Timeline for Regular $n$-gon with diagonals: bounds on area of largest cell?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2023 at 11:21 | comment | added | Dan | @FedorPetrov I do not know how to prove that. | |
| Jan 7, 2023 at 9:28 | history | edited | YCor |
edited tags
|
|
| Jan 7, 2023 at 8:30 | comment | added | Fedor Petrov | Can you prove at least that no cell except the central contains a circle of radius $10000/\sqrt{n}$? | |
| Jan 7, 2023 at 7:10 | comment | added | Dan | The largest quadrilateral thus cutoff, excluding the centre quadrilateral, is at least as large as a quadrilateral next to the centre quadrilateral, which has an area of approximately $1/4$ for large $n$. But $n/4$ is unbounded. | |
| Jan 7, 2023 at 4:24 | comment | added | user44143 | Here is a strategy for a reasonable upper bound: Don’t look at all the diagonals! Look only at the nearly-vertical and nearly-horizontal diagonals (i.e. diagonals from one vertex to the vertex with next-largest x- or y-coordinate); the area of the largest quadrilateral thus cutoff will be an upper bound for the largest area cut off by all the diagonals. | |
| Jan 7, 2023 at 2:34 | history | edited | Dan | CC BY-SA 4.0 |
added 162 characters in body
|
| Dec 17, 2022 at 13:23 | history | asked | Dan | CC BY-SA 4.0 |