Timeline for Are there such numbers?
Current License: CC BY-SA 3.0
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| Apr 20, 2013 at 16:39 | comment | added | Op_Bgh | @Pietro: Thank you for your answer, but why is it among the 12? | |
| Apr 17, 2013 at 8:43 | comment | added | Pietro Majer | 4) If we shrink the convex quadrilateral, leaving P and V fixed, and moving the other vertices towards P, to the same distance as V, we obtain a rectangle included in the quadrilateral, whose minimum altitude is the same (by the above characterization). | |
| Apr 17, 2013 at 8:19 | comment | added | Pietro Majer | 1) In a triangle, the altitude of minimum length (among the three) joins a vertex and a point of the opposite side (not in the prolongation of the side, otherwise it is not the minimum one). 2) Hence, in a convex quadrilateral, the minimum altitude (among the 12) joins a vertex and a point on a diagonal (not on an edge, because there is a shorter altitude to a diagonal). 3) Therefore, in a convex quadrilateral, the minimum altitude is the one from the closest vertex V to the intersection point P of the diagonals, to the other diagonal. | |
| Nov 22, 2012 at 15:54 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Nov 22, 2012 at 12:18 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Nov 22, 2012 at 10:44 | history | answered | Pietro Majer | CC BY-SA 3.0 |