Cauchy's Arm Lemma on a Growing Sphere
Computational Geometry
2008-04-08 v1
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.
Cite
@article{arxiv.0804.0986,
title = {Cauchy's Arm Lemma on a Growing Sphere},
author = {Zachary Abel and David Charlton and Sebastien Collette and Erik D. Demaine and Martin L. Demaine and Stefan Langerman and Joseph O'Rourke and Val Pinciu and Godfried Toussaint},
journal= {arXiv preprint arXiv:0804.0986},
year = {2008}
}