V2EX convex polygon

Convex Polygon

Definition / 定义

凸多边形:一种多边形,满足任意两点连线都完全落在图形内部或边界上;等价地说,它的所有内角都小于 180°,并且所有对角线都在多边形内部。(“polygon”也可泛指多边形;此处强调“convex/凸”的性质。)

Pronunciation / 发音

/kn.veks pl..n/
/kn.veks p.l.n/

Examples / 例句

A triangle is a convex polygon.
三角形是一种凸多边形。

In a convex polygon, every interior angle is less than 180 degrees, which makes many geometry proofs simpler.
在凸多边形中,每个内角都小于 180 度,这会让许多几何证明更简洁。

Etymology / 词源

convex 来自拉丁语 convexus,意为“向外拱起的、凸起的”。
polygon 来自希腊语 *poly-*(“多”)+ gōnia(“角”),字面意思是“多角形/多边形”。合起来 convex polygon 就是“凸的多边形”。

Related Words / 相关词

Literary Works / 文学作品

  • Euclid Elements(《几何原本》):系统讨论多边形与几何性质,凸多边形相关的基本概念常以经典几何命题形式出现。
  • Edwin A. Abbott Flatland(《平面国》):以“多边形居民”构建寓言式叙事,涉及各类多边形(常以规则凸多边形形象出现)。
  • H. S. M. Coxeter Regular Polytopes(《正多胞形》):在讨论规则图形与对称性时,频繁涉及凸多边形与其推广概念。
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