V2EX symmedian

Symmedian

定义 Definition

symmedian(对称中线):三角形中的一种共线线段(cevian)。它是把某条中线(median)关于对应顶角的角平分线(angle bisector)做镜像反射后得到的直线(或线段)。常与对称中线点/勒莫瓦点(Lemoine point)等性质一起出现。
(在较少见的语境中也可能指与对称中线相关的点或性质,但最常用的是上述几何意义。)

发音 Pronunciation (IPA)

/smmidin/

词源 Etymology

由 **sym-**(表示“共同、对称”,源自希腊语 syn “一起”)+ median(“中线/中位的”,源自拉丁语 medianus “在中间的”)构成。整体含义可理解为“与中线对称对应的线”。

例句 Examples

The symmedian of a triangle is the reflection of a median across the angle bisector.
三角形的对称中线是把一条中线关于角平分线反射得到的。

In advanced triangle geometry, the symmedians intersect at the Lemoine point, revealing deep relationships among cevians, isogonal conjugates, and ratios on the sides.
在高等三角形几何中,三条对称中线交于勒莫瓦点,揭示了共线线段、等角共轭以及边上分点比之间的深层联系。

相关词 Related Words

文学/著作引用 Literary Works

  • H. S. M. Coxeter & S. L. Greitzer, Geometry Revisited(讨论三角形几何中的重要线与点,常涉及对称中线思想)
  • Roger A. Johnson, Advanced Euclidean Geometry(系统讲解三角形几何,包含 symmedian 与相关定理)
  • Clark Kimberling, Triangle Centers and Central Triangles(三角形中心理论中常出现 symmedian 与勒莫瓦点)
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