Timeline for Intersections and curvature in the plane
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2021 at 18:00 | comment | added | David E Speyer | I don't really think any of the digressions are useful here. I wanted to be able to assume that the center of the circle was in $R$ so that I could parametrize $\partial R$ in polar coordinates; that didn't turn out to matter. I proved a bound of $2$ that Noam improved to $\pi$; I don't see that argument as helping. I spent some time realizing that there wasn't going to be a useful bound for how long $\partial R$ spends in the arcs outside the circle; that was very helpful in figuring out where to focus but I don't see why to keep it in the final answer. | |
| Feb 12, 2021 at 17:54 | comment | added | Deane Yang | @DavidESpeyer, I agree with Noam about the digressions. I include them shamelessly in my answers. | |
| Feb 12, 2021 at 15:38 | comment | added | Noam D. Elkies | David: Thanks. Maybe keep the "digressions", which could have independent interest, and end with a pointer to a new (possibly CW) answer. | |
| Feb 12, 2021 at 15:22 | comment | added | Deane Yang | Yes. Using Sturm comparison is what I had in mind. | |
| Feb 12, 2021 at 13:37 | comment | added | David E Speyer | Very nice! At some point, I'll rewrite my answer to remove the digressions, and then we'll have a complete solution. | |
| Feb 12, 2021 at 5:58 | comment | added | Noam D. Elkies | It seems that this result can also be obtained from the Sturm(-Picone) comparison theorem. | |
| Feb 12, 2021 at 5:50 | history | answered | Noam D. Elkies | CC BY-SA 4.0 |