Timeline for Does every ellipse inside a tetrahedron inside a ball fit in a triangle inside the ball?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2017 at 11:32 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image link broken; now fixed.
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| Sep 28, 2012 at 15:36 | comment | added | Joseph O'Rourke | Thanks everyone---I stand corrected! I will leave my "answer" intact as an instructional error. :-) | |
| Sep 28, 2012 at 15:06 | comment | added | Douglas Zare | This is a nice picture, but I think there is a discontinuity in the set of ellipses you can inscribe in a tetrahedron when you degenerate to a rectangle. By the way, a square would work as well. | |
| Sep 28, 2012 at 15:03 | comment | added | Gerhard Paseman | Turn it into a (dis-?)proof by embedding an ellipse into a cross-section of the tetrahedron. I think this is a beautifully misleading picture, because it suggests that a tetrahedral cross section can be almost as big as two of the faces, which I believe is never the case for tetrahedra of positive volume with faces of roughly equal area. Gerhard "Almost Like Sixty-Five Equals Sixty-Four" Paseman, 2012.09.28 | |
| Sep 28, 2012 at 14:33 | comment | added | Matt Pusey | Thanks. I agree that that ellipse looks like it won't fit in a triangle, but I don't agree that it fits inside the tetrahedron. If you try to make a thin tetrahedron like that then a typical cross-section through it will be a diamond which your ellipse wouldn't fit into. If you have Mathematica, the code at pastebin.com/UCAYTPpc shows the sort of tetrahedron I think your talking about and lets you look at cross-sections through it. | |
| Sep 28, 2012 at 13:15 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |