This last weekend I saw an amazing thing: a bicycle with square wheels! More amazingly, it was being ridden very smoothly, with the rider suffering no awkward up or down motion. The trick, of course, was that the surface on which the bicycle was "rolling" was not straight.

What would the shape of the surface have to be in order to have the bicycle with square wheels "roll" smoothly?

For a more challenging question, consider the same problem for a bicycle whose wheels are in the shape of an arbitrary rectangle, or (even more challenging) in the shape of an (equilateral, maybe?) triangle!

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