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.)
It is also where is the nth number in the Fibonacci sequence. In other words, if you divide the nth term of the Fibonacci series over the (n-1)th term, the result approaches as n increases.
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
- is also commonly used to represent Euler's totient function.