Re: [math-fun] Inverse cycloid problem ?

On 11/26/12, Henry Baker <hbaker1@pipeline.com> wrote:

A cycloid is produced by a point on a circle as the circle rotates without slipping on a surface.

I think this may have been intended to read something like: "A cycloid is the curve described by a point on a circle as the circle moves rigidly in the plane, while maintaining contact with a fixed line without slipping."

What if we turn the problem around ?

What curves can be produced by another curve rotating without slipping on a surface ?

E.g., a semicircle is produced by a line segment "rotating without slipping" on a surface.

But I'm afraid I still can't decipher this description ... WFL