Misplaced Pages

Googol: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editNext edit →Content deleted Content addedVisualWikitext
Revision as of 20:57, 19 June 2017 view sourceBemji djsjdjd (talk | contribs)7 edits Added contentTags: canned edit summary section blanking Mobile edit Mobile web edit← Previous edit Revision as of 20:57, 19 June 2017 view source Bemji djsjdjd (talk | contribs)7 editsNo edit summaryTags: Mobile edit Mobile web editNext edit →
Line 1: Line 1:
{{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.

== Size == == 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). 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).

Revision as of 20:57, 19 June 2017

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 subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game. Kasner used it to illustrate the difference between an unimaginably large number and infinity, 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 10 kg, can be compared to the mass of the visible universe, estimated at between 10 and 10 kg. It is a ratio in the order of about 10 to 10, or only about one ten-billionth of a googol (0.00000001% of a googol).

Carl Sagan points out that the total number of elementary particles in the universe is around 10 (the Eddington number) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10. He also notes the similarity of the first calculation to that of Archimedes in The Sand Reckoner.

The decay time for a supermassive black hole of roughly 1 galaxy-mass (10 solar masses) due to Hawking radiation is on the order of 10 years. Therefore, the heat death of the universe is lower-bounded to occur a googol years in the future.

Properties

A googol is approximately 70! (factorial of 70). Using an integral, binary numeral system, one would need 333 bits to represent a googol, i.e., 1 googol ≈ 2, or exactly 2 ( 100 / l o g 10 2 ) {\displaystyle 2^{(100/\mathrm {log} _{10}2)}} . However, a googol is well within the maximum bounds of an IEEE 754 double-precision floating point 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, ... (sequence A066298 in the OEIS)

Cultural impact

Widespread sounding of the word occurs through the name of the company Google, with the name "Google" being an accidental misspelling of "googol" by the company's founders, which was picked to signify that the search engine was intended to provide large quantities of information. 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; 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.

The word is notable for being the subject of the £1 million question in a 2001 episode of the British quiz show Who Wants to Be a Millionaire?, when contestant Charles Ingram cheated his way through the show with the help of an accomplice.

See also

References

  1. Elert, Glenn; et al. "Mass of the Universe".
  2. Sagan, Carl (1981). Cosmos. Book Club Associates. pp. 220–221.
  3. 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).
  4. Koller, David (January 2004). "Origin of the name "Google"". Stanford University. Archived from the original on July 4, 2012. Retrieved July 4, 2012. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  5. "Google! Beta website". Google, Inc. Archived from the original on February 21, 1999. Retrieved October 12, 2010. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  6. "Have your Google people talk to my `googol' people".
  7. Cade Metz (8 February 2010). "Google doppelgänger casts riddle over interwebs". The Register. Retrieved 30 December 2015.
  8. "What is 1e100.net?". Google. Retrieved 30 December 2015.
  9. Falk, Quentin; Falk, Ben (2005), "A Code and a Cough: Who Wants to Be a Millionaire? (1998–)", Television's Strangest Moments: Extraordinary But True Tales from the History of Television, Franz Steiner Verlag, pp. 245–246, ISBN 9781861058744.

External links

Large numbers
Examples
in
numerical
order
Expression
methods
Notations
Operators
Related
articles
(alphabetical
order)
Categories: