Finally I had some time to address the problem and proved it, but only with a very inelegant procedure ultimately relying on the graph of a cubic and showing that of the 3 roots, only one was usable and it was the correct one, using the sqrt(5) as derived from the other direction.
I also worked at this, and first noted that the ratio of the diagonal to the side of a pentagon appeared to be the golden ratio, then proved it with algebra. (this was in the process of making a geodetic mobile using all 6 of the polyhedrons with equilateral sided faces plus ones made in the manner of Buckminster Fuller's domes).
Polyhedrons
And like Omnivorous, I spent many a night after college trying to trisect an angle. I developed a methodology that got close enough for practical use (imho), but never an exact solution. Wish I'd had access to the internet and the formula provided by Chiroptera.
Enjoy.
we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
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