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

作　　者：王姿婷 朱一心[2] WANG Zi-ting;ZHU Yi-xin(Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China;School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)

机构地区：[1]清华大学数学科学系,北京100084 [2]首都师范大学数学科学学院,北京100048

出　　处：《数学的实践与认识》2024年第10期245-256,共12页Mathematics in Practice and Theory

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.The paper classifies hypocycloids based on two characteristic relationships(the ratios of the radi 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 

分 类 号：O18[理学—数学]