关于曲率的深入研究

Revisiting Curvature

本文就曲线上一点处曲率的存在条件做了讨论,提出了曲率存在的一个定理,给出了单侧曲率的概念,从而说明了曲率并非在光滑曲线上的每一点处都存在.

By investigating the existence of the curvature of a plane curve at a point,we obtain a theorem and a definition of one-side curvature,which shows that curvature does not need to exist at every point of a smooth curve.