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.) <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 (<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.) <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>. | ||
| − | < | + | <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 <cmath>\phi</cmath> in decimal representation are: 1.61803398874989... | The first fifteen digits of <cmath>\phi</cmath> in decimal representation are: 1.61803398874989... | ||
| − | < | + | <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. |
==See also== | ==See also== | ||
Revision as of 15:50, 22 September 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.) 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 
.
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 ![\[\phi\]](http://latex.artofproblemsolving.com/a/8/a/a8a1946b4fc68a5c01e6f0ac3094cd1c424ffa09.png)
in decimal representation are: 1.61803398874989...
is also commonly used to represent Euler's totient function.
appears in many uses, including Physics, Biology and many others.
See also
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