We all know that if you take the Fibonacci sequence out far enough you come to the point where the ratio of the next sequential number is phi, the golden ratio. (1+sqr(5))/2 or about 1.618.

But I wondered, why start with 0 and 1? Why not start with any two random numbers, say 7 and 3? Which creates a different set of numbers than 3 and 7. I tried it several times and I always got phi!

Can this be proven though? For any two random numbers will the Ratios always converge to phi?

SLD