First page . . . Back to page 24
55 : http://www.sf.airnet.ne.jp/ts/language/largenumber.html A Japanese page, titled approximately "Beyond immeasurably large numbers", which describes several systems of names for large powers of ten. Near the end is a complete table of the Avatamsaka Sutra's numbers of the form 107×2N, with Kanji names and Hiragana transliteratons.
56 : http://lass.calumet.purdue.edu/cca/jgcg/2007/fa07/jgcg-fa07-tyler.htm Eiko Tyler, Globalization and A Mathematical Journey. Lists some of the avatamsaka sutra numbers and references the Japanese source 55.
57 : http://en.wikipedia.org/wiki/History_of_large_numbers Wikipedia article, History of large numbers.
58 : Ian Stewart, From Here to Infinity, pp. 129-131. The same information also appeared in New Scientist magazine, issue 1941, 03 September 1994, page 18, "Fun and games in four dimensions"..
59 : Zarko Bizaca, A Handle Decomposition of an Exotic R4, J. Differential Geometry, vol. 39 (1994) p. 496.
60 : http://groups.google.com/group/sci.math/browse_thread/thread/b38318e328ca461c/482554d283535ba2 Lee Rudolph, sci.math article responding to a question about Skewe's Number, 1994 June 27.
61 : http://www.entsoc.org/resources/faq.htm?/print#triv1 Entomological Society of America, FAQ.
62 : Martin Gardner, The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, W. W. Norton (2001), ISBN 0393020231. Coconuts: pp. 3-9; also published in 63.
63 : Martin Gardner, The Second Scientific American Book of Puzzles & Diversions: A New Selection Simon and Schuster (1961). Coconuts: pp. 104-111.
64 : Weisstein, Eric W. "Monkey and Coconut Problem." From MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/MonkeyandCoconutProblem.html
65 : Knuth, Donald E., Coping With Finiteness, Science vol. 194 n. 4271 (Dec 1976), pp. 1235-1242.
66 : Degrazia, Joseph, Math is Fun, Emerson Books (1973). 2592: problem 141; 1000000001: problem 137.
67 : [Crandall 1997] Richard Crandall, "The Challenge of Large Numbers", Scientific American no. 276 (Feb. 1997), pp. 74-79.
68 : Dale K. Hathaway and Stephen L. Brown, Fibonacci Powers and a Fascinating Triangle, The College Mathematics Journal, Vol. 28, No. 2 (Mar 1997), pp. 124-128
69 : http://www.research.att.com/~njas/sequences/a010048conj.png Ralf Stephan, A recurrence for the fibonomials
70 : http://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis Wikipedia, "Dirac large numbers hypothesis", 2008 May 7: "Dirac noted that the ratio of the size of the visible universe [...] to the size of a quantum particle [is about] 10^{40] ..."
71 : http://en.wikipedia.org/wiki/Proton Wikipedia, "Proton"
72 : http://en.wikipedia.org/wiki/HAKMEM Wikipedia, "HAKMEM". Describes AI Memo 239, a collection of algorithms, numerical facts and other information compiled at the MIT AI Lab in the early 1970's. Specific entries relate to the numbers 216, 239, 4.63×10170, and of course several others. A PDF file of a 1972 version of the memo is here.
73 : http://en.wikipedia.org/wiki/Jargon_File Wikipedia, "Jargon File". Describes a glossary of slang developed by computer pioneers at MIT, Stanford and elsewhere.
74 : http://en.wikipedia.org/wiki/69105_(number) Wikipedia, "69105 (number)".
75 : www.phys.uconn.edu/icap2008/invited/icap2008-gabrielse.pdf G. Gabrielse, New Measurement of the Electron Magnetic Moment and the Fine Structure Constant, submitted to the 21st International Conference on Atomic Physics, Storrs, Connecticut, USA; 2008 July 27.
76 : http://www.nbi.dk/~predrag/papers/PRD18-78.pdf P. Cvitanovic, B. Lautrup and R. B. Pearson, The number and weights of Feynman diagrams, Physical Review D vol. 18, pp. 1939-1949 (1978).
77 : Lamoreaux and Thorgerson, Phys. Rev. D 69, 121701 (2004).
78 : http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2008/HarvardMagneticMoment2008.pdf D. Hanneke, S. Fogwell, and G. Gabrielse, New Measurement of the Electron Magnetic Moment and the Fine Structure Constant Phys. Rev. Lett. 100, 120801 (2008).
79 : Dan Graham, personal correspondence, 2009.
80 : Wikipedia, "5th millennium", http://en.wikipedia.org/wiki/5th_millennium
81 : Wilipedia, "Mesoamerican Long Count calendar", http://en.wikipedia.org/wiki/MesoamericanLongCount_calendar
82 : Wikipedia, "Monstrous moonshine", http://en.wikipedia.org/wiki/Monstrous_moonshine
83 : Wikipedia, "Partition (number theory)", http://en.wikipedia.org/wiki/Partition(numbertheory)
84 : Louis Epstein, personal communication.
85 : Weisstein, Eric W. "Prime Counting Function." From MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/PrimeCountingFunction.html
86 : Weisstein, Eric W. "Barnes G Function." From MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/BarnesG-Function.html
87 : Weisstein, Eric W. "K Function." From MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/K-Function.html
88 : Weisstein, Eric W. "Panmagic Square." From MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/PanmagicSquare.html
89 : Weisstein, Eric W. "Associative Magic Square." From MathWorld — A Wolfram Web Resource. http://mathworld.wolfram.com/AssociativeMagicSquare.html
[90] 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."
[91] 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.
[92] Nancy Bowers and Pundia Lepi, Kaugel Valley systems of reckoning, Journal of the Polynesian Society 84 (3), pp. 309-324.
[93] Carl Sagan, Ann Druyan and Steven Soter (creators), Cosmos: a Personal Voyage (television series), 1980. Episode 9 has the googol quote.
[94] Georges Ifrah, The Universal History of Numbers, ISBN 0-471-37568-3. (1999).
[95] Erich Friedman, Problem of the month (August 2000), web page, 2000-2009.
[96] Erich Friedman, What's Special About This Number?, web page, 2000-2009.
[97] Dario Alpern, Known 3-digit prime factors of Googolplexplex - 1, web site, 2004. http://www.alpertron.com.ar/glpxm1.pl?digits=3
[98] Gordon, Raymond G., Jr. (ed.), Ethnologue: Languages of the World (15th edition), SIL International, Dallas (2005). Online version at www.ethnologue.com
[99] Don N. Page, Susskind's challenge to the Hartle-Hawking no-boundary proposal and possible resolutions, 2006. arXiv:hep-th/0610199v2
[100] 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.
[101] David de Neufville, personal correspondence.
[102] Ken Auletta, Googled : the end of the world as we know it (New York : Penguin Press, 2009) ISBN 9781594202353.
[103] CNN Beat 360, Anderson Cooper Daily Podcast for July 15th, 2009.
[104] Huffington Post, Man Charged 23 Quadrillion..., July 15th, 2009.
[105] Andrei Linde and Vitaly Vanchurin, How many universes are in the multiverse?, 2009. arXiv:0910.1589v2
[106] WMUR TV-9 (Manchester NH), Man's Debit Card Charged $23 Quadrillion..., July 15th, 2009.
[107] WTOV, Card Users Hit With $23 Quadrillion Charge, July 15th, 2009.
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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