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http://en.wikipedia.org/wiki/Golden_ratio

http://en.wikipedia.org/wiki/Fibonacci_number

The fibonacci sequence is pretty magical. It's definition is very simple

f(0) = 1

f(1) = 1

f(x) = f(x-1) + f(x-2), for all x >= 2

But is miraculously related to a ton of mathematical phenomena, especially in number theory.

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= \dfrac{1}{1 + \dfrac{1}{1+\frac{1}{1+...}}} = \phi\][/tex] or the golden ratio. Also, note (since phi is defined by those recursive sequences) that [tex]\frac{1}{\phi} = \phi -1[/tex]

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