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

Suppose we were to figure out the formula for a surface (S) that would result in square wheels rolling about smoothly.

We have already shown pretty convincingly that such a surface would be made up of "humps", shaped like arcs of a circle (I have explained earlier why I think these are 90 degree arcs).

Now my guess is that on such a surface regular round wheels would behave in a fashion similar to the way that square wheels behave on a flat surface. (This is partly an intuitive guess on my part.)

Suppose then, we had some surface which consisted of equal stretches of flat surface and surface S. The behavior of both a round wheel and a square wheel would be identical on this surface: periods of smooth rolling will alternate with "bumpy" periods.

I think that this solution addresses both the spirit and the letter of the quastion as it is presented.

Posted by levik on 2002-11-25 16:02:54