一类弧长与弦长成比例的曲线的构造  

The Construction for a Class of Curve Whose Arc Length Is Proportional to Its Chord Length

作　　者：明万元[1] 黄香蕉[1] 杨海波[1] MING Wanyuan;HUANG Xiangjiao;YANG Haibo(College of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《大学数学》2023年第5期81-84,共4页College Mathematics

基　　金：国家自然科学基金项目(11801259,11861039);江西省研究生优质课程线上转化项目(2020-36);南昌航空大学校级教改项目(JY21056,JY22070,JY22071,SZ2243)。

摘　　要：从河流的弯曲现象出发,分别在平面直角坐标系与极坐标系下构造了一类弧段上任一点到起点的弧长与弦长成π倍的理想曲线,探讨了该类曲线的存在性与唯一性.最后,将所得结论推广至空间中弧长与弦长成k倍的情形.Inspired by the curving phenomenon of rivers,a class of ideal curve whose arc length isπtimes its chord length from any point of this curve to its start point is constructed under rectangular coordinate and polar coordinate respectively,and the existence and uniqueness of this class of curve are discussed.Finally,the obtained results are generalized to the case of space curve and the proportion is k.

关 键 词：弧长 弦长 对数螺旋线 

分 类 号：O13[理学—数学]