Googol

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This article is about the large number. For the Internet company and search engine, see Google. For the author, see Nikolai Gogol.

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A googol is the large number 10¹⁰⁰, that is, the digit 1 followed by one hundred zeros (in decimal representation). One way of grasping its size is to multiply 1,000,000 by itself 16 times, then multiply the result by ten thousand. The ultimate product of this operation is one googol (10¹⁰⁰). The term was coined in 1920 by nine-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination.

A googol is of the same order of magnitude as the factorial of 70 (70! being approximately 1.198 googol, or 10 to the power 100.0784), and its only prime factors are 2 and 5 (100 of each). In binary it would take up 333 bits.

The googol is of no particular significance in mathematics, but is useful when comparing with other incredibly large quantities such as the number of subatomic particles in the visible universe or the number of possible chess games. Kasner created it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics.

The Internet search engine Google was named after this number. Larry Page, one of the founders, was fascinated with mathematics and 'Googol', even during high school. They ended up with 'Google' due to a spelling mistake on a cheque that investors wrote to the founders.

1 Writing out a googol
2 The shrinking googol
3 Googolplex
4 Googol and comparable large numbers
5 Miscellaneous
6 See also
7 References
8 External link

[edit] 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

Its "conventional" English number name, on the short scale, is ten dotrigintillion, or on the long scale, ten thousand sexdecillion.

[edit] The shrinking googol

Back when it was named in 1938(?) ( 1920 ), the googol was undeniably large. 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. Computations of a googol steps are still completely out of reach.

[edit] Googolplex

Main article: googolplex

A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol:

<math>\mbox{googolplex} = {10}^{\mbox{googol}} = {10}^{({10}^{100})} .</math>

[edit] Googol and comparable large numbers

Avogadro's number, 6.022x10²³, can loosely be thought of as the number of hydrogen atoms in a gram of hydrogen gas, and is perhaps the most widely known large number from chemistry and physics. Avogadro's number is much less than a googol.
A little googol is 2¹⁰⁰, or about 1.267x10³⁰
A googol is greater than the number of particles in the known universe, which has been variously estimated from 10⁷² up to 10⁸⁷.
Black holes are presumed to evaporate because they faintly give off Hawking radiation; if so, a supermassive black hole would take about a googol years to evaporate. [1]
If seventy people were lining up to enter a concert, how many different ways could they be arranged? Just over a googol, 1.19785717 × 10¹⁰⁰ approximately, or seventy factorial (70!).
The Shannon number is a rough estimate of the number of possible chess games, and it is very much more than a googol, around the order of 10¹²⁰.
A googol is considerably less than the number described in the ancient Greek story of The Sand Reckoner, namely <math>10^{8 \times 10^{16}}</math>.
A little googolplex is <math>2^{2^{100}}</math> or about <math>10^{3.8 \times 10^{29}}</math>.
"A googol is precisely as far from infinity as is the number one." - Carl Sagan, Cosmos

[edit] Miscellaneous

Googol was the answer to the million-pound question on Who Wants to Be a Millionaire? when Major Charles Ingram allegedly attempted to defraud the quiz show on 10 September 2001.
In one Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Schroeder responds "about a googol to one."
A Googolagon with a small diameter can be considered a circle.

[edit] See also

[edit] References

Kasner, Edward & Newman, James Roy Mathematics and the Imagination (London: Penguin, 1940; New York: Simon and Schuster, 1967; Dover Pubns, April 2001, ISBN 0-486-41703-4).
"Searching for the birth of the googol"
"An evening with Google's Marissa Mayer"
"Google and Larry Page"
"There Could Be No Google Without Edward Kasner", Carl Bialik, The Wall Street Journal Online, June 14 2004.