Phi
Phi (in lowercase, either or ; capitalized, ) is the 21st letter in the Greek alphabet. It is used frequently in mathematical writing, often to represent the constant . (The Greek letter tau () was also used for this purpose in pre-Renaissance times.)
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[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 Usages
- is also commonly used to represent Euler's totient function.