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
[hide]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.