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| Related to google | |||
| {{distinguish|Google}} | |||
| {{Expand German|Googol|date=July 2015}} | |||
| A '''googol''' is the ] 10<sup>100</sup>. In decimal notation, it is written as the ] 1 followed by one hundred ]s: <!-- DO NOT USE GAPS TEMPLATE, BREAKS MOBILE --> | |||
| 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. | |||
| ==Concept== | |||
| The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. ] ].<ref>{{cite journal | title = There Could Be No Google Without Edward Kasner| first = Carl | last = Bialik | journal = The Wall Street Journal Online | date = June 14, 2004 |url=https://www.wsj.com/articles/SB108575924921724042 }} (retrieved March 17, 2015)</ref> Kasner popularized the concept in his 1940 book '']''.<ref>{{cite book |author1=Kasner, Edward |author2=Newman, James R.| title=Mathematics and the Imagination| url=https://books.google.com/books?id=Ad8hAx-6m9oC&lpg=PP1&dq=Mathematics%20and%20the%20Imagination&pg=PP1#v=onepage&q&f=false| year = 1940| publisher = Simon and Schuster, New York| isbn = 0-486-41703-4}} The relevant passage about the googol and googolplex, attributing both of these names to Kasner's nine-year-old nephew, is available in {{cite book|ref=harv|editor=James R. Newman|title=The world of mathematics, volume 3|publisher=Dover Publications|location=Mineola, New York|year=2000|origyear=1956|isbn=978-0-486-41151-4|pages=2007–2010}}</ref> Other ] for googol include '''ten duotrigintillion''' on the ], '''ten thousand sexdecillion''' on the ], or '''ten sexdecilliard''' on the ]. | |||
| == Size == | |||
| A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of ] in the visible universe or the number of hypothetical possibilities in a ] game. Kasner used it to illustrate the difference between an unimaginably large number and ], and in this role it is sometimes used in teaching mathematics. To give a sense of how big a googol really is, the mass of an electron, just under {{val|e=-30|u=kg}}, can be compared to the mass of the visible universe, estimated at between {{val|e=50}} and {{val|e=60|u=kg}}.<ref>{{cite web|author=Elert, Glenn|title=Mass of the Universe |url=http://hypertextbook.com/facts/2006/KristineMcPherson.shtml|display-authors=etal}}</ref> It is a ratio in the order of about 10<sup>80</sup> to 10<sup>90</sup>, or only about one ten-billionth of a googol (0.00000001% of a googol). | |||
| ] points out that the total number of elementary particles in the universe is around 10<sup>80</sup> (the ]) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10<sup>128</sup>. He also notes the similarity of the first calculation to that of ] in ].<ref>{{cite book|last=Sagan|first=Carl|authorlink=Carl Sagan|title=Cosmos|year=1981|publisher=Book Club Associates|pages=220–221}}</ref> | |||
| The decay time for a supermassive ] of roughly 1 galaxy-mass (10<sup>11</sup> ]es) due to ] is on the order of 10<sup>100</sup> years.<ref name=page>Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N. Page, ''Physical Review D'' '''13''' (1976), pp. 198–206. {{doi|10.1103/PhysRevD.13.198}}. See in particular equation (27).</ref> Therefore, the ] is lower-bounded to occur a googol years in the future. | |||
| == Properties == | |||
| A googol is approximately ''70!'' (] of 70). Using an ], ], one would need 333 bits to represent a googol, i.e., 1 googol ≈ 2<sup>332.19280949</sup>, or exactly <math>2^{(100/\mathrm{log}_{10}2)}</math>. However, a googol is well within the maximum bounds of an ] ] ] type. | |||
| The series of residues (mod ''n'') of one googol is: | |||
| :0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 4, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 16, 10, 5, 0, 1, 4, 25, 28, 10, 28, 16, 0, 1, 4, 31, 12, 10, 36, 27, 16, 11, 0, ... {{OEIS|id=A066298}} | |||
| == Cultural impact == | |||
| Widespread sounding of the word occurs through the name of the company ], with the name "Google" being an accidental misspelling of "googol" by the company's founders,<ref>{{cite web|url=http://graphics.stanford.edu/~dk/google_name_origin.html |title=Origin of the name "Google" |last=Koller |first=David |date=January 2004 |publisher=Stanford University |accessdate=July 4, 2012 |archiveurl=http://www.webcitation.org/68ubHzYs7?url=http://graphics.stanford.edu/~dk/google_name_origin.html |archivedate=July 4, 2012 |deadurl=yes |df= }}</ref> which was picked to signify that the search engine was intended to provide large quantities of information.<ref>{{cite web|url=https://www.google.com/company.html |title=Google! Beta website |publisher=Google, Inc. |archiveurl=https://web.archive.org/web/19990221202430/http://www.google.com/company.html |archivedate=February 21, 1999 |accessdate=October 12, 2010 |deadurl=yes |df= }}</ref> In 2004, family members of Kasner, who had inherited the right to his book, were considering suing Google for their use of the term googol;<ref>{{cite web|title= Have your Google people talk to my `googol' people|url=http://articles.baltimoresun.com/2004-05-16/entertainment/0405150243_1_google-googol-internet-search-engine}}</ref> however, no suit was ever filed. | |||
| Since October 2009 Google has been assigning domain names to its servers under the domain "1e100.net", the scientific notation for 1 googol, in order to provide a single domain to identify servers across the Google network.<ref>{{cite web |url=http://www.theregister.co.uk/2010/02/08/google_mystery_domain/ |title=Google doppelgänger casts riddle over interwebs |date=8 February 2010 |accessdate=30 December 2015 |publisher=The Register |author=Cade Metz}}</ref><ref>{{cite web |url=https://support.google.com/faqs/answer/174717?hl=en |title=What is 1e100.net? |accessdate=30 December 2015 |publisher=Google}}</ref> | |||
| The word is notable for being the subject of the £1 million question in a 2001 episode of the British quiz show '']'', when contestant ] ] with the help of an accomplice.<ref>{{citation|title=Television's Strangest Moments: Extraordinary But True Tales from the History of Television|first1=Quentin|last1=Falk|first2=Ben|last2=Falk|publisher=Franz Steiner Verlag|year=2005|isbn=9781861058744|url=https://books.google.com/books?id=4L7pA2tKumsC&pg=PA245|pages=245–246|contribution=A Code and a Cough: Who Wants to Be a Millionaire? (1998–)}}.</ref> | |||
| ==See also== | |||
| * ] | |||
| * ] | |||
| * ] | |||
| * '']'' | |||
| ==References== | |||
| {{Reflist|30em}} | |||
| ==External links== | |||
| * {{MathWorld | urlname=Googol | title=Googol}} | |||
| * {{PlanetMath | urlname=Googol | title=googol}} | |||
| * {{cite web|title=Googol and Googolplex|url=http://www.numberphile.com/videos/googolplex.html|work=Numberphile|publisher=]|author=Padilla, Tony|author2=Symonds, Ria}} | |||
| {{Wiktionary}} | |||
| {{Large numbers}} | |||
| ] | |||
| ] | |||
| ] | |||
Revision as of 16:24, 17 May 2017
Related to google