Difference between revisions of "Phi"
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<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> 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== | ==Golden ratio== | ||
− | <math>\phi</math> is also known as the | + | <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 <math>1.61803398874989</math> | The first fifteen digits of <math>\phi</math> in decimal representation are <math>1.61803398874989</math> |
Revision as of 17:09, 28 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.