V2EX epitrochoid

Epitrochoid

Definition / 释义

epitrochoid(数学)指一种平面曲线:由一个圆在另一个圆外侧滚动时,附着在滚动圆上某一点(该点可以在圆内、圆上或圆外)所描出的轨迹。它是更一般的“旋轮线(roulette)/摆线类曲线”的一种;当该点恰好在滚动圆周上时,会退化为 epicycloid(外摆线)

Pronunciation / 发音

/ptrokd/

Examples / 例句

An epitrochoid can be drawn with a Spirograph.
外旋轮线可以用“万花尺/齿轮绘图板(Spirograph)”画出来。

In analytic geometry, the epitrochoid is often described using parametric equations based on two rolling circles.
在解析几何中,外旋轮线常用由两个滚动圆引出的参数方程来描述。

Etymology / 词源

词由 **epi-**(希腊语前缀,意为“在……之上/外侧”)+ trochoid(源自希腊语 trokhos,意为“轮子”)构成,字面含义可理解为“在外侧滚动所形成的轮迹曲线”。

Related Words / 相关词

Literary Works / 文学与著作

  • A Treatise on the Theory of Screws(Robert Stawell Ball)在讨论几何运动与轨迹时会涉及相关的旋轮线思想与术语体系。
  • Spirals: From Theodorus to Chaos(H. S. M. Coxeter)涵盖多种经典曲线与几何构造,相关曲线家族(含外侧滚动生成的曲线)常在此类著作中出现。
  • Mathematical Models(H. Martyn Cundy & A. P. Rollett)介绍用简单机械/几何方法生成与绘制曲线,常会提到包括 epitrochoid 在内的摆线与旋轮线类曲线。
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