Difference between revisions of "Phi"
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| − | Phi (<math>\phi</math>) is | + | '''Phi''' (in lowercase, either <math>\phi</math> or <math>\varphi</math>; capitalized, <math>\Phi</math>) is the 21st letter in the Greek alphabet. It is used frequently in mathematical writing, often to represent the constant <math>\frac{1+\sqrt{5}}{2}</math>. (The Greek letter tau (<math>\tau</math>) was also used for this purpose in pre-Renaissance times.) |
==Use== | ==Use== | ||
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==Other useages== | ==Other useages== | ||
| − | *<math>\phi</math> is also commonly used to represent [[Euler's totient function]]. | + | * <math>\phi</math> is also commonly used to represent [[Euler's totient function]]. |
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==See also== | ==See also== | ||
* [[Irrational number]] | * [[Irrational number]] | ||
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* [[Geometry]] | * [[Geometry]] | ||
* [[Zeckendorf representation]] | * [[Zeckendorf representation]] | ||
[[Category:Constants]] | [[Category:Constants]] | ||
Revision as of 09:54, 18 December 2007
Phi (in lowercase, either 
or 
; capitalized, 
) is the 21st letter in the Greek alphabet. It is used frequently in mathematical writing, often to represent the constant 
. (The Greek letter tau (
) was also used for this purpose in pre-Renaissance times.)
Contents
Use
appears in a variety of different mathematical contexts: it is the limit of the ratio of successive terms of the Fibonacci sequence, as well as the positive solution of the quadratic equation 
.
Golden ratio
is also known as the Golden Ratio. It was commonly believed by the Greeks to be the most aesthetically pleasing ratio between side lengths in a rectangle. The Golden Rectangle is a rectangle with side lengths of 1 and ; it has a number of interesting properties.
The first fifteen digits of in decimal representation are 
Other useages
is also commonly used to represent Euler's totient function.
