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