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Powers of phi

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 = Φ10

Φ3 = Φ21

This can be further written as

Φn+2= Φn+1+ Φn

Φn = Φn-1 + Φn-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

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