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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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David E. Blair. Tatsuo Konno. "Discrete torsion and its application for a generalized van der Waerden’s theorem." Proc. Japan Acad. Ser. A Math. Sci. 87 (10) 209 - 214, December 2011. https://doi.org/10.3792/pjaa.87.209

Information

Published: December 2011
First available in Project Euclid: 1 December 2011

zbMATH: 1238.51006
MathSciNet: MR2863416
Digital Object Identifier: 10.3792/pjaa.87.209

Subjects:
Primary: 51M04
Secondary: 51M20 , 52C30 , 53A04

Keywords: discrete curvature , discrete torsion , polygonal line

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 10 • December 2011
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