Desargues仿射平面斜域中共线点比率的不变变换与保持变换进展
Progress in Invariant and Preserving Transforms for the Ratio of Co-Linear Points in the Desargues Affine Plane Skew Field
AI总结：
该研究基于Desargues仿射平面公理与斜域性质，证明反演、自然平移、自然伸缩、Mobiüs变换、平行投影、平移及伸缩均保持共线两点或三点的比率。
摘要：
本文介绍了在Desargues仿射平面斜域中保持两个或三个共线点比率的不变变换。这里给出的结果基于Desargues仿射平面公理体系以及斜域性质的定义，具有简洁的几何表述。本文的主要结果为：（1）在Desargues仿射平面的一条直线上，两点和三点的比率在反演、自然平移、自然伸缩和Mobiüs变换下是“不变的”；（2）Desargues仿射平面中一对直线的平行投影保持两点和三点的比率；（3）Desargues仿射平面中的平移保持2点和3点的比率；（4）Desargues仿射平面中的伸缩保持2点和3点的比率。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
