|
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.