Timeline for On the trajectory followed by a point P on a planar convex region C when P is mapped repeatedly to the farthest point to it on C
Current License: CC BY-SA 4.0
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| Dec 6 at 17:41 | comment | added | Nandakumar R | Thanks for the pointer to 'farthest point maps'. And yes, the regular 2N+1-gon does seem to work all right as a simple answer to the basic question above! thanks. Guess it could be more interesting to see if we can achieve exactly N iterations before first repetition with a C that has no ties. | |
| Dec 6 at 17:34 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 6 at 17:19 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 6 at 17:13 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 6 at 15:02 | comment | added | Kostya_I | If we are free to break ties in any way we want, doesn't a regular (2N+1)-gon work? each vertex has two farthest points that are also vertices, and the trajectory that always chooses the one on the right will not repeat itself until it visits all vertices. | |
| Dec 6 at 12:58 | comment | added | Joseph O'Rourke | My colleague Costin Vilcu pointed to Schwartz, Richard Evan. "The Farthest Point Map on the Regular Octahedron." Experimental Mathematics 31, no. 4 (2022): 1086-1097, and its ten references on related investigations of the farthest point map. | |
| Dec 5 at 18:19 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 5 at 7:42 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 5 at 6:54 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 3 at 14:23 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Dec 2 at 15:19 | history | asked | Nandakumar R | CC BY-SA 4.0 |