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

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

David E. Blair¹  Tatsuo Konno² 

[1] Department of Mathematics, Michigan State University;College of Engineering, Nihon University

关键词: Discrete curvature;    discrete torsion;    polygonal line.;   

DOI  :  10.3792/pjaa.87.209

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown