SUMS: Poladian -- Origami is mightier than the compass

To the ancient greeks, the straight line and the circle were the
epitome of perfection.
Many useful tasks were possible using only a straight-edge and compass
such as bisecting intervals and angles.
However certain problems, like trisecting the angle or doubling the
cube were impossible.
I’ll show how the japanese art of paper-folding, when interpreted as a
system of geometric constructions, is vastly superior to the
straight-edge and compass and can solve both of these problems.