Binet's Fibonacci Number Formula

Binet's formula is a special case of the  Binet form with , corresponding to the th Fibonacci number,

			(1)
			(2)

where  is the golden ratio. It was derived by Binet in 1843, although the result was known to Euler, Daniel Bernoulli, and de Moivre more than a century earlier.

REFERENCES:

Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, p. 108, 2002.

Séroul, R. Programming for Mathematicians. Berlin: Springer-Verlag, p. 21, 2000.

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 62, 1986.