曲率和曲率中心公式的一次性推导

Derivation of the Formula of Curvature and Curvature Center in One step

在高等数学教材中,曲率和曲率中心公式的推导都过于繁琐,而且先要导出弧微分公式作准备,本文仅依据曲率和曲率圆的密切联系,对曲率连同曲率中心公式作了一次性的推导。推导方法简明扼要,可供教材更新作参考。

It′s very complicated to derive the formula of curvature and curvature center in conventional advanced mathematics textbook. In addition, the are differential formula must be given in advance. In this paper, a one step derivation for the formula of curvature and curvature center is presented on the basis of the close relation between curvature and curvature circle. This method is brief and to the point. It can be used for renewing the advanced mathematics textbook.