Phi

Phi () is a letter in the Greek alphabet. It is often used to represent the constant . (The Greek letter was also used in pre-Renaissance times.) 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 .

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 ; it has a number of interesting properties.

The first few 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.

See also

• Irrational number
• Irrational base
• Phinary
• Geometry
• Zeckendorf representation

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