内摆线的形态、叉点个数及局部近似拟合
Morphology,Crossing Points and Partial Fitting of Hypocycloids
王姿婷 1朱一心2
作者信息
- 1. 清华大学数学科学系,北京 100084;首都师范大学数学科学学院,北京 100048
- 2. 首都师范大学数学科学学院,北京 100048
- 折叠
摘要
将内摆线按动圆与定圆的半径比、轴长与动圆的半径大小关系进行分类,分析了不同类别的内摆线单调性、凹凸性等形态特征,给出了内摆线叉点个数的计数公式,得到了用新内摆线对给定内摆线内侧进行局部近似拟合的计算办法.
Abstract
The paper classifies hypocycloids based on two characteristic relationships(the ratios of the radii of the rolling and fixed circles,as well as the relationship between the axis length and the radius of the rolling circle).It examines the monotonicity,convexity,and other morphological characteristics of different categories of hypocycloids,offers a formula for determining the number of crossing points of a hypocycloid and suggests a method for partially fitting the inner contour of a given hypocycloid using a new one.
关键词
内摆线/单调性/凹凸性/叉点/拟合Key words
hypocycloid/monotonicity/convexity/crossing points/fitting引用本文复制引用
出版年
2024
NETL
NSTL
万方数据