Define a ``slice'' curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops on a plane without self-intersection. The key tool used is a generalization of Cauchy's arm lemma to permit nonconvex ``openings'' of a planar convex chain.
- Pub Date:
- June 2000
- Computer Science - Computational Geometry;
- Computer Science - Discrete Mathematics;
- 11 pages, 8 figures. Earlier version replaced after I discovered Schur's 1921 theorem, whose proof can be followed to establish the key generalization of Cauchy's arm lemma, my Theorem 1. Paper revised accordingly. New (2006) version corrects two errors in the proofs found by Raghavan Dhandapani