The derivation of the equation most commonly used to find the value of phi appears above. To see a more detailed explanation, click here.

      This equation helps to show why phi is irrational--there is no solution for the square root of five.

      Another equation associated with phi is the infinite continued fraction appearing below. If you're having trouble with this one, try substituting 1 for the value of phi. you should end up with fractions that are ratios of successive Fibonacci numbers...which are approximately equal to phi.