Abstract
Cauchy’s “Arm Lemma” may be generalized to permit nonconvex “openings” of a planar convex chain. Although this (and further extensions) were known, no proofs have appeared in the literature. Here two induction proofs are offered. The extension can then be employed to establish that a curve that is the intersection of a plane with a convex polyhedron “develops” without self-intersection.
Supported by NSF grant CCR-9731804.
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O’Rourke, J. (2001). An Extension of Cauchy’s Arm Lemma with Application to Curve Development. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_27
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DOI: https://doi.org/10.1007/3-540-47738-1_27
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