欧几里得几何

在抽象系统的角度上，欧几里得几何是不是完备而自洽的，是有待于探讨一下的。

In the modern separation of mathematics from science , it became necessary to ask whether Euclidean geometry was , regarded as an abstract exercise , a complete and consistent whole .

我们都学习过，欧几里得几何中对勾股定理的证明方法，从繁杂的欧氏几何的公理开始，邦，邦邦，邦邦，邦邦。

And we learned how to prove the Pythagorean Theorem in Euclidean geometry , starting with the various axioms in Euclidean geometry , ba , ba-ba , ba-ba , ba-ba , ba bum .

他不承认非欧几里得几何的独立存在性。

He did not grant independent existence to the noneuclidean geometries .

（1826－1866）非欧几里得几何的创立者。

Pioneer of non-Euclidean geometry ( 1826-1866 ) .

混凝土断裂试件断口蕴涵着丰富的力学信息，而传统的欧几里得几何难以对复杂的断口形貌进行描述。

The broken surface of concrete fracture specimen comprises plenty of mechanic information that is worthy of being studied carefully .

欧几里得的《几何原本》及几何学古典公理法

The Elements of Euclid and the Classical Axiom Method of Geometry

本文将描述欧几里得空间内几何对象的关联维推广到了基于拓扑结构的复杂网络，并据此分析了复杂网络的分形结构。

We generalize correlation dimension describing geometric objects in Euclidean space to complex networks based on topol-ogy , and accordingly analyze fractal structure of complex networks .