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单词 Klein model
释义

Klein model

中文百科

凯莱-克莱因模型 Beltrami–Klein model

(重定向自Klein model)
双曲平面射影模型中的直线。红线之间的绿线都平行于黑线。
Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model
A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection
Lines in the projective model of the hyperbolic plane

几何中,凯勒-克莱因模型Cayley–Klein model),也称为射影模型projective model)、克莱因圆盘模型Klein disk model)或贝尔特拉米-克莱因模型Beltrami–Klein model),是 n-维双曲几何的一个模型,其中点由 n-维单位球(二维时或称单位圆盘)中的点表示,直线由端点位于边界球面的直线段(即弦)表示。此模型最先出现于贝尔特拉米1868年的两篇论文中,首先是 n = 2 然后是一般的 n,用于证明双曲几何与通常欧几里得几何的等兼容性(equiconsistency)。

英语百科

Beltrami–Klein model 凯莱-克莱因模型

(重定向自Klein model)
Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model
A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection
Lines in the projective model of the hyperbolic plane
Circles in the Klein disk model

In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or n-dimensional unit ball) and lines are represented by the chords, straight line segments with ideal endpoints on the boundary sphere.

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更新时间:2025/6/21 22:17:53