Difference between revisions of "Phi"
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| − | Phi (<math>\phi</math>) is a letter in the Greek alphabet. It is often used to represent the constant <math>\frac{1+\sqrt{5}}{2}</math>. (The Greek letter tau (<math>\tau</math>) was also used in pre-Renaissance times.) | + | Phi (<math>\phi</math>) is a letter in the Greek alphabet. It is often used to represent the constant <math>\frac{1+\sqrt{5}}{2}</math>. (The Greek letter tau (<math>\tau</math>) was also used in pre-Renaissance times.) |
| + | ==Use== | ||
| + | <math>\phi</math> 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]] <math>x^2-x-1=0</math>. | ||
| + | ==Golden ratio== | ||
<math>\phi</math> 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 <math>\phi</math>; it has a number of interesting properties. | <math>\phi</math> 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 <math>\phi</math>; it has a number of interesting properties. | ||
| − | The first fifteen digits of <math>\phi</math> in decimal representation are | + | The first fifteen digits of <math>\phi</math> in decimal representation are <math>1.61803398874989</math> |
| − | <math>\phi</math> is also commonly used to represent [[Euler's totient function]]. | + | ==Other useages== |
| − | + | *<math>\phi</math> is also commonly used to represent [[Euler's totient function]]. | |
| − | <math>\phi</math> appears in many uses, including [[Physics]], [[Biology]] and many others. | + | *<math>\phi</math> appears in many uses, including [[Physics]], [[Biology]] and many others. |
==See also== | ==See also== | ||
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* [[Zeckendorf representation]] | * [[Zeckendorf representation]] | ||
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[[Category:Constants]] | [[Category:Constants]] | ||
Revision as of 13:50, 26 October 2007
Phi (
) is a letter in the Greek alphabet. It is often used to represent the constant 
. (The Greek letter tau (
) was also used 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.- appears in many uses, including Physics, Biology and many others.
