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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

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In

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

Gerver says:

Balanced

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.

          Sofa

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  • $\begingroup$ Related: "Sofa in a snaky 3D corridor." $\endgroup$
    – Joseph O'Rourke
    Commented Jun 13, 2017 at 10:25
  • $\begingroup$ Thanks, this is very helpful, and I've already seen your questions, it was fun to read. $\endgroup$
    – user108974
    Commented Jun 13, 2017 at 12:04

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