论高斯的几何学思想及其意义

Study on the Thought and the Significance of Gauss' Geometry

高斯的几何学思想意在揭示欧氏几何不具有惟一的(物理的)必然性,而高斯的内蕴微分几何学则深刻地揭示了几何空间的非欧本质。文章考察高斯几何学思想中几个核心概念的发现及其深远意义,探究高斯几何学思想的思维轨迹及其与现代微分几何的联系。

The thought of Gauss＇ geometry is intended to reveal that the Euclidean geometry does not have the only physics necessity. Gauss＇ intrinsic differential geometry, however, has deeply revealed the Non-Euclidean nature of geometry spaces. This paper studies on the discovery of the core concepts and its far-reaching significance of the thought of Gauss＇ geometry. The thinking path of Gauss＇ geometry is reconstructed historically,and the relations between Gauss＇ geometry and modern differential geometry are discussed.