Talk:Tennis ball theorem

C1 or C2?
recently added a source (Thorbergsson and Umehara) which is more careful than most at defining what class of curves this theorem applies to and how to define an inflection point precisely for this class of curves. This new source clearly says that the curves should be C2. But it seems to me that only C1 is needed for this problem to be well-defined (we need C1 to define a tangent at each point and therefore to identify the inflection points using the curvature-free definition from the new source). Angenent is one of the ones who is not careful about what smoothness assumptions he is making, but it also seems to me that Angenent's curve-shortening proof clearly applies to C1 curves, because curve shortening can be applied to non-smooth curves, instantaneously making them infinitely differentiable, and in that instantaneous time it can't create any new inflection points (?). On the other hand Weiner uses curvature in his definition of inflection points so even though he is also not careful he appears to need C2. And I wouldn't want to change this here without a source. Can anyone find a source saying clearly that this theorem does (or doesn't) apply in the C1 case?

In particular, the four-semicircles model of the tennis ball seam is only C1. So it would be good to have a statement of the theorem that applies to this curve. —David Eppstein (talk) 04:46, 4 June 2018 (UTC)


 * I think it would be interesting to also ask this question in MathOverflow or Math StackExchange :)
 * Between, sorry for not adding the reference in the same citation format... I thought that using the Automatic option of the "Add Citation" tool would already put the citation in a standard format. Maybe this could be a nice improvement for this tool. Saung Tadashi (talk) 02:53, 5 June 2018 (UTC)
 * The problem is there is not a single standard format — different articles do it differently, and the correct thing to do is to conform to however that particular article does it. Unfortunately, the tool is not smart enough to recognize when an article is already in one consistent format and to use that format instead of the one format it is capable of generating. Anyway, at your suggestion I tried asking at MathOverflow. —David Eppstein (talk) 03:37, 5 June 2018 (UTC)