Cauchy's Arm Lemma on a Growing Sphere

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Authors
Abel, Zachary
Charlton, David
Collette, Sebastien
Demaine, Erik D.
Demaine, Martin L.
Langerman, Stefan
O'Rourke, Joseph
Pinciu, Val
Toussaint, Godfried
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Abstract
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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.
Keywords
Computer Science - Computational Geometry
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