Cauchy’s Arm Lemma on a Growing Sphere

Authors

Zachary Abel, Harvard University
David Charlton, Boston University
Sébastien Collette, Universite Libre de Bruxelles
Erik D. Demaine, Massachusetts Institute of Technology
Martin L. Demaine, Massachusetts Institute of Technology
Stefan Langerman, Universite Libre de Bruxelles
Joseph O'Rourke, Smith CollegeFollow
Val Pinciu, Southern Connecticut State University
Godfried Toussaint, McGill University

Document Type

Article

Publication Date

4-7-2008

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.

Comments

Author’s submitted manuscript.

Recommended Citation

Abel, Zachary; Charlton, David; Collette, Sébastien; Demaine, Erik D.; Demaine, Martin L.; Langerman, Stefan; O'Rourke, Joseph; Pinciu, Val; and Toussaint, Godfried, "Cauchy’s Arm Lemma on a Growing Sphere" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/42