Talk:Four-vertex theorem

Missing hypothesis
Discrete variations 1-3 presumably require a minimum number of sides, or non-regularity, or something else, but what? -- Trɔpʏliʊm • blah 18:11, 5 June 2009 (UTC)

pointy bits
Does an extremum of curvature necessarily imply a cusp on the evolute? —Tamfang (talk) 06:25, 1 December 2019 (UTC)

Dead link correction
There is a dead-link in the references section. I found a working link but am unable to edit the references. I have no idea why.

Here is the correct link https://www.math.ucla.edu/~pak/book.htm for reference number 8 Pak, I. Lectures on Discrete and Polyhedral Geometry — Preceding unsigned comment added by Telugujoshi (talk • contribs) 20:01, 20 May 2020 (UTC)

Problematic statement
The section Definition and examples contains this sentence:

"An ellipse has exactly four vertices: two local maxima of curvature where it is crossed by the major axis of the ellipse, and two local minima of curvature where it is crossed by the minor axis."

But many people consider a circle to be a special case of an ellipse.

Even the linked Wikipedia article Ellipse states that an ellipse is a generalization of a circle.

I hope someone knowledgeable on this subject can fix this.

(No doubt any project as large as Wikipedia must contradict itself, but we should avoid this when possible.) 2601:200:C000:1A0:F4CF:60FC:DCAC:F9C5 (talk) 19:58, 6 June 2022 (UTC)
 * Given that the very next sentence is about circles, I think we can trust readers not to be deliberately obtuse and to understand that the part about ellipses really means non-circular ellipses. —David Eppstein (talk) 20:20, 6 June 2022 (UTC)