非欧几何的发展史及其启示

摘 要

在数学史上,非欧几何占有特殊的地位.人们常将非欧几何引起的变革与哥白尼的革命相比拟.本文以非欧几何的发明过程为基本线索，探讨其对对数学学科本身、人类文化、哲学思想的影响；也研究了其对数学科研者、数学教育者、中学生、高校学生的启示。
关键词：非欧几何；罗巴切夫斯基几何；黎曼几何；启示

The history of non-Euclidean geometry and the development of its revelation

Abstract

The non-Euclidean geometry holds the special status in the history of mathematics. People usually compare the revolution of Copernicus with the transformation of Non-Euclidean geometry. This article take the non-Euclidean geometry invention process as the basic clue, has discussed the impact of the mathematical Science itself ，humanity culture and the philosophy thought；also studied its revelation to mathematics researchers, mathematics teachers， the middle-school students and the university students.     
Key words：Non-Euclidean geometry；Lobatchevskian geometry；Riemannian geometry；revelation；