The golden ratio satisfies the equation x² = 1 + x/2

Explanation

It is the unique positive solution to the quadratic equation x² = x + 1, which is equal to (1 + √5)/2 or approximately 1.618. Another way to write x² = x + 1 is x = 1 + 1/x, meaning the golden ratio is equal to one plus its own reciprocal.