Timeline for Repeating an operation infinitely makes any convex $n$-gon a regular $n$-gon?
Current License: CC BY-SA 3.0
6 events
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| Oct 29, 2013 at 12:54 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Oct 29, 2013 at 12:31 | comment | added | mathlove | @Joseph O'Rourke: Thank you very much for pointing it out. I forgot to write a very important word 'isosceles'. | |
| Oct 29, 2013 at 12:12 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Oct 29, 2013 at 12:10 | comment | added | Jean Raimbault | Nice drawing. Also, related to the indefiniteness of each step of the process: one can choose the new points arbitrarily close to any one of the endpoints of the hypothenus of the triangle, and so end up with something that degenerates to a polygon with less vertices (by choosing $P_{j,k+1}$ and $p_{j+1,k+1}$ at distance $1/(k+1)$), or a polygon arbitrarily close to the original one (by choosing $P_{j,k+1}$ at distance $m^{-k-1}$ of $P_{j,k}$, say). | |
| Oct 29, 2013 at 12:06 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Oct 29, 2013 at 11:59 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |