Notable Properties of Specific Numbers  


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Bibliography

[125] Kasner and Newman, Mathematics and the Imagination, (Simon and Schuster, New York) 1940 (also republished in 1989 and in 2001). The story can also be found online — search for Googol plus the leading sentence "Words of wisdom are spoken by children at least as often as by scientists."

[126] T. Nagell, The diophantine equation x2+7=2n. Archiv fur Mathematik 4(13) pp. 185-187 (1960). Available from Springer

[127] S. Knapowski, On sign-changes of the difference π(x) - li x. Acta Arithmetica 7, 107-119 (1962).

[128] Dmitri Borgmann, "Naming the Numbers", Word Ways: the Journal of Recreational Linguistics 1 (1), February 1968. Cover and contents are here and article is here.

[129] Dennis Ritchie, Fifth Edition UNIX (Bell Laboratories), sqrt.s (PDP-11 assembler source code for a C library routine), June 1974. Archive created by The Unix Heritage Society. (I first found this on a mirror here).

[130] Nancy Bowers and Pundia Lepi, Kaugel Valley systems of reckoning, Journal of the Polynesian Society 84 (3), pp. 309-324.

[131] Ted Bastin et al., On the physical interpretation and the mathematical structure of the combinatorial hierarchy, Int. J. Theor. Phys. 18 p. 445 (1979). PDF here.

[132] Donald E. Knuth and Allan A. Miller, "A Programming and Problem-Solving Seminar" (notes from Stanford CS 204, Fall 1980), pages 4-12. PDF here: Programming and Problem-Solving Seminar

[133] Carl Sagan, Ann Druyan and Steven Soter (creators), Cosmos: a Personal Voyage (television series), 1980. Episode 9 has the googol quote.

[134] J. H. Conway and N. J. A. Sloane, Lorentzian forms for the Leech lattice. Bulletin of the American Mathematical Society 6(2) (March 1982), pp. 215-217.

[135] John Horton Conway and Richard Guy, The Book of Numbers, New York: Springer-Verlag (1996). ISBN 038797993X.

[136] Richard Guy, The strong law of small numbers. The American Mathematical Monthly 95(8) pp. 697-712 (1988). This has been used for several university courses and when I last checked was available here, here and here.

[137] The Compact Oxford English Dictionary (Second Edition), 1991. This is the version that has 21473 pages photographically reduced into a single book of about 2400 pages.

[138] Linda Scele Drawings Collection, Scele drawing 4087, 1993.

[139] James G. Gilson, Calculating the fine structure constant, 1995. PDF here

[140] Maurice Mignotte and Attila Pethö, On the system of diophantine equations x2-6y2=-5 and x=2z2-1. Mathematica Scandinavica 76, pp. 50-60 (1995). Available from the publisher here

[141] H. Pierre Noyes. Measurement, accuracy, bit-strings, Manthey's quaternions, and RRQM. In Entelechies (Proc. ANPA 16), K. G. Bowden, ed., University of East London. pp. 27-50. PDF here

[142] H. Pierre Noyes. Some remarks on discrete physics as an ultimate dynamical theory. PDF here

[143] Jim Blinn, Floating-point tricks, IEEE Computer Graphics and Applications, 1997.

[144] Richard Crandall, "The Challenge of Large Numbers", Scientific American no. 276 (Feb. 1997), pp. 74-79.

[145] J. H. E. Cohn, The diophantine system x2-6y2=-5, x=2z2-1. Mathematica Scandinavica 82, pp. 161-164 (1998). Available from the publisher here

[146] Eric Weisstein, The CRC Concise Encyclopedia of Mathematics (CRC Press), 1998. ISBN 0849396409.

[147] Richard Borcherds, The Leech lattice and other lattices. Ph.D. thesis, Trinity College (originally given June 1984), as corrected in 1999.

[148] Georges Ifrah, The Universal History of Numbers, ISBN 0-471-37568-3. (1999).

[149] Erich Friedman, Problem of the month (August 2000), web page, 2000-2009.

[150] Erich Friedman, What's Special About This Number?, web page, 2000-2009.

[151] John Baez, The Fano Plane (web page) 2001. (Part of a collection describing the Octonions)

[152] David Eberly, Fast inverse square root, 2002 (as archived on 2003 Apr 26 by the Internet Archive Wayback Machine).

[153] David Eberly, Fast inverse square root (revisited), 2010.

[154] Michael Janssen, The Trouton experiment and E=mc2 (handout, PDF file), 2002.

[155] Toshio Fukushima, A new precession formula. Public Relations Center, NAOJ, 2003.

[156] Max Tegmark, Parallel Universes, 2003. Available from arxiv.org.

[157] M. Agrawal et al., PRIMES is in P. Annals of Mathematics 160(2) pp. 781-793 (2004). Available from the editors here.

[158] Dario Alpern, Known 3-digit prime factors of Googolplexplex - 1, web site, 2004. http://www.alpertron.com.ar/glpxm1.pl?digits=3

[159] Maohua Le, On the diophantine system x2-Dy2=1-D AND x=2z2-1. Mathematica Scandinavica 95, pp. 171-180 (2004). Available from the publisher here.

[160] Gordon, Raymond G., Jr. (ed.), Ethnologue: Languages of the World (15th edition), SIL International, Dallas (2005). Online version at www.ethnologue.com

[161] John Baez, Klein's Quartic Curve (web page) July 28, 2006.

[162] Andrew Granville and Greg Martin, Prime number races, The American Mathematical Monthly 113(1) pp. 1-33 (2006). Available from the AMM here; a 2004 preprint is on arxiv.org.

[163] Don N. Page, Susskind's challenge to the Hartle-Hawking no-boundary proposal and possible resolutions, 2006. arXiv:hep-th/0610199v2

[164] Mark Ronan, Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, 2006. ISBN 0-19-280723-4

[165] Alan H. Guth, Eternal inflation and its implications, 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology (IRGAC2006), Barcelona, Spain, 11-15 July 2006.

[166] David de Neufville, personal correspondence.

[167] John Baez, My Favorite Numbers (web page) 2008. Includes videos and slides from three talks given in 2008 at University of Glasgow.

[168] Andrew Granville, Prime number patterns, The American Mathematical Monthly 115(4) pp. 279-296 (2008). Available from the MAA here and from the author here.

[169] My Math Forum, discussion thread, 2008 Oct 10

[170] Ken Auletta, Googled : the end of the world as we know it (New York : Penguin Press, 2009) ISBN 9781594202353.

[171] Daan van Berkel, On a curious property of 3435. (2009) arXiv:0911.3038

[172] CNN Beat 360, Anderson Cooper Daily Podcast for July 15th, 2009.

[173] Huffington Post, Man Charged 23 Quadrillion..., July 15th, 2009.

[174] Andrei Linde and Vitaly Vanchurin, How many universes are in the multiverse?, 2009. arXiv:0910.1589v2

[175] WMUR TV-9 (Manchester NH), Man's Debit Card Charged $23 Quadrillion..., July 15th, 2009.

[176] WTOV, Card Users Hit With $23 Quadrillion Charge, July 15th, 2009.

[177] Jeffrey Hankins, personal correspondence, 2010.

[178] Theodore P. Hill, Ronald F. Fox, Jack Miller, A Better Definition of the Kilogram

(note on page 5: "At this point in time, it is not yet possible to obtain exact counts of individual atoms, even when they are in a crystal lattice, but that is merely a question of time.")

[179] David Stuart, Notes on Accession Dates in the Inscriptions of Coba, 2010. Available here.

[180] Ivan Panchenko, personal correspondence, 2011.

[181] Marek Wolf, The Skewes number for twin primes: counting sign changes of π2(x) − C2Li2(x), 2011. Available from arxiv.org.

[182] Gottfried Helms, The Lucas-Lehmer-test for Mersenne-numbers and the number Λ ~1.389910663524..., April 4 2012.

[183] Randall Munroe, xkcd 1047 -- Approximations (online comic strip), April 25 2012.

Note : This strip mentions my ries program because Munroe used it to derive some of the expressions, near-equalities and approximations shown in the strip. He and I did not communicate prior to the publication of the strip, and all of the material in the strip was found by him. Answering a presumably large volume of responses, he specifically commented on this fact in a note at the top of the comic (which was visible for a while on the first day) by stating:

"Note: '1 year = π × 107 seconds' is popular with physicists. For this list, I've tried to stick to approximations that I noticed on my own."

There are a few obvious exceptions which were included for their amusement value: the Rent approximation 525600×60 ≅ 31556952, and 1/140 as an approximation to the reciprocal of the fine-structure constant (the comment "I've had enough of this 137 crap" refers to the fanatical cult of 137).

[184] TrueNews.org, "The Origin of Life -- Evolution's Dilemma (web page), accessed 2010 April 29.

[185] Wolfram Alpha, "computational knowledge engine" online resource.

[186] This is close.

Quick index: if you're looking for a specific number, start with whichever of these is closest:    0.065988...    1    1.618033...    3.141592...    4    12    16    21    24    29    39    46    52    64    68    89    107    137.03599...    158    231    256    365    616    714    1024    1729    4181    10080    45360    262144    1969920    73939133    4294967297    5×1011    1018    5.4×1027    1040    5.21...×1078    1.29...×10865    1040000    109152051    101036    101010100    — --    footnotes    Also, check out my large numbers and integer sequences pages.

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