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Mathematical constant

A mathematical constant is a quantity whose value does not change; it is thus the opposite of a variable. Unlike physical constants, mathematical constants are defined independently of any physical measurement.

Mathematical constants are typically elements of the field of real numbers or complex numbers. Mathematical constants that one can talk about are definable numbers (and almost always also computable).

Table of some 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

Symbol Value Name Field N First described # of known digits
π ≈ 3.14159 26535 89793 23846 26433 83279 50288 Pi, Archimedes' constant or Ludoph[?]'s number Gen T ? 206,158,430,000
e ≈ 2.71828 18284 59045 23536 02874 71352 66249 Napier's constant, base of Natural logarithm Gen T   12,884,901,000
√2 ≈ 1.41421 35623 73095 04880 16887 24209 69807 Pythagoras' constant, square root of two Gen I   137,438,953,444
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 · 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
L ≈ 1.08366 Legendre's constant[?] NuT      
μ ≈ 1.45136 92348 83381 05028 39684 85892 027 Ramanujan-Soldner constant[?], Soldner's constant[?] NuT     75,500
EB ≈ 1.60669 51524 15291 763 Erdös-Borwein constant NuT I    

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