﻿ 初等几何的实践性基础及其应用———几何学的产生

# 初等几何的实践性基础及其应用———几何学的产生Practicalities Foundations of Elementary Geometry and Its Applications———The Produce of Geometry

Abstract:
There is a gap between the current geometry theory and its practice applications. The point, straight line, ray, parallel line and plane in current geometry possess the character of ideal all. They are the limit of se- quence of approximation point, straight line, ray, parallel line and plane separately, when the error bounds tend to zero. But the limit possesses the characteristic that could not be arrived at. Therefore, the character of only existence and ideal congruence of ideal point, straight line, ray, parallel line and plane must apply axi- oms to affirm them. In researching three-dimensional actual space, for ideal geometry element, the system of Euclidean geometry is suitable and necessary; but it needs a process of “negation of the negation” to apply it in reality question. Two questions of consistency of the axiom system and practice function of axioms could not be settled by the method of formal logic and the method of mathematical logic. The settlement of the two questions must apply the method of materialist dialectics.

[1] 李云普 (1990) 任国朝, 编. 几何基础. 高等教育出版社, 北京, 53, 54, 59, 111.

[2] 孙小孔 (1963) 裘光明, 译. А. Д. 亚历山大洛夫, 著. 数学——它的内容、方法和意义. 科学出版社, 北京, 24.

[3] 曹俊云 (2009) 杨键辉, 合著. 全能近似分析数学理论基础及其应用. 北京中国水利水电出版社, 北京, 19-42.

[4] 马忠林, 译 (1955) Д.И.ПЕРЕПЁЛКИН, 著[苏]. 初等几何学教程. 高等教育出版社, 北京, 4-5, 39, 141.

[5] 黄宏荃, 彭灏, 译 (1979) [苏]В. И. 瑞德尼克, 著. 量子力学史话. 科学出版社, 北京, 87-90.

[6] H. Jerome Keisler, 著[美] (1976) Elementary calculus. Printed in the United States of America, 1, 28.

[7] 曹俊云, 曹凯 (2012) 无穷的概念与实数理论问题. 理论数学, 4, 207-215.

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