Timeline for The rain hull and the rain ridge
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2017 at 12:02 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image link broken; now fixed.
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 14, 2011 at 0:28 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Fixed physically incorrect figure.
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| Jul 13, 2011 at 18:54 | comment | added | Gil Kalai | A little celebration of the occasion is here: gilkalai.wordpress.com/2011/07/12/joes-100th-mo-question | |
| Jul 11, 2011 at 14:55 | answer | added | Joel David Hamkins | timeline score: 4 | |
| Jul 11, 2011 at 14:36 | comment | added | Joel David Hamkins | Also, if you are fixing the diagram, then the water level in the tube in (a) does not quite seem high enough to me. | |
| Jul 11, 2011 at 14:32 | comment | added | Joseph O'Rourke | @Joel: Oh, you are right! I'll have to fix that figure. I also intended that the little basin catch to the right is somehow protected from the rain and only fills if that to the left fills fully. | |
| Jul 11, 2011 at 14:13 | comment | added | Joel David Hamkins | Is the right-most part of the narrow tube in (b) part of the rain hull? You shaded it blue, but after all, water would drain out of that part of the tube into and overspilling the little cup. So I would instead think that the rain hull only included up to about 3/4 of the tube, up to the horizontal line tangent to the bottom part of where the tube makes its final turn. | |
| Jul 11, 2011 at 1:07 | comment | added | Gerhard Paseman | I can imagine an iterative solution to calculate Mbar for those portions of the island which satisfy the TIN assumption, and do an approximation for the rest. However, I am still mulling over your picture above. Perhaps one can calculate mhat easily, where mhat is the result of pretending TIN holds, and then prove that Mbar differs on a set of sufficiently small measure. Another approach is to run the rain backwards, to capture essential aspects of the rain hull. Gerhard "Wild Guesses Are Our Specialty" Paseman, 2011.07.10 | |
| Jul 10, 2011 at 23:43 | comment | added | Joseph O'Rourke | @Gehard: That is the TIN assumption of GIS researchers. It seems more mathematically interesting to assume full generality, and to specialize to terrains (as they call them) if necesary. | |
| Jul 10, 2011 at 23:31 | comment | added | Gerhard Paseman | Can we assume M and/or Mbar pass the z-axis test? I.e. is M= f(x,y) for some function f and coordinatization of the ocean containing the island? If so, maybe topographers have the answer. Gerhard "Email Me About System Design" Paseman, 2011.07.10 | |
| Jul 10, 2011 at 22:36 | comment | added | Joseph O'Rourke | This is my 100th MO question :-) | |
| Jul 10, 2011 at 22:36 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |