论文标题
Desargues线性点比率的几何形状的进步
Advances in the Geometry of the Ratio of Linear Points in the Desargues Affine Plane Skew Field
论文作者
论文摘要
本文介绍了Desargues仿射平面一条线的比率的几何形状的进步，我们认为这是偏斜场元素的比率，该元素是在Desargues仿射平面的一条线上构建的。此处给出的结果具有基于干净的几何表现，基于DESARGUS AFFINE PLAN AXIOMAMICS以及该平面线上点上点的添加和乘法的定义，以及用于偏斜的场属性。本文的结果是：（1）在Desargues仿生平面上的一条线中研究两个点和三个点的特性。另外，我们讨论了与“线条链”特征相关的案例，何时是两个案例，并且与两个不同。 （2）我们已经构建了比率集的图，以两个和三个点构建图，并证明该地图是线的两种线。 （3）与点的添加和乘法相比，比率点集（分别为两个点，为三个点），形成一个偏斜字段，对于更多，此偏斜字段是Desargues仿射平面上“线路 - 弯曲场”的子键字段。 （4）DESARGUES仿射平面中包含共线比顶点的每个Dyck多边形都有一个自由组呈现。
This paper introduces advances in the geometry of the ratio of either two or three points in a line in the Desargues affine plane, and we see this as a ratio of elements of skew field which are constructed over a line in Desargues affine plane. The results given here have a clean, geometric presentation based Desargues affine plan axiomatics and definitions of addition and multiplication of points on a line in this plane, and for skew field properties. The results in this paper are: (1) study of properties for ratio of two and three points, in a line on Desargues affine plane. Also, we discuss the cases related to the "line-skew field" characteristic, when it is two and when it is different from two. (2) we have construct the maps for ratio points-set, for two and three points, and have prove that, this maps are bijections of the lines. (3) set of ratio points (for two and for three points) with addition and multiplication of points, forms a skew fields, for more, this skew fields are sub-skew fields of the 'line-skew field' on Desargues affine plane. (4) Every Dyck polygon containing co-linear ratio vertices in the Desargues affine plane has a free group presentation.
