Cauchy's Arm Lemma on a Growing Sphere
  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. 
Zachary Abel, David Charlton, Sebastien Collette, Erik D. Demaine,   Martin L. Demaine, Stefan Langerman, Joseph O'Rourke, V...