Timeline for Transport tubes in a sphere
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2017 at 23:15 | comment | added | Ilya Bogdanov | @Gerhard: Another objection is that it does not suffice to cover every point by a cylinder; you need (or not?) to cover any pair of points (which are far enough) by a cylinder, which is a bit diferent. | |
| Sep 21, 2017 at 20:28 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Sep 21, 2017 at 17:22 | comment | added | Gerhard Paseman | @Ilya, upon reflection, I now think they are weakly equivalent in that each problem informs the solution of the other. Technically though, they are different and may end up being inequivalent in how they are solved. I'm inspired to post an informal analysis. Gerhard "Maybe Looking Through Dark Matter" Paseman, 2017.09.21. | |
| Sep 21, 2017 at 16:11 | comment | added | Ilya Bogdanov | @Gerhard: I do not think the last reformulation is the same, since you can switch from one tube to another one (can you?)... | |
| Aug 1, 2017 at 2:37 | comment | added | Gerhard Paseman | I like this formulation even better; I recommend that you include it in your post. Given d, How small a radius r is needed to cover a unit d-ball with d cylinders of radius r and height 2 ? If this question is not equivalent to yours, it should provide a method for a nice upper bound. Gerhard "Finds Covering Problems More Intuitive" Paseman, 2017.07.31. | |
| Jul 31, 2017 at 20:45 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 86 characters in body
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| Jul 31, 2017 at 20:42 | comment | added | Joseph O'Rourke | @GerhardPaseman: Yes, precisely a space geodesic path: nice formulation! | |
| Jul 31, 2017 at 20:39 | comment | added | Gerhard Paseman | I recommend an alternate formulation to clarify (or contrast): take a space geodesic path (so perpendiculars off a tube to a point on the surface or on another tube) and distance will be the min of the sum of the perpendiculars. Your mention of sphere makes me think of walking on the surface to a tube entrance, not burrowing down to the tube. Gerhard "Is Exhausted By Public Transportation" Paseman, 2017.07.31. | |
| Jul 31, 2017 at 20:23 | comment | added | Joseph O'Rourke | (I posed a variant of this question at the 2017 Canadian Conference on Computational Geometry.) | |
| Jul 31, 2017 at 20:21 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |