Fibonacci and Lucas Numbers-Continued Fraction Expansion

Abstract

In modern science, there are lots of applications of Fibonacci and Lucas numbers have been used in number theory, computer science, applied mathematics and biology. In this paper, I have discussed Fibonacci number, Lucas number, the golden ratio, and their relations to them. I study numerous new properties of these sequences and focused to the generalized the formula for the Fibonacci number, Lucas number and some important identity; some observation of sunflower the head is carried out with the angular momentum velocity and represented continued fraction expansion of such number based on the golden ratio.