Timeline for Put as many points as possible in an equilateral triangle of side 1 with their minimal distance greater than 1/n
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2011 at 13:06 | comment | added | Tony Huynh | Loosely related problem. en.wikipedia.org/wiki/Random_geometric_graph | |
| Mar 10, 2011 at 11:23 | answer | added | Gerry Myerson | timeline score: 5 | |
| Mar 10, 2011 at 7:49 | comment | added | Christian Elsholtz | The Heilbronn triangle problem asks a similar question about areas, rather than distances. mathworld.wolfram.com/HeilbronnTriangleProblem.html What is the maximum (taken over all configurations of $n$ points in the in the unit equilateral triangle) of the minimum area of all $\binom{n}{3}$ triangles. Heilbronn conjectured the order of magnitude is $ \ll 1/n^2$, which was disproved. | |
| Mar 10, 2011 at 7:18 | comment | added | Gjergji Zaimi | One way to observe that $\lim m(n)/n^2 \le 5/6$ is that inside a regular hexagon of edge $a$ there are at most 5 points at distance $>a$ from each other. On the other hand an easy observation is that $m(n)\geq n(n-1)/2$. | |
| Mar 10, 2011 at 6:52 | comment | added | Gjergji Zaimi | I can't think of a way to find the exact form of $m(n)$ yet. but it is already interesting to ask what is $\lim m(n)/n^2$? | |
| Mar 10, 2011 at 6:13 | history | asked | Fei Gao | CC BY-SA 2.5 |