Golden numbers

The golden ratio ϕ =(1+√5)/2 = 1/61803398874... is theroot of the polynomial x^2 − x − 1 = 0, and is the one of the im portant numbers in mathematics. The golden ratio is also used in many fields of science. The golden ratio appears in some pat terns in nature, including the spiral arrangement of leaves and other plant parts. In this paper, we present a sequence of golden numbers {ϕn}n and study their properties.