Eric Chandler offered this perpetual-motion scheme for Edward Barbeau’s “Fallacies, Flaws and Flimflam” column in the *College Mathematical Journal*. Points *A* and *B* are at the same height, and *C* is halfway between them. The ramp *AC* is a segment of a cycloid, a curve designed to produce the fastest descent under gravity.

A ball released at

Arolls down the rampACtoCcovering a greater distance in a shorter time than it would have had it rolled downBCtoC. The relationVelocity = Distance/Timethus implies that the ball arrives atCwith greater velocity than it would have had it rolled downBC. This added velocity enables the ball to roll fromCup toand past Bto a pointDa little farther along. It then returns toAalong the inclined rampDAto repeat the cycle endlessly.

Where is the error?