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>. | + | 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 <math>\tau</math> was also used in pre-Renaissance times.) <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>. |
Phi 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. | Phi 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. | ||
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==See also== | ==See also== | ||
| − | * [[ | + | * [[Irrational number]] |
| − | * [[ | + | * [[Irrational base]] |
| − | * [[ | + | * [[Phinary]] |
| − | * [[ | + | * [[Geometry]] |
* [[Zeckendorf representation]] | * [[Zeckendorf representation]] | ||
{{stub}} | {{stub}} | ||
[[Category:Constants]] | [[Category:Constants]] | ||
Revision as of 15:48, 22 September 2007
Phi (
) is a letter in the Greek alphabet. It is often used to represent the constant 
. (The Greek letter 
was also used in pre-Renaissance times.) 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 
.
Phi 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 few digits of Phi in decimal representation are: 1.61803398874989...
Phi is also commonly used to represent Euler's totient function.
Phi appears in many uses, including Physics, Biology and many others.
See also
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