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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 | ||
| 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.
- 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/
All Wikipedia text is available under the terms of the GNU Free Documentation License
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