V2EX lemoine point

Lemoine Point

Definition / 定义

Lemoine point(勒莫因点):三角形的一个重要三角形中心,又称 symmedian point(对称中线点/对称中线交点),通常记为 K。它是三条对称中线(symmedians)的交点;等价地,它是三角形在重心坐标/重心几何中与边长权重相关的一个特殊点。除这一含义外,“Lemoine”也可作人名。

Pronunciation / 发音

/lmwn pnt/

Examples / 例句

The Lemoine point lies inside any acute triangle.
勒莫因点位于任何锐角三角形的内部。

In barycentric coordinates, the Lemoine point can be written using side-length weights, which makes it useful in proving triangle-center relationships.
在重心坐标中,勒莫因点可以用与边长相关的权重来表示,因此常用于证明各类三角形中心之间的关系。

Etymology / 词源

Lemoine point 以法国数学家 mile Lemoine(埃米尔勒莫因,18401912)命名。该点在经典欧式几何与三角形中心理论中被系统研究;英文名称中的 “point” 直译为“点”,整体即“勒莫因(所研究的)点”。

Related Words / 相关词

Literary Works / 文学作品

  • Triangle Centers and Central Triangles(Clark Kimberling)
  • Advanced Euclidean Geometry(Roger A. Johnson)
  • Geometry Revisited(H. S. M. Coxeter & S. L. Greitzer,书中相关章节讨论三角形几何与类似中心点思想)
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