This document summarizes famous mathematical constants in three parts: (1) it lists keywords of constants, (2) it provides two tables that approximate some constants as fractals and sorts them by value for easy reference, and (3) it plots the distributed constants on a scale from 0 to 1. The document references other works on approximations of pi, squaring the circle, the twin prime counting function, and testing the Mertens theorems.

1. Famous constants, sorted and with fractal approximations
version: 2
Chris De Corte
chrisdecorte@yahoo.com
December 29, 2016
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2. 1 KEY-WORDS
1 Key-Words
Morse Thue, Gelfond, Liouville, Chapernowne, MRB, Feigenbaum delta, Copeland Erd¨os,
Meissel Mertens, Bernstein, Reciprocal Fibonacci, Pr´evost, Log 2, Gauss Kuzmin Wirs-
ing, L´evy, Archimedes, Hafner Sarnak McCurley, Frans´en Robinson, Euler, Khinchin, Artin,
Hilbert, Sierpinski, Feigenbaum alpha, Universal parabolic, Landau, Brun twin, Euler Mascheroni,
Omega, Theodorus, Niven, Golden ratio, Erd¨os Borwein, Golomb Dickman, Rise time prob-
ability, Cahen, Lieb’s square ice, Twin prime, Laplace limit, Porter, Backhouse, Ramanu-
jan Soldner, Embree Trefethen, Pythagoras, Grossman, Dottie, Plastic, Landau Ramanujan,
Mills, Conway, Glaisher Kinkelin, Delian, Alladi Grinstead, Rayleigh, Ap´ery, Gauss, Brun
quadruplet, Viswanath, Lengyel, Catalan.
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3. 2 FAMOUS CONSTANTS
2 famous constants
In next 2 tables, I summarize the approximation of some famous constants as a fractal. As
can be calculated, they are accurate up to the displayed number of digits. Moreover, I sorted
the constants so one can quickly find a constant based on the number he is looking for. I
didn’t put any effort in explaining where the constants come from as they can be easily found
on the web.
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4. 2 FAMOUS CONSTANTS
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5. 3 DISTRIBUTION
3 Distribution
In a last figure, I plot the different constants on a scale from 0 to 1. One can see that they
seem to be evenly distributed.
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6. 4 REFERENCES
4 References
1. en.wikipedia.org ; Mathematical constant
2. http://www.numericana.com/answer/constants.htm
3. http://sprott.physics.wisc.edu/pickoveR/trans.html
4. Chris De Corte (2013); Approximations in drawing pi and squaring the circle ; Research
Gate ; DOI: 10.13140/RG.2.1.1843.9525
5. Chris De Corte (2016); The twin prime counting function v4 ; Research Gate ; DOI:
10.13140/RG.2.1.1184.4964
6. Chris De Corte (2015); Testing the Mertens theorems ; Research Gate ;
DOI: 10.13140/RG.2.1.3081.0726
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