Phi

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

$\phi$ 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...

$\phi$ is also commonly used to represent Euler's totient function.

$\phi$ appears in many uses, including Physics, Biology and many others.

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Phi

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