Yeah man, the golden ratio is a ratio that's appealing to the eye. It's the only real number whose inverse is exactly one less than its value.
We had to solve for this in my math class. In which I came up with this quadratic:
X = (1/X) + 1
X = (1 + X)/X
X�= 1 + X
X� - X - 1 = 0
Which can be solved with the quadratic forumula...
Yielding (1 � √5)/2
Voilla, the golden ratio.
And that's about as much as I know about it.
I've never actually used it in anything i've written, but I would be interested in seeing what could be done with it.