non-Euclidean geometry

A simple proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry;

非欧几何中极限三角形面积有限性的简单证明

From the study of the parallel postulate to the establishment of the non-Euclidean geometry;

从平行公设的研究到非欧几何的创立

In this paper, the author queried a few conclusions in [1] , and elaborated different views on several problems, such as relations between non-Euclidean geometry and real space, relations between mathematical logic and thinking, the significance of Godel s second incompleteness theorem, and so on.

本文对文〔1〕的几个论断提出一些疑问 ,并在“非欧几何与现实空间”、“数理逻辑与思维”、“哥德尔不完备性定理的意义”等若干问题上表述了与《数学是什么》一文中不同的观点。

In this paper, the metric equations of bifundamental figurate in non-Euclidean space obtained by Yang Shiguo are improved.

本文改进了杨世国关于非欧空间中基本图形的度量方程,建立一个一般意义下的、应用更为方便的广义度量方程,作为其初步应用,导出了非欧空间中两个单形之间的一些有趣的几何关系。

wA mathematical model so called “Poincaré Model” is introduced to solve these problems by using the theorems of Euclidean geometry stead of Non Euclidean geometry.

提供一种用模型法证明非欧几何定理的证明方法 ,在证明中可以使用欧氏几何的定理 ,从而使学生对非欧几何有更深刻的认