If the small part is called S and the large part is called L, the proportions can be mathematically stated as follows:
S/L = L/S+L
That is about as far as my mathematics descriptions will take me, but if you need more, or a precise visual, then here's the place to go for some "Golden Geometry"
This is my aproximation that bares only a symbolic, but nowhere near technically correct, representation of the above described process.
In Fascinating Fibonaccis by Trudi Hammel Garland, Golden Triangles are explained thusly:
It is an isosceleles triangle with one short side in golden proportion to each of the two longer, equal sides. Fibonacci numbers can be used to construct such triangles... Among the interesting properties of the golden triangle is the fact that the bisector of a base angle (which is always 72o) cuts the side opposite it into the golden proportions. That bisector also cuts the triangle into two new isosceles triangles...whose areas are in golden proportion to each other. The process can be repeated endlessly.
Playing with the Numbers (Previous Page)
Aesthetically Pleasing Fibonacci? (Next)
The Formulas for the Fibonacci Sequence.
Bibliography and some great Fibonacci links.