Can someone explain to me what balanced polygons are and how they are used in calculations?

Particularly in Gerver's Sofa, Here is the link for the research, page 16

Thanks in regard



Gerver, Joseph L. "On moving a sofa around a corner." Geometriae Dedicata 42.3 (1992): 267-283.

Gerver says:


As to "how they are used in calculations," I don't think there is a simple answer. Gerver defined an infinite sequence of balanced polygons that converge to what has now called Gerver's sofa (below). I don't think balanced polygons play a role outside of Gerver's particular proof.


  • $\begingroup$ Related: "Sofa in a snaky 3D corridor." $\endgroup$ Jun 13 '17 at 10:25
  • $\begingroup$ Thanks, this is very helpful, and I've already seen your questions, it was fun to read. $\endgroup$
    – user108974
    Jun 13 '17 at 12:04

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