The Golden Ratio

The Golden Ratio can occur anywhere. In plain English we can say that two lengths are in the Golden proportion if the ratio of the shorter lenth to the longer length is equal to the ratio of the longer length to the sum of both lengths. Let S=shorter length and L=longer length. Then using mathematical notation: S/L = L/(S+L).

We can solve this equation for S in terms of L and we find that L=S*(1+5^.5)/2 or approximately L=1.6S. (If you know how to solve the equation above by using the quadratic formula, then porve th yourself that this is true.) So this is the unique case where the two lengths are in the Golden Ratio.

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