index of important irrational constants
The following table lists some of the most important irrational constants in mathematics.
Of course importance is sometimes debatable. Hardly anyone disputes the importance of $\pi $ or $e$ (in fact, these are the only two constants in the OEIS to have the keyword “core” attached to them), but for other constants it is not quite clear cut. In general, if a given constant has a name (especially a name hyphenating two famous mathematicians’ last names) I consider it important.
Irrationality is not always clear cut either, e.g., it might be a mistake to exclude the Euler-Mascheroni constant $\gamma $ from this list.
The constants are given to 20 decimal places.
0.1149420448532962007 | Kepler-Bouwkamp constant or polygon-inscribing constant |
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0.1234567891011121314 | Champernowne’s constant ${C}_{10}$ |
0.2078795763507619085 | ${i}^{i}$ (has no imaginary part) or ${e}^{\frac{-\pi}{2}}$ |
0.2357111317192329313 | http://planetmath.org/CopelandErdsConstantCopeland-Erdős constant |
0.2614972128476427837 | Meissel-Mertens constant |
0.3275822918721811159 | Lévy’s constant |
0.4146825098511116602 | The prime constant $\rho $ |
0.5926327182016361971 | Lehmer’s constant |
0.6079271018540266286 | $\frac{6}{{\pi}^{2}}$, the probability that a random integer is squarefree^{} |
0.6434105462883380261 | Cahen’s constant |
0.7642236535892206629 | Landau-Ramanujan constant |
0.8346268416740731862 | Gauss’s constant |
0.8862269254527580136 | $\mathrm{\Gamma}(\frac{3}{2})=\frac{1}{2}\sqrt{\pi}$ |
0.9159655941772190150 | Catalan’s constant $K$ |
1.2020569031595942853 | Apéry’s constant $\zeta (3)$ |
1.2254167024651776451 | $\mathrm{\Gamma}(\frac{3}{4})$ |
1.3063778838630806904 | Mills’ constant |
1.3247179572447460260 | The plastic constant |
1.4142135623730950488 | Square root^{} of two $\sqrt{2}$ |
1.4513692348833810502 | Ramanujan-Soldner constant |
1.6066951524152917637 | Erdős-Borwein constant |
1.6180339887498948482 | The golden ratio^{} $\varphi $ |
1.6449340668482264364 | $\zeta (2)=\frac{{\pi}^{2}}{6}$, the solution to the Basel problem^{} |
1.7320508075688772935 | Square root of three $\sqrt{3}$ |
1.7579327566180045327 | Vijayaraghavan’s infinite nested radical $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\mathrm{\dots}}}}}}$ |
1.7724538509055160273 | $\mathrm{\Gamma}(\frac{1}{2})=\sqrt{\pi}$ |
2.2360679774997896964 | Square root of five $\sqrt{5}$ |
2.6651441426902251887 | ${2}^{\sqrt{2}}$ |
2.6854520010653064453 | Khinchin’s constant |
2.4142135623730950488 | The silver ratio ${\delta}_{S}$ |
2.5849817595792532170 | Sierpiński’s constant |
2.7182818284590452354 | The natural log base $e$ |
3.1415926535897932385 | The ratio of a circle’s radius to its circumference^{} $\pi $ |
3.6256099082219083119 | $\mathrm{\Gamma}(\frac{1}{4})$ |
4.1327313541224929385 | $\sqrt{2e\pi}$ |
4.6692116609102990671 | Feigenbaum’s constant $\delta $ |
7.3890560989306502272 | ${e}^{2}$ |
14.1347251417346937904 | The imaginary part of the first nontrivial zero of the Riemann zeta function^{} (the real part is $\frac{1}{2}$) |
15.1542622414792641898 | ${e}^{e}$ |
36.4621596072079117710 | ${\pi}^{\pi}$ |
In looking these up in the OEIS, you can simply type them with a decimal point and no commas between the digits. If you get no results, try chopping off a couple of the least significant digits.
References
Title | index of important irrational constants |
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Canonical name | IndexOfImportantIrrationalConstants |
Date of creation | 2013-03-22 17:03:10 |
Last modified on | 2013-03-22 17:03:10 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 17 |
Author | PrimeFan (13766) |
Entry type | Topic |
Classification | msc 00A08 |