where 
xn is term number n xn 1 is the previous term n 1 xn 2 is the term before that n 2 the golden ratio of 1 618 important to mathematicians scientists and naturalists for centuries is derived from the fibonacci sequence the quotient between each successive pair of fibonacci numbers in the sequence approximates 1 618 or its inverse 0 618 the golden ratio is derived by dividing each number of the fibonacci series by its immediate predecessor where f n is the nth fibonacci number the quotient f n f n 1 will approach the limit 1 618 known as the golden ratio many things in nature have dimensional properties that adhere to the ratio of 1 618 like the honeybee if you divide the female bees by the male bees in any given hive you will get a number near 1 618 the golden ratio also appears in the arts and rectangles whose dimensions are based on the golden ratio appear at the parthenon in athens and the great pyramid in giza 1