V2EX cevian

Cevian

Definition / 释义

(几何)三角形的“塞瓦线”:从三角形的一个顶点出发,连接到对边(或其延长线)上一点的线段。常用于讨论塞瓦定理(Ceva’s theorem)等共点性质。

Pronunciation / 发音

/sivin/

Examples / 例句

The segment from vertex A to a point on BC is a cevian.
从顶点 A 连接到边 BC 上某一点的线段是一条塞瓦线。

In triangle ABC, the three cevians are concurrent if and only if they satisfy Ceva’s theorem.
在三角形 ABC 中,三条塞瓦线当且仅当满足塞瓦定理时共点。

Etymology / 词源

cevian 来自意大利数学家 Giovanni Ceva(乔瓦尼塞瓦) 的姓氏,他在三角形共点条件方面的研究(即塞瓦定理)使这一类线段以其名命名。

Related Words / 相关词

Literary Works / 文献与作品中的用例

  • H. S. M. Coxeter & S. L. Greitzer, Geometry Revisited(讨论塞瓦定理与相关共点性质时使用 “cevian”)
  • H. S. M. Coxeter, Introduction to Geometry(平面三角形几何章节涉及 cevians)
  • V. Prasolov, Problems in Plane and Solid Geometry(大量三角形几何题目中出现 “cevian/cevians”)
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