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Newbie here, I'm studying the proof of Cauchy's rigidity theorem, but couldn't find any good resources. I read the chapter about it Proofs from THE BOOK, but it's really brief and I was not able to fully understand it. Can someone recommend me some resources or places to search? The main part about creating a spherical polygon from a polyhedron and a sphere is pretty straight forward (once you know about the existence of a required vertex) (I will welcome arguments saying the opposite), but especially the Cauchy's arm lemma and the induction is not so easy to grasp.

Thanks.

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    $\begingroup$ Have you looked at the book Geometric Folding Algorithms by Erik Demaine and Joesph O'Rourke? $\endgroup$
    – Liviu Nicolaescu
    Commented Apr 2, 2021 at 14:26
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    $\begingroup$ Igor Pak's book "Lectures on Discrete and Polyhedral Geometry" available from math.ucla.edu/~pak/book.htm may also be helpful. $\endgroup$
    – j.c.
    Commented Apr 2, 2021 at 14:59
  • $\begingroup$ Thanks guys, I'll take a look at both of them! $\endgroup$
    – McDuck
    Commented Apr 2, 2021 at 15:02
  • $\begingroup$ M. Berger, Geometry, vol. 2 $\endgroup$
    – Alexandre Eremenko
    Commented Apr 3, 2021 at 0:56

1 Answer 1

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This paper (and its references) may help:

O’Rourke, Joseph. "An extension of Cauchy’s arm lemma with application to curve development." In Japanese Conference on Discrete and Computational Geometry, pp. 280-291. Springer, Berlin, Heidelberg, 2000. Springer link.

Fig1

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  • $\begingroup$ Thanks! I sent you a request for the paper on researchgate.net. I'll be really glad if you accept it. $\endgroup$
    – McDuck
    Commented Apr 2, 2021 at 14:49
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    $\begingroup$ Download from this link. $\endgroup$
    – Joseph O'Rourke
    Commented Apr 2, 2021 at 15:04
  • $\begingroup$ Thank you, I appreciate it. $\endgroup$
    – McDuck
    Commented Apr 2, 2021 at 15:26

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