Timeline for Smallest regular $m$-gon covering a regular $n$-gon
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 5, 2021 at 16:04 | comment | added | Max Alekseyev | Related question: how many intersection points do the borders of two polygons in an optimal configuration have? | |
| Mar 3, 2021 at 21:20 | comment | added | Luis Ferroni | As follows from what @Robert Israel said (as an answer), the optimal configuration for $n=5$ and $m=7$ is obtained with non-concentric polygons. | |
| Mar 3, 2021 at 18:46 | answer | added | Robert Israel | timeline score: 5 | |
| Mar 3, 2021 at 16:18 | comment | added | Alapan Das | For any $n$-gon the distance from centre to any point at $\theta$ which is already tilted at an angle $x$, is $d_n(\theta,x,R_n)=R_n\cos(\frac{\pi}{n})\sec(\frac{\pi}{n}-\langle {\frac{n(\theta-x)}{2\pi}} \rangle \frac{2\pi}{n})$, here $\langle {.} \rangle$ stands for the distance from nearest integer. As the area only depends on $r_m$, we have to find the $x$ such that $d_m(\theta,x)>d_n(\theta, 0)$ always and $R_m$ be minimum. Though it doesn't give direct formula, it may help finding the minimum value of $R_m$. | |
| Mar 3, 2021 at 16:08 | comment | added | Joseph O'Rourke | Do you know if the best concentric covering of a pentagon by a heptagon is in fact not the optimal covering? I.e., there is a non-concentric covering that beats every concentric covering? | |
| Mar 3, 2021 at 15:41 | history | edited | Luis Ferroni | CC BY-SA 4.0 |
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| Mar 3, 2021 at 14:14 | history | asked | Luis Ferroni | CC BY-SA 4.0 |