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Nov 26, 2022 at 23:03 comment added LSpice Name of reference: Nandakumar and Ramana Rao - Fair partitions of polygons: An elementary introduction.
Jun 15, 2020 at 7:27 history edited CommunityBot
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Apr 4, 2020 at 17:45 answer added Nandakumar R timeline score: 1
Apr 4, 2020 at 12:37 history edited Nandakumar R CC BY-SA 4.0
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Apr 3, 2020 at 1:16 answer added Joseph O'Rourke timeline score: 2
Apr 2, 2020 at 19:41 comment added Nandakumar R Thanks Prof. O'Rourke. The reference does give a nice intuitive property of area bisectors. The problem with 'fair' bisectors seems that they could be just a few in number so many of the structures such as envelopes which have nice properties cannot be defined in general. Still one wonders how the intersections of fair bisectors could have structures which reflect the overall nature of the convex region.
Apr 2, 2020 at 19:33 history edited Nandakumar R CC BY-SA 4.0
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Apr 1, 2020 at 23:09 comment added Joseph O'Rourke This may be useful: Goldberg, Michael. "On area-bisectors of plane convex sets." The American Mathematical Monthly 70, no. 5 (1963): 529-531. He proves that there are convex regions with a point through which $n$ area-bisectors pass, $n \ge 4$. It is known that every convex region has a point through which at least $3$ area-bisectors pass.
Apr 1, 2020 at 16:49 history edited Nandakumar R CC BY-SA 4.0
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Apr 1, 2020 at 15:11 history edited YCor CC BY-SA 4.0
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Apr 1, 2020 at 15:04 history asked Nandakumar R CC BY-SA 4.0