Consider the billiard ball problem in an open, convex, bounded region of the plane whose boundary is C 2 and has at least one point of zero curvature. Then there are trajectories which come arbitrarily close to being positively tangent to the boundary and also come arbitrarily close to being negatively tangent to the boundary.
No takes yet. Share an insight, caveat, or question.
John N. Mather (1982) studied this question.
Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context: