Euclidean algorithm

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 。