|
|||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Googol |
A googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). The term was coined in 19381 by Milton Sirotta (1929–1980), 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. A googol has 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:
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.
Contents |
A googolplex is the number one followed by one googol zeroes, or ten raised to the power of one googol:
In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in base-10 numerals (i.e., "1,000,000,000...") would be physically impossible, since doing so would require more space than the known universe occupies.
A googol is greater than the number of atoms in the observable universe, which has been variously estimated from 1079 up to 108123.
Less than a googol Planck times have elapsed since the Big Bang (the current figure stands at around 8×1060 Planck times). Similarly, the size of the observable universe is about 9×10185 cubic Planck lengths.
From the previous figures it can be seen that a list of positions of every particle at every possible instant of time, at the maximum possible accuracy, would contain well over a googol entries (of the order of 10325), but still far less than a googolplex.
Avogadro's number, 6.02214179×1023, is exactly the number of 12C atoms in 12 grams (0.012 kg) of unbound 12C in its ground state. It is perhaps the most widely known large number from chemistry and physics. Avogadro's number is less than the fourth root of 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.4
Seventy factorial, or 70!, is 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
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
![\left[\left((10)^{(10)}\right)^{10}\right]_{10^8}=\left[10^{100}\right]_{10^8},](http://upload.wikimedia.org/math/5/9/b/59bf3ad009f6e4fe002dacf16c554e06.png)
that is, one googol in base 108
|
|||||||||||||||||||
 |
 |
 |
 |
 |
 |
 |
 |