曲率与曲率圆的几个等价定义  

SOME EQUIVALENT DEFINITIONS OF CURVATURE AND CIRCLE OF CURVATURE

作　　者：章栋恩[1] 

机构地区：[1]北京工商大学基础部数学教研室,北京100037

出　　处：《北京工商大学学报（自然科学版）》2005年第1期63-65,共3页Journal of Beijing Technology and Business University:Natural Science Edition

摘　　要：与现行的教材不同,给出和证明了曲线的曲率和曲率圆的另外几个等价定义:曲率圆可以作为曲线的二阶近似的一种特殊形式;也可以作为曲线上邻近的三个点所确定的圆的极限;曲率中心又可以作为曲线上邻近的两个点所作法线的交点的极限.Different from current text books, give and prove some equivalent definitions of curvature and circle of curvature: the circle of curvature can be defined as a special form of approximate curve in second order; it can also be regard as a limit circle of circles determined by three points on the curve; the center of curvature can be defined as a limit point of intersection points of two normal line about the curve.

关 键 词：等价定义 曲率 极限 近似 二阶 法线 曲线 证明 作法 交点 

分 类 号：G633[文化科学—教育学] O157.5[理学—数学]