高斯建立绝妙定理的历史过程

发布时间：2018-03-31 00:31

  本文选题：高斯绝妙定理　切入点：高斯曲率　出处：《自然辩证法研究》2017年09期

【摘要】：现代微分几何学与古典微分几何学的重要区别在于前者关注内蕴的几何对象以及内蕴的几何性质。带来这一历史转折的是高斯绝妙定理,高斯所发现和证明的绝妙定理使得高斯关注曲面的内蕴性质,并进而导致内蕴几何学的建立。高斯建立绝妙定理的过程是高斯内蕴几何学起源的最重要线索。但目前关于绝妙定理建立过程的历史研究,最多给出高斯相关工作的年谱。在研究原始文献和相关研究文献基础上,梳理高斯关于绝妙定理相关工作之间的历史关联,还原高斯发现和证明绝妙定理的过程,提出并回答关于绝妙定理的几个历史问题。
[Abstract]:The important difference between modern differential geometry and classical differential geometry is that the former pays close attention to the geometric object of connotation and the geometric nature of connotation. The wonderful theorem discovered and proved by Gao Si made Gao Si pay attention to the intrinsic properties of the surface. And then lead to the establishment of intrinsic geometry. Gao Si's process of establishing wonderful theorems is the most important clue to the origin of Gao Si's intrinsic geometry. At most, the chronology of Gao Si's related work is given. On the basis of studying the original literature and related research documents, this paper combs the historical correlation between the relevant work of Gao Si's work on the excellent theorem, and restores the process of discovering and proving the brilliant theorem in Gao Si. Several historical questions about the excellent theorem are put forward and answered.
【作者单位】： 西北大学科学史高等研究院;
【基金】：国家自然科学基金资助项目“从Gauss到Riemann的微分几何学之历史研究”(1166010148);“代数方程之Galois理论的若干历史问题研究”(11571276)
【分类号】：O186.1
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本文编号：1688369