The Math Behind The Perfect Man

The Vitruvian Man is a famous drawing created by Leonardo da Vinci, which is based on the correlations of ideal human proportions as decried by the ancient Roman architect Vitruvius. It is often said that the male figure appears in 2 positions - that inscribed in the circle, and that inscribed in the square.

In actuality, there are more positions that the figure could be in. If we consider that each limb could be in two different possible positions, what is the total number of positions that the Vitruvian Man could be in?

Image credit: Wikipedia
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