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Well, I guess it is about time I posted something to this section. I have not had anything really worthwhile to post and this probably doesn't qualify but hey! At least there is something here now.

Fibonacci Numbers

Let's start off by refeshing our memories regarding the fibonacci sequence. The fibonacci sequence is defined as:

Fn = Fn-1 + Fn-2 with F0 = 0 and F1 = 1

Thus, the fibonacci sequence looks like this:

0, 1, 1, 2, 3, 5, 8, 13, 21,...

With each being the sum of its two predecessors.

It is interesting to note that the ratio of two succesive fibonacci numbers approach the golden ratio: (1 + 5)/2 @ 1.618

lim Fn/Fn-1 = (1 + 5)/2
(n )

There are several methods for computing the nth fibonacci number. This one was discovered by A. de Moivre in 1718 and proved ten years later by Nicolas Bernoulli:

Fn = [((1 + 5)/2)^n - ((1 - 5)/2)^n]/5

More tomorow when I return.

Resources:

1. Schroeder, M. R., Number Theory in Science and Communication. Springer-Verlag: New York, 1997.

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