Timeline for An optimization problem for points on the sphere (master's dissertation)
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jan 30, 2011 at 22:10 | comment | added | Anton Petrunin | Here is a related problem: "Show that minimal polyhedral surface is saddle". (It is not true if you fix triangulation, but it is true if you only fix number of triangles in the triangulation). Check my list of problems for complete formulation: dl.getdropbox.com/u/1577084/problems.pdf | |
| Aug 20, 2010 at 9:47 | comment | added | Robin Saunders | Thanks for the answers and comments so far; they've certainly given me food for thought, although I'll need to wait until my return to campus in October before getting full access to some of the literature. In the meantime, I'll add that I've been having thoughts about the Voronoi diagram of the set of points illustrated at en.wikipedia.org/wiki/Fermat%27s_spiral. The plane is tiled very uniformly because of the form of the golden ratio's continued fraction. This naturally corresponds to a very uniform tiling of the sphere, i.e. a near-spherical n-hedron, for any n. | |
| Aug 9, 2010 at 18:59 | answer | added | Andrey Rekalo | timeline score: 2 | |
| Aug 9, 2010 at 14:14 | answer | added | Aaron Meyerowitz | timeline score: 5 | |
| Jun 21, 2010 at 7:44 | comment | added | Victor Protsak | Robin, you should view this as an opportunity to learn mathematical German (and French). There is nothing overly challenging about it, and you'll be able to carry out research much more easily in the future. Concerning bibliographical searches: I assume that you know and use MathSciNet, but have you checked Zmath (zentralblatt-math.org/zmath) and Jahrbuch (emis.de/MATH/JFM) databases? Knowledge of German would be a great help for reading reviews from before 1940. | |
| Jun 21, 2010 at 5:14 | comment | added | Will Jagy | It is virtually guaranteed that the Minkowski article of 1897 has been translated. I would call that the hardest part of the problem, existence for a prescribed number of sides. There are at least superficial similarities to circle packing, see the book reviews in ams.org/journals/bull/2009-46-03/home.html Indeed, your question is loosely connected with placing spherical caps of constant size on the surface of the sphere, which has sometimes been discussed on MO. Maybe I will think of something substantial, anything is possible. | |
| Jun 21, 2010 at 3:36 | history | asked | Robin Saunders | CC BY-SA 2.5 |