摘要
关于曲线y=f(x)上任意一段的长度,两三个世纪以来,一般都是用解析运算或数值计算的方法来解决的.对于解析表达式未知的情况,则无法解决.基于弧长的直观度量法原理以及弧长仪的应用,本文探讨了圆锥曲线(包括抛物线、椭圆和双曲线)的直观度量理论和方法,并提供了相应的度量工具.对尚未完全解决的问题提出了思路,为更深入的探讨开辟了途径.
The length of a section of the curve y=f (x) is obtained by using analytic operation or numerical calculation in the past two to three centuries. But those two method cannot work when the analytic expression is unknown. The authors of this paper propose a new way for measuring curve length intuitively. On the basis of the application of the invented Arc Length Ruler, this paper further studies the theory, method and related tool for intuitively measuring the length of taper curves, including parobola, ellipse and hyperbola. This paper also points out some unsolved problems in the field of curve length measurement and gives some new ideas about futher studies.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
1991年第2期45-51,共7页
Journal of Hohai University(Natural Sciences)
基金
国家自然科学基金
关键词
圆锥曲线
弧长
直观度量
弧长仪
conic section
arc length
intuitionistic measurement
graduation
arc length instrument
