Timeline for When are the main diagonals of a convex $2n$-gon concurrent?
Current License: CC BY-SA 3.0
7 events
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| Dec 9, 2016 at 15:14 | comment | added | cats | I don't really understand this last comment (in particular how you maintain the bisection property and get rid of the concurrency), but will chew on it. | |
| Dec 8, 2016 at 5:45 | comment | added | Gerhard Paseman | Even there you can play around. Start with a 2n-gon with area bisecting diagonals, color the vertices red and blue alternating, and then pull reds out and push blues in while maintain the bisection property. You might be able to prove something about the edge lengths then, but I don't know what. Gerhard "No Political Innuendo Intended. Really." Paseman, 2016.12.07. | |
| Dec 8, 2016 at 5:38 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
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| Dec 8, 2016 at 5:25 | comment | added | cats | Just for fun I guess :). The main question for me was whether or not main diagonals being area bisectors implies anything. | |
| Dec 8, 2016 at 5:09 | comment | added | Gerhard Paseman | You can play around with this anyway. For example, draw the n lines, and place a circle somewhere around the concurrent point. The intersections determine a cyclic polygon, and there may be some relationship you can develop with opposing sides or pairs of sides as in cyclic quadrilaterals. Again, I don't see where you are going with this. Gerhard "But Have Some Fun Anyway" Paseman, 2016.12.07. | |
| Dec 8, 2016 at 4:54 | comment | added | cats | thanks for this; I guess I didn't expect a nice characterization for the more general question. | |
| Dec 8, 2016 at 4:48 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |