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Around the proof of the Legendre-Cauchy lemma on convex polygons. (Russian, English) Zbl 1051.52015

Sib. Mat. Zh. 45, No. 4, 892-919 (2004); translation in Sib. Math. J. 45, No. 4, 740-762 (2004).
The author briefly describes the history of the proofs of the well-known Cauchy lemma on comparison of the distances between the endpoints of two convex open polygons on a plane or sphere, presents a rather analytical proof, and explains why the traditional constructions lead in general to inevitable appearance of nonstrictly convex open polygons. He also considers bendings one to the other of two isometric open or closed convex isometric polygons.

MSC:

52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
51M25 Length, area and volume in real or complex geometry
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