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
B´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

Note:

• The table is sorted pretty 'randomly'. See also the alternative sorting based on the continued fraction representations.

External links

• Steven Finch's page of mathematical constants: http://pauillac.inria.fr/algo/bsolve/constant/constant
• Steven Finch's alternative indexing: http://pauillac.inria.fr/algo/bsolve/constant/table
• Xavier Gourdon and Pascal Sebah's page of numbers, mathematical constants and algorithms: http://numbers.computation.free.fr/Constants/constants
• 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/