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Apr 4, 2020 at 17:10 comment added Nandakumar R Prof. O'Rourke, our experiments too indicate such patters for the envelope for perimeter bisectors - the envelope has cusps and each segment of the envelope seems to be a parabola segment (those of area bisector envelopes are hyperbola segments). For lines that cut out some other fraction t of the outer boundary length, the envelope appears to have discontinuities so on the whole they may not be as nice as envelopes that cut out a specified fraction of the area.
Apr 3, 2020 at 11:43 history undeleted Joseph O'Rourke
Apr 3, 2020 at 11:06 history deleted Joseph O'Rourke via Vote
Apr 3, 2020 at 1:16 history answered Joseph O'Rourke CC BY-SA 4.0