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Nowhere differentiable caustics

  coro256

trivlist708

Note that the symmetry of the curves is responsible for possible differentiability at some finite set of points. The symmetry is broken, if the tex2html_wrap_inline1340 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.



Oliver Knill
Fri Jun 12 13:34:37 CDT 1998