曲线的极切线坐标及其应用

Tangential Coordinates

在曲线的极切线坐标中,曲线的曲率半径可表为极简单的形式,从而在研究曲线的整体性质时,它有重要应用。本文利用极切线坐标给出了两个重要定理的新的证明§1简单介绍了曲线的极切线坐标及有关公式;§2利用Barseual公式给出了闭凸曲线的周长与所围面积的精确关系,并由此导出了著名的等周不等式§3给出了广义极切线坐标的概念并利用它证明了闭曲线的四顶点定理。

In the polar tangential coordinates of the point X on C, the Eovm- ula of radiuo of curvatune of C is vary simple, So it is vary useful when we discuss the global theorem of curve In this paper we have gi- ven new proof of two important theorem ly using the polar tangential coordinates of points on curves In § 1, the polan tangential cooidi- nate of point on curves is introduction In § 2, The relation of length of closed conuex cusue and anea bounded by that curve is given from that the isopesimetsic inequality is inatsocted In § 3, a new proof of the Four-vertex theosem is presented.