NuT 1993 λ μ ≈ 0.62432 99885 Golomb-Dickman constant[4] (http://mathworld.wolfram.com/Golomb-DickmanConstant.html ) Com NuT 1930 1964 ≈ 0.62946 50204 Cahen's constant[5] (http://www.tcaep.co.uk/science/constant/ctod.htm ) ≈ 0.66274 34193 Laplace limit[6] (http://mathworld.wolfram.com/LaplaceLimit.html ) ≈ 0.80939 40205 Alladi-Grinstead constant[7] (http://mathworld.wolfram.com/Alladi-GrinsteadConstant.html ) NuT Λ ≈ 1.09868 58055 Lengyel's constant[8] (http://mathworld.wolfram.com/LengyelsConstant.html ) Com 1992 ≈ 1.18656 91104 Khinchin-Lévy constant[9] (http://mathworld.wolfram.com/Khinchin-LevyConstant.html ) NuT ≈ 1.20205 69031 59594 28539 97381 Apéry's constant[10] (http://mathworld.wolfram.com/AperysConstant.html ) 1979 1,000,000,000 θ ≈ 1.30637 78838 63080 69046 Mills' constant[11] (http://mathworld.wolfram.com/MillsConstant.html ) NuT ? 1947 ≈ 1.45607 49485 82689 67139 95953 51116 54356 Backhouse's constant[12] (http://mathworld.wolfram.com/BackhousesConstant.html ) ≈ 1.46707 80794 Porter's constant[13] (http://mathworld.wolfram.com/PortersConstant.html ) NuT 1975 ≈ 1.53960 07178 Lieb's square ice constant[14] (http://www.mathsoft.com/mathresources/constants/discretestructures/article/0,,2265,00.html ) Com 1967 ≈ 1.70521 11401 05367 Niven's constant[15] (http://mathworld.wolfram.com/NivensConstant.html ) NuT 1969 ≈ 2.58498 17596 Sierpinski's constant[16] (http://www.tcaep.co.uk/science/constant/detail/sierpinskisconstant.htm ) ≈ 2.68545 2001 Khinchin's constant[17] (http://mathworld.wolfram.com/KhinchinsConstant.html ) NuT ? 1934 7350 F ≈ 2.80777 02420 Fransén-Robinson constant[18] (http://mathworld.wolfram.com/Fransen-RobinsonConstant.html ) Ana L ≈ .5 Landau's constant Ana 1
See also
External links Steven Finch's page of mathematical constants: http://pauillac.inria.fr/algo/bsolve/constant/constant.html Steven Finch's alternative indexing: http://pauillac.inria.fr/algo/bsolve/constant/table.html Xavier Gourdon and Pascal Sebah's page of numbers, mathematical constants and algorithms: http://numbers.computation.free.fr/Constants/constants.html Simon Plouffe's inverter: http://pi.lacim.uqam.ca/eng/ CECM's Inverse symbolic calculator (ISC) (tells you how a given number can be constructed from mathematical constants): http://www.cecm.sfu.ca/projects/ISC/
Results from FactBites:
Mathematical constant - Wikipedia, the free encyclopedia (336 words)
A mathematical constant is a quantity, usually a real number or a complex number , that arises naturally in mathematics and does not change. Therefore, f(1)/f(0) is a mathematical constant , the constant e . Mathematical constants are typically elements of the field of real numbers or complex numbers .
Encyclopedia: Mathematical constant (3463 words)
The Euler-Mascheroni constant is a mathematical constant , used mainly in number theory , and is defined as the limiting difference between the harmonic series and the natural logarithm : Intriguingly, the constant is also given by the integral: Its value is approximately γ ≈ 0. The Meissel-Mertens constant is a mathematical constant , used mainly in number theory , and is defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm : Its value is approximately M ≈ 0. The SierpiÅ„skis constant is a mathematical constant usually denoted as K. One way of defining it is by limiting the expression: where r2(k) is a number of representations of k as a sum of the form a2 + b2 for natural a and b.
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