Discrete torsion and its application for a generalized van der Waerden’s theorem

David E. Blair; Tatsuo Konno

doi:10.3792/pjaa.87.209

December 2011 Discrete torsion and its application for a generalized van der Waerden’s theorem

David E. Blair, Tatsuo Konno

Proc. Japan Acad. Ser. A Math. Sci. 87(10): 209-214 (December 2011). DOI: 10.3792/pjaa.87.209

Abstract

In this article, we study discrete curvature and torsion for spatial polygonal lines of unit sides. We express geometric conditions on polygons by using inner products of oriented sides. As a application, we prove a generalization of van der Waerden’s theorem. The theorem given in this paper and its proof clarify how the conditions on the sides affect the polygon being planar from the discrete torsion point of view.

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Citation Download Citation

David E. Blair and Tatsuo Konno "Discrete torsion and its application for a generalized van der Waerden’s theorem," Proceedings of the Japan Academy, Series A, Mathematical Sciences 87(10), 209-214, (December 2011). https://doi.org/10.3792/pjaa.87.209

Published: December 2011

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