Timeline for On $n$-gons Inscribed in convex closed curves
Current License: CC BY-SA 4.0
9 events
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| Mar 28, 2021 at 11:52 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Mar 27, 2021 at 9:50 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Mar 27, 2021 at 5:49 | comment | added | Nandakumar R | Thank you! The paper by Keikha et al give an easily checkable example (the 9-gon shown in fig 3, page 5) - and it has quite different max area and max perimeter inscribed triangles. And from mathoverflow.net/questions/78165/…, there seem to be many convex closed C's each with infinitely many max area and max perimeter inscribed n-gons; are there any C among them such that answer sets to questions 1 and 2 are disjoint (in 3D are there any closed surfaces with the answer sets to questions 1, 2, 3 disjoint)? | |
| Mar 26, 2021 at 16:35 | comment | added | Noam D. Elkies | In general there's no reason to expect that the maxima (1) and (2) coincide. Ellipses (and ellipsoids in higehr dimension) are very special cases because they have continuous families of affine automorphisms, so any maximal-area polygon moves in a continuous family. For typical $C$ there are no nontrivial automorphisms at all. | |
| Mar 26, 2021 at 16:19 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Mar 26, 2021 at 15:52 | comment | added | Timothy Chow | Do you even know if the case where $C$ is a polygon and $n=3$ is settled? If not, you could trying algorithmically searching for a counterexample, e.g., using the algorithm in the paper Maximum-Area Triangle in a Convex Polygon, Revisited. | |
| Mar 26, 2021 at 14:06 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 26, 2021 at 13:59 | history | edited | gmvh |
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| Mar 26, 2021 at 13:51 | history | asked | Nandakumar R | CC BY-SA 4.0 |