论文标题
在Desargues偏见平面偏斜场中的不变和保留转换的进展
Progress in Invariant and Preserving Transforms for the Ratio of Co-Linear Points in the Desargues Affine Plane Skew Field
论文作者
论文摘要
本文介绍了不变的变换，该变换保留了desargues仿射平面偏斜场中两个或三个共线点的比率。此处给出的结果具有基于干净的几何表现，基于偏斜属性的基于偏斜的计划和定义。本文的主要结果是（1）在变换下的两个和三点的比率为\ emph {不变}：反转，自然翻译，天然扩张，mobiüs变换，在Desargues仿射平面中。 （2）DESARGUS平面中一对线的平行投影保留了两个和三个点的比率，（3）Desargues中的翻译仿生平面中的翻译保留了2和3点的比率和（4）DESARGUE平面中的扩张效果保留了2和3点的比率。
This paper introduces invariant transforms that preserve the ratio of either two or three co-linear points in the Desargues affine plane skew field. The results given here have a clean, geometric presentation based based Desargues affine plan axiomatic and definitions with skew field properties. The main results in this paper, are (1) ratio of two and three points is \emph{Invariant} under transforms: Inversion, Natural Translation, Natural dilatation, Mobiüs Transform, in a line of Desargues affine plane. (2) parallel projection of a pair of lines in the Desargues affine plane preserves the ratio of two and three points, (3) translations in the Desargues affine plane preserve the ratio of 2 and 3 points and (4) dilatation in the Desargues affine plane preserve the ratio of 2 and 3 points.
