Mathematical constants

Source: https://aidb.si/d/mathematical-constants — Table from the Wikipedia article “List of mathematical constants” (CC BY-SA 4.0); decimal expansions there are cited to MathWorld and the OEIS.

Constant	Symbol	Value	Decimal expansion	Year	Year described	Rational	Algebraic	Period	Exponential period
Pi	π	3.141592653589793	3.14159 26535 89793 23846	-1900	1900 to 1600 BCE	false	false	true	true
Tau	τ	6.283185307179586	6.28318 53071 79586 47692	-1900	1900 to 1600 BCE	false	false	true	true
Square root of 2, Pythagoras constant	√2	1.4142135623730951	1.41421 35623 73095 04880	-1800	1800 to 1600 BCE	false	true	true	true
Square root of 3, Theodorus' constant	√3	1.7320508075688772	1.73205 08075 68877 29352	-465	465 to 398 BCE	false	true	true	true
Zero	0	0	0	-300	300 to 100 BCE	true	true	true	true
Phi, Golden ratio	φ or ϕ	1.618033988749895	1.61803 39887 49894 84820	-300	~300 BCE	false	true	true	true
Silver ratio	σ	2.414213562373095	2.41421 35623 73095 04880	-300	~300 BCE	false	true	true	true
Negative one	−1	-1	−1	-300	300 to 200 BCE	true	true	true	true
Cube root of 2, Delian constant	³√2	1.2599210498948732	1.25992 10498 94873 16476	46	46 to 120 CE	false	true	true	true
Imaginary unit	i		0 + 1i	1501	1501 to 1576	false	true	true	true
Connective constant for the hexagonal lattice	μ	1.8477590650225735	1.84775 90650 22573 51225	1593	1593	false	true	true	true
Kepler–Bouwkamp constant	K^′	0.1149420448532962	0.11494 20448 53296 20070	1596	1596
Wallis's constant		2.0945514815423265	2.09455 14815 42326 59148	1616	1616 to 1703	false	true	true	true
Euler's number	e	2.718281828459045	2.71828 18284 59045 23536	1618	1618	false	false		true
Natural logarithm of 2	ln2	0.6931471805599453	0.69314 71805 59945 30941	1619	1619 & 1668	false	false	true	true
Sophomore's dream second constant	I₂	1.2912859970626636	1.29128 59970 62663 54040	1697	1697
Lemniscate constant	ϖ	2.6220575542921196	2.62205 75542 92119 81046	1718	1718 to 1798	false	false	true	true
Basel's number	ζ(2)	1.6449340668482264	1.64493 40668 48226 43647	1734	1734	false	false	true	true
Euler's constant	γ	0.5772156649015329	0.57721 56649 01532 86060	1735	1735				true
Erdős–Borwein constant	E	1.6066951524152917	1.60669 51524 15291 76378	1749	1749	false
Square super-root of 2	√2ₛ	1.5596104694623694	1.55961 04694 62369 34997	1758	1758 & 1783	false	false
Omega constant	Ω	0.5671432904097838	0.56714 32904 09783 87299	1758	1758 & 1783	false	false
Apéry's constant	ζ(3)	1.2020569031595942	1.20205 69031 59594 28539	1780	1780	false		true	true
Laplace limit		0.6627434193491816	0.66274 34193 49181 58097	1782	~1782	false	false
Soldner constant	μ	1.451369234883381	1.45136 92348 83381 05028	1792	1792
Gauss's constant	G	0.8346268416740732	0.83462 68416 74073 18628	1799	1799	false	false		true
Second Hermite constant	γ₂	1.1547005383792515	1.15470 05383 79251 52901	1822	1822 to 1901	false	true	true	true
First continued fraction constant	C₁	0.697774657964008	0.69777 46579 64007 98201	1855	1855	false	false
Ramanujan's constant		262537412640768740	262 53741 26407 68743 .99999 99999 99250 073	1859	1859	false	false
Glaisher–Kinkelin constant	A	1.2824271291006226	1.28242 71291 00622 63687	1860	1860
Catalan's constant	G	0.915965594177219	0.91596 55941 77219 01505	1864	1864			true	true
Dottie number	D	0.7390851332151607	0.73908 51332 15160 64165	1865	1865	false	false
Meissel–Mertens constant	M	0.26149721284764277	0.26149 72128 47642 78375	1866	1866 & 1873
Cahen's constant	C	0.643410546288338	0.64341 05462 88338 02618	1891	1891	false	false
Gelfond's constant	e^π	23.14069263277927	23.14069 26327 79269 0057	1900	1900	false	false
Totient summatory constant		1.3397841535743473	1.33978 41535 74347 24659	1900	1900
Second Favard constant	K₂	1.2337005501361697	1.23370 05501 36169 82735	1902	1902 to 1965	false	false	true	true
Golden angle	g	2.3999632297286535	2.39996 32297 28653 32223	1907	1907	false	false	true	true
Sierpiński's constant	K	2.5849817595792532	2.58498 17595 79253 21706	1907	1907
Landau–Ramanujan constant	K	0.7642236535892206	0.76422 36535 89220 66299	1908	1908
First Nielsen–Ramanujan constant	a₁	0.8224670334241132	0.82246 70334 24113 21823	1909	1909	false	false	true	true
Gieseking constant	V	1.0149416064096537	1.01494 16064 09653 62502	1912	1912			true	true
Bernstein's constant	β	0.2801694990238691	0.28016 94990 23869 13303	1913	1913
Tribonacci constant	ρ	1.8392867552141612	1.83928 67552 14161 13255	1914	1914 to 1963	false	true	true	true
Kempner series's value		22.92067661926415	22.92067 66192 64150 34816	1914	1914
Kempner number	κ	0.8164215090218931	0.81642 15090 21893 14370	1916	1916	false	false
Brun's constant	B₂	1.902160583104	≈ 1.90216 05831 04	1919	1919
Twin primes constant	C₂	0.6601618158468696	0.66016 18158 46869 57392	1922	1922
Plastic ratio	ρ	1.324717957244746	1.32471 79572 44746 02596	1924	1924	false	true	true	true
Bloch's constant	B		0.4332≤B≤0.4719	1925	1925
Z score for the 97.5 percentile point	z_.975	1.9599639845400543	1.95996 39845 40054 23552	1925	1925
Landau's constant	L		0.5<L≤0.54326	1929	1929
Landau's third constant	A		0.5<A≤0.7853	1929	1929
Prouhet–Thue–Morse constant	τ	0.4124540336401076	0.41245 40336 40107 59778	1929	1929	false	false
Golomb–Dickman constant	λ	0.6243299885435508	0.62432 99885 43550 87099	1930	1930 & 1964
Constant related to the asymptotic behavior of Lebesgue constants	c	0.9894312738311469	0.98943 12738 31146 95174	1930	1930
Feller–Tornier constant	𝒞_FT	0.6613170494696223	0.66131 70494 69622 33528	1932	1932
Base 10 Champernowne constant	C₁₀	0.12345678910111213	0.12345 67891 01112 13141	1933	1933	false	false
Salem constant	σ₁₀	1.1762808182599176	1.17628 08182 59917 50654	1933	1933	false	true	true	true
Khinchin's constant	K₀	2.6854520010653062	2.68545 20010 65306 44530	1934	1934
Lévy's constant (1)	β	1.1865691104156255	1.18656 91104 15625 45282	1935	1935
Lévy's constant (2)	e^β	3.2758229187218113	3.27582 29187 21811 15978	1936	1936
Linnik's constant	L		L ≤ 3.99	1944	1944
Copeland–Erdős constant	𝒞_CE	0.23571113171923294	0.23571 11317 19232 93137	1946	1946	false
Mills' constant	A	1.3063778838630806	1.30637 78838 63080 69046	1947	1947	false
Third continued fraction constant	C₃	1.525135276160981	1.52513 52761 60981 20908	1948	1948
de Bruijn–Newman constant	Λ		0≤Λ≤0.2	1950	1950
Porter's constant	C	1.4670780794339755	1.46707 80794 33975 47289	1961	1961
Lochs constant	L	0.9702701143920339	0.97027 01143 92033 92574	1964	1964
Infinite tetration of imaginary unit			0.438283 + 0.360592i	1966	1966	false
DeVicci's tesseract constant		1.0074347568842794	1.00743 47568 84279 37609	1966	1966	false	true	true	true
Lieb's square ice constant		1.539600717839002	1.53960 07178 39002 03869	1967	1967	false	true	true	true
Growth rate constant of fixed polyomino (Klarner's constant)	λ₂		4.00253 < λ2 < 4.5252	1967	1967
Growth rate constant of fixed polycube	λ₃		6.3795 < λ3 < 9.3835	1967	1967
Niven's constant	C	1.7052111401053678	1.70521 11401 05367 76428	1969	1969
Stephens' constant	C_S	0.5759599688929454	0.57595 99688 92945 43964	1969	1969
Regular paperfolding sequence	P	0.8507361882018672	0.85073 61882 01867 26036	1970	1970	false	false
Reciprocal Fibonacci constant	ψ	3.3598856662431777	3.35988 56662 43177 55317	1974	1974	false
Chvátal–Sankoff constant for the binary alphabet	γ₂		0.788071≤γ2≤0.826280	1975	1975
Feigenbaum constant δ	δ	4.66920160910299	4.66920 16091 02990 67185	1975	1975
Chaitin's constants	Ω		In general they are uncomputables; one such number is 0.00787 49969 97812 3844.	1975	1975	false	false	false	false
Freiman's constant	F	4.527829566160879	4.52782 95661 60879 14088	1975	1975	false	true	true	true
Robbins constant	Δ(3)	0.6617071822671763	0.66170 71822 67176 23515	1977	1977	false	false	true	true
Fransén–Robinson constant	F	2.8077702420285195	2.80777 02420 28519 36522	1978	1978
Feigenbaum constant α	α	2.5029078750958926	2.50290 78750 95892 82228	1979	1979
Irrational number from Moser–de Bruijn sequence	α	3.30033	3.30033 00000 00000 33003	1982	1982	false	false
Second du Bois-Reymond constant	C₂	0.19452804946532512	0.19452 80494 65325 11361	1983	1983	false	false		true
Erdős–Tenenbaum–Ford constant	δ	0.0860713320559342	0.08607 13320 55934 20688	1984	1984
Conway's constant	λ	1.3035772690342964	1.30357 72690 34296 39125	1987	1987	false	true	true	true
Hard hexagon entropy constant	κ(1)	1.3954859724793027	1.39548 59724 79302 73522	1988	1988	false	true	true	true
Hafner–Sarnak–McCurley constant	σ	0.353236371854996	0.35323 63718 54995 98454	1991	1991
Backhouse's constant	B	1.4560749485826896	1.45607 49485 82689 67139	1995	1995
Viswanath constant	V	1.1319882487943	1.13198 82487 943	1997	1997
Komornik–Loreti constant	q	1.787231650182966	1.78723 16501 82965 93301	1998	1998	false	false
Embree–Trefethen constant	β^⋆	0.70258	0.70258	1999	1999
Heath-Brown–Moroz constant	C	0.001317641154853178	0.00131 76411 54853 17810	1999	1999
MRB constant	S	0.18785964246206713	0.18785 96424 62067 12024	1999	1999
Prime constant	ρ	0.41468250985111166	0.41468 25098 51111 66024	1999	1999	false
Somos' quadratic recurrence constant	σ	1.6616879496335941	1.66168 79496 33594 12129	1999	1999
Foias constant	α	1.1874523511265012	1.18745 23511 26501 05459	2000	2000
One	1	1	1		Prehistory	true	true	true	true
Two	2	2	2		Prehistory	true	true	true	true
One half	1/2	0.5	0.5		Prehistory	true	true	true	true
Square root of 5	√5	2.23606797749979	2.23606 79774 99789 69640			false	true	true	true
Cube root of 3	³√3	1.4422495703074083	1.44224 95703 07408 38232			false	true	true	true
Twelfth root of 2	¹²√2	1.0594630943592953	1.05946 30943 59295 26456			false	true	true	true
Supergolden ratio	ψ	1.465571231876768	1.46557 12318 76768 02665			false	true	true	true
Liouville's constant	L	0.110001	0.11000 10000 00000 00000 0001		Before 1844	false	false
Universal parabolic constant	P	2.295587149392638	2.29558 71493 92638 07403		Before 1891	false	false	true	true
Gelfond–Schneider constant	2^(√2)	2.665144142690225	2.66514 41426 90225 18865		Before 1902	false	false
Gompertz constant	δ	0.5963473623231941	0.59634 73623 23194 07434		Before 1948				true
Van der Pauw constant	π/ln2	4.532360141827194	4.53236 01418 27193 80962		Before 1958	false
Magic angle	θₘ	0.9553166181245093	0.95531 66181 245092 78163		Before 1959	false	false	true	true
Artin's constant	C_Artin	0.37395581361920227	0.37395 58136 19202 28805		Before 1961
Weierstrass constant		0.47494937998792064	0.47494 93799 87920 65033		Before 1978	false	false
Beam detection constant	L		3.1415926535 ≤ L ≤ 4.7998		Before 1980
Natural density constant of abundant numbers	d_A		0.2476171 < dA < 0.2476475		Before 1998
Logarithmic capacity of the unit disk		0.5901702995080481	0.59017 02995 08048 11302		Before 2003	false	false		true
Taniguchi constant	C_T	0.6782344919173919	0.67823 44919 17391 97803		Before 2005