Whoa, that IS neat. Thanks for sharing! A key part of his reformulation is π = α + β + γ (the sum of the internal angles of a triangle equal 2 right angles). That statement is, funny enough, equivalent to the parallel postulate.

Going on a tangent now: lately I've been thinking that the "dead horse" of the Pythagorean theorem is actually trying to tell us that flat (as opposed to fractal!) dimensions come from composable self-similarity (squares).