On what kind of surface would a square wheel function the same as a round wheel?

I just saw this problem for the first time.

The problem asks, 'On what kind of surface would a square wheel function the same as a round wheel?'. Meaning, find a surface on which both a square wheel and a round wheel would bahave the same way.

It does not say that the square wheel's behaviour on this surface should be the same as a round wheel's behaviour on a flat surface. Nor does it say anything about rolling; smoothly or otherwise.

All the comments have either assumed one or the other of these (non) requirements, or failed to furnish adequate proof. The official solution does not provide any answer either. It merely comments on the comments, without taking any position.

In my opinion the answer should be: A frictionless surface. In the absence of any traction, both types of wheels will slide, rather than roll; and fairly smoothly at that.

Posted by Sanjay on 2003-06-08 12:56:40