
Note that the symmetry of the curves is responsible for possible differentiability at some finite set of points. The symmetry is broken, if the are no longer real. We expect then examples with nowhere differentiability without exceptions. Because by a theorem of Banach, nowhere differentiable functions are Baire generic among continuous functions [19], we expect also that a "general" curve of constant width produces nowhere differentiable caustics. Finally, we remark that because every convex curve which is not too long can be extended to a curve of constant width, there are many tables for which the caustic is nowhere differentiable in some interval.