SIMPLE explanation of the golden ratio?

Answer 1

Two quantities are in a Golden Ratio if the ratio of the bigger quantity to the smaller quantity is the same as the ratio of the sum of the two quantities to the bigger quantity.

In algebraic form, if the two quantities are x and y, and x is the bigger of the two, then they are in the Golden Ratio if

x/y = (x+y)/x

and that ratio is the Golden Ratio. which equals (1 + √5)/2.