Timeline for Is the ratio Perimeter/Area for a finite union of unit squares at most 4?
Current License: CC BY-SA 3.0
14 events
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| Feb 25, 2014 at 23:30 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
replaced deprecated tag 'geometry'; rewrote title
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| Feb 25, 2014 at 21:01 | vote | accept | domotorp | ||
| Feb 25, 2014 at 21:01 | answer | added | domotorp | timeline score: 16 | |
| Jul 3, 2013 at 13:09 | history | edited | domotorp | CC BY-SA 3.0 |
added 86 characters in body
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| Mar 13, 2010 at 22:08 | answer | added | gowers | timeline score: 4 | |
| Mar 13, 2010 at 16:24 | comment | added | domotorp | If U is very big and only a very small part of S is out from it, then this is the case. | |
| Mar 13, 2010 at 11:15 | comment | added | gowers | Suppose you have an arbitrary union U of unit squares and another unit square S. Is it possible that the ratio of the length of the part of the boundary of S that is not in U to the area of S\U is greater than 4? I presume it is, or else there would be an easy inductive proof. Or is it that this is essentially the question one wants to answer? | |
| Mar 13, 2010 at 8:04 | answer | added | user1688 | timeline score: 1 | |
| Feb 17, 2010 at 14:54 | comment | added | Pandelis Dodos | If Conjecture 8.3 in Gyenes' Thesis is true, then if (S_1,...,S_n) is an extreme set of unit squares (i.e. perimeter(H)/Area(H)=4 where H is the union of S_1,...,S_n) then every subset of (S_1,...,S_n) is extreme. Can someone prove this property directly (i.e. without characterizing the extreme cases)? | |
| Feb 13, 2010 at 18:23 | history | edited | domotorp | CC BY-SA 2.5 |
added 35 characters in body; edited tags
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| Feb 13, 2010 at 16:40 | comment | added | Anton Petrunin | If you have this thesis, could you scan it and make it available? | |
| Feb 13, 2010 at 16:17 | comment | added | TonyK | Don't be so sensitive François! You don't have to answer, even though you were commanded to :-) | |
| Feb 13, 2010 at 15:30 | comment | added | François G. Dorais | Note how your question is phrased as a command. | |
| Feb 13, 2010 at 15:14 | history | asked | domotorp | CC BY-SA 2.5 |