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Saturday, February 11, 2006

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 (mathematical constant). f is also a periodic function, and the absolute value of its period is another mathematical constant, 2. Mathematical constants are typically elements of the field (mathematics) of real numbers or complex numbers. Mathematical constants that one can talk about are definable numbers (and almost always also computable number). 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 - Mathematics, 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
� 3.14159 26535 89793 23846 26433 83279 50288 Pi, Archimedes constant or Ludolph van Ceulens number Mathematics, Mathematical analysis transcendental number 1,241,100,000,000
e � 2.71828 18284 59045 23536 02874 71352 66249 e (mathematical constant), base of Natural logarithm Mathematics, Mathematical analysis transcendental number 50,100,000,000
v2 � 1.41421 35623 73095 04880 16887 24209 69807 Pythagoras constant, square root of two Mathematics irrational number,algebraic number 137,438,953,444
v3 � 1.73205 08075 68877 29352 74463 41505 Theodorus constant, square root of three Mathematics irrational number,algebraic number
G � 0.57721 56649 01532 86060 65120 90082 40243 Euler-Mascheroni constant Mathematics, Number theory 108,000,000
F � 1.61803 39887 49894 84820 45868 34365 63811 Golden mean Mathematics algebraic number 3,141,000,000
� 0.70258 Embree-Trefethen constant Number theory
� 4.66920 16091 02990 67185 32038 20466 20161 Feigenbaum constant chaos theory
� 2.50290 78750 95892 82228 39028 73218 21578 Feigenbaum constant chaos theory
C2 � 0.66016 18158 46869 57392 78121 10014 55577 Twin prime conjecture Number theory 5,020
M1 � 0.26149 72128 47642 78375 54268 38608 69585 Meissel-Mertens constant Number theory 1866
1874
8,010
B2 � 1.90216 05823 Bruns constant for twin prime Number theory 1919 10
B4 � 0.87058 83800 Bruns constant for prime quadruplets Number theory
� 2.7 � 109 de Bruijn-Newman constant Number theory 1950?
K � 0.91596 55941 77219 01505 46035 14932 38411 Catalans constant combinatorics 201,000,000
K � 0.76422 36535 89220 66 Landau-Ramanujan constant Number theory irrational number (?) 30,010
K � 1.13198 824 Viswanaths constant 1 Number theory 8
B�L � 1.08366 Legendres constant Number theory
� 1.45136 92348 83381 05028 39684 85892 027 Ramanujan-Soldner constant Number theory 75,500
EB � 1.60669 51524 15291 763 Erd�s-Borwein constant Number theory irrational number
O Chaitins constant Algorithmic information theory transcendental number
� 0.28016 94990 Bernsteins constant analysis Ana � 0.30366 30029 Gauss-Kuzmin-Wirsing constant >� 0.35323 63719 Hafner-Sarnak-McCurley constant theory NuT � 0.62432 99885 Golomb-Dickman constant Number theory � 0.62946 50204 Cahens constant >� 0.66274 34193 Laplace limit >� 0.80939 40205 Alladi-Grinstead constant theory NuT � 1.09868 58055 Lengyels constant >� 1.18656 91104 Khinchin-L�vy constant theory NuT � 1.20205 69031 59594 28539 97381 Ap�rys constant > 1,000,000,000
T � 1.30637 78838 63080 69046 Mills constant theory NuT � 1.45607 49485 82689 67139 95953 51116 54356 Backhouses constant >� 1.46707 80794 Porters constant theory NuT � 1.53960 07178 Liebs square ice constant >� 1.70521 11401 05367 Nivens constant theory NuT � 2.58498 17596 Sierpinskis constant >� 2.68545 2001 Khinchins constant theory NuT � 2.80777 02420 Frans�n-Robinson constant analysis Ana �.5 Landaus constant Mathematical analysis Mathematical constant/Alternative sorting based on the continued fraction representations
Physical constants

1 Comments:

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