V2EX circumradius

Circumradius

Definition / 定义

circumradius(外接圆半径):在几何中,指一个多边形(常见为三角形)的外接圆的半径;也就是从外心(circumcenter)到任一顶点的距离。该词也常用于正多边形与圆的关系中。

Pronunciation / 发音

/skmredis/

Examples / 例句

The circumradius of an equilateral triangle is \( \frac{s}{\sqrt{3}} \).
等边三角形的外接圆半径是 \( \frac{s}{\sqrt{3}} \)。

Using the side lengths and the area, you can compute the circumradius with \( R=\frac{abc}{4\Delta} \).
利用三边长和面积,可以用公式 \( R=\frac{abc}{4\Delta} \) 计算外接圆半径。

Etymology / 词源

由 **circum-**(“环绕、周围”,源自拉丁语 circum)+ radius(“半径”,源自拉丁语 radius,本义有“光线、辐条”之意)构成,字面意思即“环绕(外接圆的)半径”。

Related Words / 相关词汇

Literary Works / 文学作品

  • Euclid, Elements(《几何原本》):讨论圆与三角形/多边形的外接关系,是“外接圆半径”概念的经典来源之一。
  • H. S. M. Coxeter & S. L. Greitzer, Geometry Revisited:在三角形几何中系统使用外心、外接圆与外接圆半径等术语。
  • Adrien-Marie Legendre, Elements of Geometry(《几何原理》/《几何学原本》):在平面几何章节中涉及三角形外接圆与相关度量(包含外接圆半径的用法)。
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