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

(In reply to re: I dont know why but.... by levik)

I'm not sure that the word is right, but I think that the idea is a corregated road made up of the 3-dimensional analog of a cycloid -- a series of "near semi-circles" produced by tracing the path of a point on the circimference of a circlular wheel rolling along a flat road. (See the first illustration at http://astronomy.swin.edu.au/~pbourke/curves/cycloid/) The period of the corregations would have to be such that the arclength of each "semi-circle" is the same as the length of a side of the square wheel.

Posted by TomM on 2002-11-16 10:13:48