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。
The algorithm is based on a modification of Euclid s algorithm.
在扩展欧几里得算法的基础上提出了有限域乘法逆元的计算方法。
The development of calculus was based on not very strict but practical thought instead of Euclid s strict thought.
微积分是在不很严格、讲究实用的基础上 ,而不是在欧几里得严密思想的基础上发展起来的 。
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
Examination of the possible world in Europead s geometrical system based on pure deduction;
对欧几里德几何体系之可能世界的考察——以纯粹演绎的观点为基础