Last night I spoke about the golden ratio. It comes about as one of the roots of x^2 -x -1 =0
Most of what I spoke about last night was forklore. It looks close but isn't exact and what is math but exact.
Here is some more information:
Defined:
http://en.wikipedia.org/wiki/Golden_ratio
Myths:
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm
http://www.maa.org/devlin/devlin_05_07.html