Timeline for Biggest parallelogram inside the union of two translated parallelograms
Current License: CC BY-SA 3.0
10 events
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| Apr 17, 2015 at 17:16 | comment | added | Pietro Majer | Since linear maps preserves ratios of measures, it may be assumed wlog that the two parallelograms are squares. This simplifies the problem... | |
| Apr 17, 2015 at 17:12 | comment | added | Joseph O'Rourke | Nice observations. So, fixing $a$, $b$, and $v$, the potential parallelogram solutions form a one-parameter family. | |
| Apr 17, 2015 at 16:31 | comment | added | Gerhard Paseman | It convinces me that a maximal solution will be a parallelogram with no sides parallel to the original, and that it is a matter of computing the area when the line through R induces such a parallelogram. This area should vary as a simple quadratic in the x-intercept of the line through R, whose maximum is easily determined. Gerhard "Still Working On The Details" Paseman, 2015.04.17 | |
| Apr 17, 2015 at 16:25 | comment | added | Gerhard Paseman | Your illustration suggests to me a simple linear program which probably can be made simpler. Consider the intersection U of the two parallelograms, and look at the point of U closest to the letter P in your diagram; call this point R. A line drawn through R at various angles will form the side of an inscribed centrally symmetric parallelogram, and you can compare its area with one of the two answers with sides parallel to the original parallelograms: it will always be larger and will increase until it meets a corner. Gerhard "Stay Tuned For Part II" Paseman, 2015.04.17 | |
| Apr 17, 2015 at 11:52 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Apr 17, 2015 at 10:48 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Apr 17, 2015 at 10:47 | history | undeleted | Joseph O'Rourke | ||
| Apr 17, 2015 at 0:47 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Apr 17, 2015 at 0:45 | history | deleted | Joseph O'Rourke | via Vote | |
| Apr 17, 2015 at 0:35 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |