Binet's formula is an equation which gives the 
th Fibonacci number as
a difference of positive and negative 
th powers of the golden ratio 
. It can be written as
 |  |  |
(1)
|
 |  |  |
(2)
|
Binet's formula is a special case of the 
Binet form with 
It was derived by Binet in 1843, although the result was
known to Euler, Daniel Bernoulli, and de Moivre more than a century earlier.
