Showing posts with label googol. Show all posts
Showing posts with label googol. Show all posts

4/13/07

Googol and comparable large numbers

A googol is greater than the number of particles in the observable universe, which has been variously estimated from 1079 up to 1081.[3][4]
A little googol is 2100, or about 1.267x1030, while a little googolplex is or about .
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.[5]
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, a rough estimate of the number of possible chess games, 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

Googolplex

Main article: googolplex
A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol:
googolplex=10E googolex

The shrinking googol

When it was named in 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. However, computations of a googol steps are still completely out of reach.

Writing out a googol

A googol can be written in conventional notation as follows:
1 googol = 10E100 =
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 is ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale

Googol

This article is about the large number. For the Internet company and search engine, see Google. For the author, see Nikolai Gogol.
A googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). One googol is written as: 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. 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. Indeed, it is not even a round figure. Its formal name is ten duotrigintillion.
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.
The word "google" or "googol," regardless of spelling, suggests the wide-eyed look of a baby, and the comic strip character Barney Google who began appearing in the 1910s