十九世纪几何学统一的途径
哪一个摘 要
非欧几何的出现打破了长期以来只有一种几何学即欧几里得几何学的局面。十九世纪中叶以后，通过否定欧氏几何中这样或那样的公理、公设，产生了各种新的几何学，加上与非欧几何并行发展的射影几何、微分几何以及较晚出现的拓扑学等，这个时期的几何学出现了百花齐放的局面。由此，用统一的观点解释它们便成为数学家们的重要任务。克莱因以变换群的思想统一几何学，但该思想却未能包括所有的几何学领域。希尔伯特提出了另一条对现代数学影响深远的统一几何学的途径——公理化方法，这种方法已经远远超出几何学的范围而和集合论思想成为现代数学统一化趋势的两大推手。
关键词：几何学的统一；非欧几何；公理化方法
The Way of 桂华秋皎洁Unifying Geometr爱国诗y in the 19th Century
Abstract
The non-Euclid geometry appearance has broken the situation of the only kind of geometry that is Euclidean geometry for a long time. After the middle of the nineteenth century, by denying all justice and axiom of Euclidean geometry, all sorts of new geometry, projective geometry, differential geometry which is parallel with non-Euclid 性的功能geometry and topology which emerged later emerged, in this period geometry足球比赛作文 possd infinite and wide development prospects. Thus, using unified view to explain their will become an important task of mathematicians. Klein unified ge孕妇食谱ometry by the thought of the transformation group, but the thought failed to include all of the geometry. Hilbert put forward another way to unify交通处罚 geometry which influenced modern mathematics profoundly. The method that is axiomatic method has gone far beyond the scope of the geometry. Axiomatic method and t theory thought became two big push unified trend of modern mathematics.
五个严禁Key word: The unity of the geometry; Non-Euclid geometry; Axiomatic met
