——几何学的产生

曹俊云¹，曹凯²

（1. 河南理工大学数信学院，河南焦作，454000;  2. 河南理工大学电气学院，河南焦作，454000）

摘要：现行几何理论与实践是有差距的。现行几何理论中的点、直线、平行线、射线、平面都具有理想性。它们分别是误差界趋向于零时近似点、近似直线、近似射线、近似平行线、近似平面序列的极限。极限具有不可达到的性质，所以理想点、理想直线、理想射线、理想平行线、理想平面的存在唯一性和理想合同性都需要用公理的方法去确定。在三维现实空间研究中，欧几里德体系下的初等几何是适当的、需要的；但在应用这个理论于现实问题时，需要有一个“否定之否定”式的过程。几何公理体系的无矛盾性、公理的实际意义都是形式逻辑和数理逻辑无法解决的问题。解决这两个问题都必须使用唯物辩证法。

关键词：点；直线；数轴；平行线；顺序；合同

中图分类号：0123 0181                      文献标识码 A

Practicalities Foundations of ElementaryGeometry and Its Applications ——The produce ofGeometry

CaoJunyun¹, Cao Kai²

(1. School of Mathematics andInformation engineering, Henan Polytechnic University,Jiaozuo 454000;

2. School of Electrical Engineeringand Automation, Henan Polytechnic University,Jiaozuo 454000,)

Abstract: Thereis a gap between the current geometry theory and its practice applications. Thepoint, straight line, ray, parallel line, plane in current geometry possess thecharacter of ideal all; they are the limit of sequence separately of approximationpoint, straight line, ray, parallel line, plane separately, when the errorbounds tend to zero. But the limit possesses the characteristic of that couldnot be arrived; therefore, the character of only existence and ideal congruenceof ideal point, straight line, ray, parallel line, plane must apply axioms toaffirm all. In researching to three-dimensional actual space, the system of Euclideangeometry are suitable and necessary; but need a process of “negation of the negation”， to apply it in reality question. Twoquestions of consistency of the axiom system and practice function of axiomscould not be settled by the method of formal logic and the method ofmathematical logic all. The settlement of the two questions must apply themethod of materialist dialectics.

Keywords: Point; Straight line; Number axis; Parallel line; Order;Congruence

11初等几何的实践(已改).doc