Mathematical constant
Symbol Value Name Field N First described # of known digits
0 = 0 Zero Gen R by c. 500 BC all
1 = 1 One , Unity Gen R all
i = √ -1 Imaginary unit , unit imaginary number Gen , Ana A by c. 1500 all
π ≈ 3.14159 26535 89793 23846 26433 83279 50288 Pi , Archimedes ' constant or Ludolph 's number Gen , Ana T by c. 2600 BC 50,000,000,000,000
e ≈ 2.71828 18284 59045 23536 02874 71352 66249 e , Napier 's constant , or Euler 's number Gen , Ana T 1618 8,000,000,000,000
√ 2 ≈ 1.41421 35623 73095 04880 16887 24209 69807 Pythagoras ' constant , square root of 2 Gen A by c. 800 BC 10,000,000,000,000
√ 3 ≈ 1.73205 08075 68877 29352 74463 41505 87236 Theodorus ' constant , square root of 3 Gen A by c. 800 BC 2,000,000,000,000
√ 5 ≈ 2.23606 79774 99789 69640 91736 68731 27623 square root of 5 Gen A by c. 800 BC 2,000,000,000,000
γ { \displaystyle \gamma } ≈ 0.57721 56649 01532 86060 65120 90082 40243 Euler-Mascheroni constant Gen , NuT 1735 14,922,244,771
ϕ { \displaystyle \phi } ≈ 1.61803 39887 49894 84820 45868 34365 63811 Golden ratio Gen A by c. 200 BC 100,000,000,000
Λ { \displaystyle \Lambda } 0 ≤ Λ ≤ 0.22 { \displaystyle 0\leq \Lambda \leq 0.22 } de Bruijn-Newman constant NuT , Ana 1950 none
M 1 ≈ 0.26149 72128 47642 78375 54268 38608 69585 Meissel-Mertens constant NuT 1866 1874 8,010
β { \displaystyle \beta } ≈ 0.28016 94990 23869 13303 Bernstein 's constant Ana
λ { \displaystyle \lambda } ≈ 0.30366 30028 98732 65859 74481 21901 55623 Gauss-Kuzmin-Wirsing constant Com 1974 385
σ { \displaystyle \sigma } ≈ 0.35323 63718 54995 98454 35165 50432 68201 Hafner-Sarnak-McCurley constant NuT 1993
L ≈ 0.5 Landau 's constant Ana 1
Ω ≈ 0.56714 32904 09783 87299 99686 62210 35554 Omega constant Ana T
λ { \displaystyle \lambda } , μ { \displaystyle \mu } ≈ 0.62432 99885 43550 87099 29363 83100 83724 Golomb-Dickman constant Com , NuT 1930 1964
≈ 0.64341 05462 Cahen 's constant T 1891 4000
C 2 ≈ 0.66016 18158 46869 57392 78121 10014 55577 Twin prime constant NuT 5,020
Table of selected mathematical constants
Main article : List of mathematical constants Abbreviations used : R – Rational number , I – Irrational number ( may be algebraic or transcendental ) , A – Algebraic number ( irrational ) , T – Transcendental number ( irrational ) Gen – General , NuT – Number theory , ChT – Chaos theory , Com – Combinatorics , Inf – Information theory , Ana – Mathematical analysis
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a symbol or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory, and calculus. What it means for a constant to arise naturally, and what makes a constant interesting, is ultimately a matter of taste, and some mathematical constants are notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places. All named mathematical constants are definable numbers and usually are also computable numbers (Chaitin's constant being a significant exception).