Googol
From Wikipedia, the free encyclopedia
Googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). The term was coined in 1920 by nine-year-old Milton Sirotta (1911–1981), nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination (1940).
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.
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. Edward 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.
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 official English number name is ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.
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[edit] Googolplex
A googolplex is 1 followed by a googol zeroes, or ten raised to the power of a googol:
- 10googol = 1010100.
In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in numerals (i.e., "1,000,000,000...") would be physically impossible, since doing so would require more space than the known universe occupies.
[edit] Googol and comparable large numbers
- A googol is greater than the number of elementary particles in the observable universe, which has been variously estimated from 1079 up to 1081,[1][2].
- A little googol is 2100 (about 1.268x1030), or 1,267,650,600,228,229,401,496,703,205,376, while a little googolplex is <math>2^{2^{100}}</math> or about <math>10^{3.8 \times 10^{29}}</math>.
- Avogadro's number, 6.0221415x1023, can loosely be thought of as the number of carbon atoms in twelve grams of elemental carbon, and is perhaps the most widely known large number from chemistry and physics. Avogadro's number is much less than a googol.
- 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.[3]
- Seventy factorial, or 70!, is just over a googol, 1.19785717 × 10100. This means that there are over a googol ways to arrange seventy items (or people) in a sequence (such as a line to a concert).
- The Shannon number, 10120, a rough lower bound on the number of possible chess games, is more than a googol.
- A googol is considerably less than the number described in the ancient Archimedes' story of The Sand Reckoner, namely <math>\left((10^8)^{(10^8)}\right)^{(10^8)}=10^{8\cdot 10^{16}}.</math> But it should be noted that the system invented by Archimedes is reminiscent of a positional numeral system with base 108, so that Archimedes' number could be written <math>\left[\left((10)^{(10)}\right)^{10}\right]_{10^8}=\left[10^{100}\right]_{10^8}</math>, that is, 1 googol in base 108.
[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 the January 23, 1963 Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Schroeder responds "Oh, I'd say about 'googol' to one."
- In an episode of the animated series Teenage Mutant Ninja Turtles: Fast Forward, the "Gaminator" video games system is said to have a "3 googolhertz processor."
- "A googol is precisely as far from infinity as is the number one." — Carl Sagan, Cosmos
The name Google has been derived from the word "Googol" and has been spelled wrong by the founders Larry Page and Sergey Brin, as published in the book "The Google Story"- by David A. Vise.
[edit] See also
[edit] References
- ^ Estimate of the number of particles in the Universe; 1079 up to 1081
- ^ Another estimate of the number of particles in the Universe; 4x1079
- ^ On the dark side, p.4
[edit] External links
- History from the Google website
- Eric W. Weisstein, Googol at MathWorld.
- googol at PlanetMath.
- "Tridecabillion" by Paul Niquetteast:Googol
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