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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 [[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 <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 ($\phi$) is a letter in the Greek alphabet. It is often used to represent the constant $\frac{1+\sqrt{5}}{2}$. (The Greek letter tau ($\tau$) was also used in pre-Renaissance times.)

Use

$\phi$ 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 $x^2-x-1=0$.

Golden ratio

$\phi$ 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 $\phi$; it has a number of interesting properties.

The first fifteen digits of $\phi$ in decimal representation are $1.61803398874989$

Other useages

See also

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