A cycloid's the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line. It's an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid's the solution to the brachistochrone problem (for example it's the curve of fastest descent under gravity) and the related tautochrone problem (for example the period of a ball rolling back and forth inside this curve doesn't depend on the ball’s starting position). H… (More on Cycloid)