Fibonacci number (idea)

The Nth number in the Fibonacci sequence can be found approximately by this formula:

        / 1 + sqrt(5) \ n
F(n) = |  -----------  |   / sqrt(5)
        \      2      /

The nearest integer is the Nth Fibonacci number.
Notice that the bracketted expression (1 + sqrt(5)) / 2 is the golden ratio.

In code (BASIC, at least), that would be: Fn = int( ( ( ( 1 + sqrt(5) ) / 2 ) ^ n ) / sqrt(5) + 0.5 )

For more of this kind of thing, point your browser at
http://www.maa.org/devlin/devlin_3_99.html