Famous Mathematical Constants
Constant↕ | Symbol↕ | Approximate Value↕ | Field↕ | Known For↕ |
|---|---|---|---|---|
Pi | pi | 3.14159265358979... | Geometry, analysis | Ratio of circle's circumference to diameter, ubiquitous in math |
Euler's Number | e | 2.71828182845904... | Calculus, analysis | Base of natural logarithm, growth and compound interest |
Golden Ratio | phi | 1.61803398874989... | Geometry, aesthetics | Appears in Fibonacci, pentagons, art and nature |
Imaginary Unit | i | sqrt(-1) | Complex analysis | Foundation of complex numbers, unlocks whole new math |
Euler-Mascheroni Constant | gamma | 0.57721566490153... | Number theory, analysis | Limit of harmonic series minus ln(n), still unknown if rational |
Catalan's Constant | G | 0.91596559417721... | Combinatorics, analysis | Appears in combinatorics, unknown if irrational |
Apery's Constant | zeta(3) | 1.20205690315959... | Number theory | Riemann zeta at 3, proven irrational by Apery in 1978 |
Feigenbaum Constant | delta | 4.66920160910299... | Chaos theory | Universal ratio in period-doubling bifurcations |
Khinchin's Constant | K | 2.68545200106530... | Number theory | Geometric mean of continued fraction coefficients for almost all reals |
Champernowne Constant | C_10 | 0.12345678910111213... | Number theory | Normal number formed by concatenating integers |
Plastic Number | rho | 1.32471795724474... | Geometry, architecture | Minimal Pisot number, golden ratio's 3D cousin |
Conway's Constant | lambda | 1.30357726903429... | Combinatorics | Growth rate of look-and-say sequence |
Silver Ratio | delta_S | 2.41421356237309... | Geometry | Equals 1 + sqrt(2), appears in regular octagon |
Ramanujan-Soldner Constant | mu | 1.45136923488338... | Number theory | Only positive zero of logarithmic integral function |
Twin Prime Constant | C_2 | 0.66016181584686... | Number theory | Density constant for twin primes conjecture |
Mills' Constant | A | 1.30637788386308... | Number theory | Smallest A such that floor(A^(3^n)) is always prime |
Gelfond's Constant | e^pi | 23.14069263277926... | Number theory | Proven transcendental by Gelfond, solves Hilbert's 7th problem |
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