[math-fun] Rolling a ball (without slipping) along a smooth curve

The problem of rolling a ball (without slipping) along a smooth curve seems quite interesting in itself. PUZZLE: Suppose a unit sphere rolls on the plane, once around the unit circle about the origin. What net spatial rotation (as a 3x3 matrix) does this impart to the sphere? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele