Timeline for Complexity of computing kissing numbers of triangles with given side lengths
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 21, 2017 at 7:45 | answer | added | Moritz Firsching | timeline score: 3 | |
| May 28, 2017 at 13:07 | comment | added | Joseph O'Rourke | Tangentially related: "The kissing number of a square, cube, hypercube?." | |
| May 28, 2017 at 8:36 | comment | added | Stefan Kohl♦ | @fedja: For equilateral triangles, it's indeed 12, and not 13 -- cf. e.g. Likuan Zhao, The kissing number of the regular polygon. | |
| May 28, 2017 at 1:29 | comment | added | Gerhard Paseman | For an example that is 13, I don't have that at present. For an example that is over 13, try 501,501,999. Gerhard "Odd Examples While U Wait" Paseman, 2017.05.27. | |
| May 28, 2017 at 1:25 | comment | added | Gerhard Paseman | Also, as I understand it, 12 is the minimum for any triangle, not just equilateral. Gerhard "Checking For Agreement On Understanding" Paseman, 2017.05.27. | |
| May 28, 2017 at 1:23 | comment | added | Gerhard Paseman | I was working in Euclidean geometry of two dimensions. In that geometry, the upper bound is a little less than 13. Of course, if you are working in hyperbolic geometry, the estimate doesn't work. If you have an example of 13 (disjoint) unit equilateral triangles in the Euclidean (or any other) plane kissing the same unit equilateral triangle simultaneously, I'd like to see it. Gerhard "Can Stand Being Proven Wrong" Paseman, 2017.05.27. | |
| May 28, 2017 at 1:12 | comment | added | fedja | @GerhardPaseman So, are you sure that the kissing number of the equilateral triangle is not 13? (I surmise I've seen a discussion like that already somewhere). If you are, what is the closest (in any reasonable sense you want) to the equilateral triangle for which it becomes 13? | |
| May 28, 2017 at 1:04 | comment | added | Gerhard Paseman | Also, the minimum is 12. Gerhard "Taking Care Of A Detail" Paseman, 2017.05.27. | |
| May 27, 2017 at 21:11 | comment | added | Gerhard Paseman | Let R be the ratio of the perimeter to the smallest altitude, and N the smallest number such that N times the smallest angle is at least 2pi radians. I conjecture that N+2R is a strict upper bound for the kissing number, and that there is a family of isosceles triangles that approaches this bound. Gerhard "Geometrical Conjecturing While U Wait" Paseman, 2017.05.27. | |
| May 27, 2017 at 21:01 | comment | added | Gerhard Paseman | Isn't it a function of the smallest angle of the triangle? Maybe also the ratio of the longest side to the shortest altitude? Gerhard "Miniscule Experience With Kissing (Number)" Paseman, 2017.05.27. | |
| May 27, 2017 at 20:43 | history | asked | Stefan Kohl♦ | CC BY-SA 3.0 |