How many revolutions on this Pythagorean ellipse? Suppose an ellipse rolls over a sine curve in such a way that one revolution of the ellipse equals to one period of the curve, how are the axes of the ellipse related to the amplitude. The answer is surprisingly related to the Pythagorean theorem. This is a really cool Putnam problem that we solve using calculus and multivariable calculus, more precisely by calculating arclength two ways with integrals and using a u substitution. It’s a must see for calculus and geometry lovers.

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