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非欧几何的发展史及其启示

时间:2017-08-11 数学毕业论文 我要投稿

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;

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