Subject: Fibonacci Numbers Sender: Gary Nelb I'm doing a project on fibonacci numbers and I'm using different starting values and finding out if different starting values to see whether or not the ratios still get closer to phi. I was wondering, what numbers should I use. Should I use two of the same # like 2 and 2, or numbers like 1 and 2, or even something totally different. I need your help! Hi Gary, THe fibonacci recurrence is f(n) f(n1)f(n2) = 0. With it we associate its characteristic equation, x^{2} x  1 = 0. The roots are (1+SQRT(5))/2 and (1SQRT(5))/2. This tells us that f(n) looks like f(n) = A((1+SQRT(5))/2)^{n} + B((1SQRT(5))/2)^{n}, for suitable constants A and B which depend upon the initial conditions. Thus it doesn't matter what numbers that you start with initially, the ratios will always tend to phi = (1+SQRT(5))/2.
Cheers,
