Cauchy's Arm Lemma on a Growing Sphere

Zachary Abel; David Charlton; Sebastien Collette; Erik D. Demaine; Martin L. Demaine; Stefan Langerman; Joseph O'Rourke; Val Pinciu; Godfried Toussaint

arXiv · 0804.0986

Cauchy's Arm Lemma on a Growing Sphere

Zachary Abel·David Charlton·Sebastien Collette·Erik D. Demaine·Martin L. Demaine·Stefan Langerman·Joseph O'Rourke·Val Pinciu·Godfried Toussaint

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Abstract

We propose a variant of Cauchy's Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its endpoints increases. The main focus of this work is a comparison of three alternate proofs, to show the links between Toponogov's Comparison Theorem, Legendre's Theorem and Cauchy's Arm Lemma.

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Zachary Abel, David Charlton, Sebastien Collette, Erik D. Demaine, Martin L. Demaine, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Godfried Toussaint. 2008-04-07. Cauchy's Arm Lemma on a Growing Sphere. https://arxiv.org/abs/0804.0986

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