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单词 Finite geometry
释义

Finite geometry

中文百科

有限几何学

2阶有限仿射平面,包含4个点和6条线。相同颜色的线是“平行”的。
Fano 平面的图解

在数学中,有限几何是满足某些几何学公理,但仅含有限个点的几何系统。欧氏几何并非有限,因为它必包含一条欧氏直线,其上的点一一对应于实数。

有限几何系统可以依维度分类,为简单起见,以下仅介绍低维度的情形。

英语百科

Finite geometry 有限几何学

Finite affine plane of order 2, containing 4 points and 6 lines. Lines of the same color are
Finite affine plane of order 3, containing 9 points and 12 lines.
Duality in the Fano plane: Each point corresponds to a line and vice versa.

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry. While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity. Other significant types of finite geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs such as higher finite inversive geometries.

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更新时间:2025/6/17 11:42:13