Timeline for Cutting convex sets
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2010 at 17:31 | answer | added | Louigi Addario-Berry | timeline score: 2 | |
| May 28, 2010 at 17:58 | answer | added | Joseph O'Rourke | timeline score: 16 | |
| May 14, 2010 at 2:43 | history | edited | Anton Petrunin |
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| May 12, 2010 at 10:34 | comment | added | domotorp | I added the open-problem tag as this is a well known open problem. | |
| May 12, 2010 at 10:33 | history | edited | domotorp |
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| May 12, 2010 at 10:24 | comment | added | Roland Bacher | Thanks, especially to Takenov for the link, mentionning exactly the same problem. After reflection, I am convinced that the answer must always be yes by a dimension argument (for $n=3$, you can choose an arbitrary interior point $P$ together with a ray starting at $P$ thus determining uniquely two other rays cutting the convex set into $3$ pieces of equal area. We have moreover to satisfy two identities coming from the equal perimeter requirement and we have three degrees of liberty. The solution should thus exist and should not be unique.) | |
| May 12, 2010 at 10:18 | answer | added | Igor Pak | timeline score: 5 | |
| May 12, 2010 at 9:58 | comment | added | Nurdin Takenov | It's "fair partition problem". May be this site would be helpful - garden.irmacs.sfu.ca/?q=op/… | |
| May 12, 2010 at 9:45 | comment | added | Zsbán Ambrus | Try looking in Jiri Matousek, Using the Borsuk-Ulam theorem, because it mentions similar problems. I don't think it talks about convex sets, but instead cutting arbitrary shapes to equal pieces with straight lines. Expect to find lots of hard and unsolved questions. | |
| May 12, 2010 at 9:15 | history | edited | Roland Bacher | CC BY-SA 2.5 |
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| May 12, 2010 at 9:03 | history | asked | Roland Bacher | CC BY-SA 2.5 |