Question

What did the Greeks use to establish ideal proportions in the human body architecture and other forms of art

Answer 1

Generally (at least in architecture) it is the 5 / 8 rule (8 long to 5 wide). More specifically it is phi which has a definition of (-1+/- sqrt(5))/2 which is about 5/8. The Greeks really liked the phi although they could not do better than approximate it to 5/8
5/8 = 0.625
phi = 0.618 which because of their numbering system, is remarkably close.