论文标题
高斯定理周围的内在微分几何形状的哲学思考
Philosophical Reflections on Intrinsic Differential Geometry around the Gauss-Bonnet Theorem
论文作者
论文摘要
高斯河内定理的陈述提出了一种意外的反思性形式（数学哲学的主要概念），因此几何形状在其中考虑了自己。因此，高斯曲率的革命性和多方面的概念触发了欧几里得几何以上的新概念。在这里，总曲率和Euler特征的整体之间的平等表明，拓扑性质的概念等于表达几何性质概念的数字。这进一步表明，数学是通过彼此之间的不同学科的干预来发展的，因为观察工具，正式的结构，新的统一观点。
The statement of the Gauss-Bonnet theorem brings up an unexpected form of reflexivity (major concept of philosophy of mathematics), so that geometry contemplates itself in it. It is therefore the revolutionary and multifaceted concept of Gaussian curvature that triggers a new conceptuality above Euclidean geometry. Here, the equality between integral of total curvature and Euler characteristic indicates that a concept of topological nature is equal to a number which expresses a concept of geometric nature. This further demonstrates that mathematics develops through the intervention of different disciplines on top of each other, as observation tools, formal structuring, new unifying points of view.
