Googol
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A googol is the large number 10100, that is, the digit 1 followed by one hundred zeroes. The term was coined in 1938 by nine-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner announced the concept in his book Mathematics and the Imagination.
A googol is "approximately" equal to the factorial of 70, and its only prime factors are 2 and 5. In binary it would take up 333 bits.
The googol is of no particular significance in mathematics, nor does it have any practical uses. Kasner created it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in mathematics teaching.
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Writing out a googol
A googol can be written in conventional notation, as follows:
- 1 googol = 10100 = 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
Relation to -illion number names
Using the short scale, a Googol is equal to ten duotrigintillion.
The shrinking googol
Back when it was named in 1938, the googol was undeniably large, and from a physical standpoint, a googol of anything would not fit in the known universe. However, with the invention of fast computers and fast algorithms, computation with numbers the size of a googol has become routine. For example, even the difficult problem of prime factorization is now fairly accessible for 100 digit numbers.
The largest number that can be represented by a typical pocket calculator for high school or scientific use is slightly less than a googol (e.g. 9.9999999 E+99, i.e. 9.9999999<math>\times<math>1099, or 0.99999999 googol). However, some models allow exponents larger than 99.
Trivia
Googol was the answer to the million-pound question on Who Wants to Be a Millionaire when Major Charles Ingram attempted to defraud the quiz show on 10 September 2001.
If we drew a regular polygon with a googol sides that was 1027 times the size of the known universe, it would still appear circular, even on the scale of a Planck length.
A googol is greater than the number of particles in the known universe, which has been variously estimated from 1072 up to 1087.
A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol: <math>{10}^\mbox{googol}<math> = <math>\,\!{10}^{{10}^{100}}<math>.
Since a googol plus 1 is the number of digits in a googolplex, it would therefore not be possible to write down or store the digits of a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.
A little googol is 2^100 ~= 1.267*10^30 and a little googolplex is 2^(2^100) ~= 10^(3.8*10^29).
The Internet search engine Google was named as a pun on this number. The original founders were going for 'Googol', but ended up with 'Google' due to a spelling mistake. Larry Page: "Lucas Pereira: 'You idiots, you spelled 'Googol' wrong!' But this was good, because google.com was available and googol.com was not. Now most people spell 'Googol' 'Google', so it worked out OK in the end."
See also
References
- Kasner, Edward & Newman, James Roy Mathematics and the Imagination (London: Penguin, 1940; New York: Simon and Schuster, 1967; Dover Pubns, April 2001, ISBN 0486417034).
- 'Searching for the birth of the googol' (http://afr.com/articles/2004/06/18/1087245103935.html)
- 'An evening with Googles Marissa Mayer' (http://alan.blog-city.com/read/1003011.htm)
- 'Google and Larry Page' (http://www.j-bradford-delong.net/movable_type/2003_archives/000032.html)da:Googol
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