Powers of phi

Phi is the Greek letter which represent the golden number 1.618. Phi is the only number whose square is greater than itself by one, when expressed mathematically

Φ² = Φ + 1 = 2.618

We can derive the above equation in the following ways.

Φ² = Φ¹+Φ⁰

Φ³ = Φ²+Φ¹

This can be further written as

Φⁿ⁺²= Φⁿ⁺¹+ Φⁿ

Φⁿ = Φ^n-1 + Φ^n-2

Another significant fact about phi is, its the only number whose reciprocal is less than itself by one, which can be expressed as 1/Φ = Φ - 1 = 0.618.

Symbol of phi in upper case is represented as Φ. Symbol of phi in lower case is represented as φ