Timeline for Cylinders dividing $\mathbb{R}^{3}$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2012 at 20:44 | comment | added | Gerhard Paseman | VCF: I think you should ask Joseph's help with this one. The cylinder one was easy because I could start with two unit cylinders to get 10 regions, and then lengthen each. For the ellipsoids, I can't do that. I think 6 is the most, but Joseph has programs that can likely resolve this for you. Gerhard "My Thinking Isn't That Twisty" Paseman, 2012.09.19 | |
| Sep 19, 2012 at 11:39 | comment | added | Victor | @Gerhard: This is just my mind wondering, but if we have two ellipsoids of the same size I think we can arrange arrange them so that we get 8 regions. First make a perfect cross (this yiels 6 regions) and then slide the vertical ellipsoid to the right so that two mnew patches appear thus yielding 2 more regions. What do you think? | |
| Sep 16, 2012 at 0:45 | comment | added | Joseph O'Rourke | @Gerhard: I believe one can partition an end-capped cylinder into four surface patches that meet the criteria I now set out more clearly in my posting. | |
| Sep 15, 2012 at 23:33 | comment | added | Gerhard Paseman | Another motivating example is to use two helical cylinders. I doubt that such a shape could be produced from a finite arrangement of regular cylinders, but if it could, the potential for growing the number of regions is (in my view) dramtically increased. Gerhard "Ask Me About Twisty Thinking" Paseman, 2012.09.15 | |
| Sep 15, 2012 at 23:24 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |