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For any point on the globe, I believe there is (by the mean value theorem) at least one great circle containing that point and dividing the world's land area (or water mass, or population, whatever) into equal halves.

Assuming that the stuff to be bisected has no nontrivial symmetries, can we say anything interesting about the set of such circles? For example, do their poles all lie on a finite number of circles?

(As usual, I hope for help with the tags)

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  • $\begingroup$ +1 for the question, even though I think it is too wide. Can you add more details? $\endgroup$ – the_candyman Jan 6 at 22:02
  • $\begingroup$ I suppose you don't really care about the real world (estimates of) water mass or population etc. Do you mean to consider a family of mathematical distributions over the sphere and their respective mass-bisecting-circles? $\endgroup$ – Lee David Chung Lin Jan 29 at 11:20
  • $\begingroup$ @LeeDavidChungLin, correct. $\endgroup$ – Anton Sherwood Jan 30 at 0:18

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