Timeline for Pair of curves joining opposite corners of a square must intersect---proof?
Current License: CC BY-SA 2.5
5 events
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| Aug 14, 2010 at 12:19 | comment | added | George Lowther | Yes, at first I thought that they proved it directly from the game of Hex. The result asked for would follow from the result that you can't have a state in which both players have a winning line, but the references only show directly that at least one person must win. However, the first link does have a short proof of the result asked for, albeit using the fixed point theorem (and a proof of that). So, it's not as direct and elementary as I thought at first. Still, it answers the question. | |
| Aug 14, 2010 at 6:09 | comment | added | Victor Protsak | As much as I like the connection with Hex, Gale comments on, but doesn't give the proof of, the additional statement "not both" in the Hex theorem, which is the Hex analogue of the intersection property. Thus for the purposes of this question, Hex is a distraction. | |
| Aug 13, 2010 at 19:55 | history | edited | George Lowther | CC BY-SA 2.5 |
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| Aug 13, 2010 at 19:35 | history | edited | George Lowther | CC BY-SA 2.5 |
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| Aug 13, 2010 at 19:28 | history | answered | George Lowther | CC BY-SA 2.5 |