Mathematical constant
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.
For example, up to multiplication with nonzero complex numbers, there is a unique holomorphic function 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.
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 ).
However, there are still some mathematical constants for which only very rough estimates are known.
An alternate sorting may be found at Mathematical constant (sorted by continued fraction representation)
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 primeNuT
1919
10
B4
≈ 0.87058 83800
Brun's constant for prime quadrupletsNuT
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 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]
Ana
λ
≈ 0.30366 30029
Gauss-Kuzmin-Wirsing constant [2]
Com
1974
385
D (1)
≈ 0.35323 63719
Hafner-Sarnak-McCurley constant [3]
NuT
1993
λ μ
≈ 0.62432 99885
Golomb-Dickman constant [4]
Com NuT
1930 1964
≈ 0.62946 50204
Cahen's constant [5]
≈ 0.66274 34193
Laplace limit [6]
≈ 0.80939 40205
Alladi-Grinstead constant [7]
NuT
Λ
≈ 1.09868 58055
Lengyel's constant [8]
Com
1992
≈ 1.18656 91104
Khinchin-Lévy constant [9]
NuT
≈ 1.20205 69031 59594 28539 97381
Apéry's constant [10]
1979
1,000,000,000
θ
≈ 1.30637 78838 63080 69046
Mills' constant [11]
NuT ?
1947
≈ 1.45607 49485 82689 67139 95953 51116 54356
Backhouse's constant [12]
≈ 1.46707 80794
Porter's constant [13]
NuT
1975
≈ 1.53960 07178
Lieb's square ice constant [14]
Com
1967
≈ 1.70521 11401 05367
Niven's constant [15]
NuT
1969
≈ 2.58498 17596
Sierpinski's constant [16]
≈ 2.68545 2001
Khinchin's constant [17]
NuT ?
1934
7350
F
≈ 2.80777 02420
Fransén-Robinson constant [18]
Ana
L
≈ .5
Landau's constant
Ana
1
See also
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