Some of these are mistakes made by Euclid that can be remedied.

Where Euclid unconsciously assumed the infinitude of straight lines.

欧几里得不自觉地假定了直线的无限性.

Cauchy-Buniakowski inequality is one of the important bases of the theories of Euclid ( or unitary ) spaces .

Cauchy -Buniakowski 不等式是Euclid空间 理论的重要基石之一,文献[1,2]都给出了该不等式的 向量 内积形式.

His style shows how deeply he was influenced by Euclid's treatment of ration and proportions.

牛顿书中的写法表明,他深受欧几里得对量和比例分析的影响.

The concept of the cross product of vectors in Euclid space is introduced.

在欧式空间中引进了向量叉积的概念.

Archimedes and Euclid writings are still relevant today.

阿基米德和欧几里得的著作今天仍有意义.

Euclid requires no prior study of mathematics.

读欧几里德不需要先研究数学.

Euclid, Euler and all the others discovered and put into words things that were already there.

欧几里德 、 欧拉,以及其他数学家们,只不过是发现了这些规律,加以文字表述而已.

Lastly, we extend Erd s-Mordell inequality to n dimensional Euclidean space E ~ n ( n 3 ).

并将Erds-Mordell不等式推广到n维欧氏空间E ( n3 ).

These are Regular Triangles in Non-Euclidean plane.

这些都是非欧平面上的正三角形,像不像扇子?

But none of the mathematicians believed that these basic non-Euclidean geometries would be physically significant.

但数学家们无人相信这些基本的 非 欧几里德几何必然有物理意义.

Economics is not a straightforward discipline like Newtonian mechanics or Euclidean geometry.

经济学不像牛顿力学或者欧几里德几何,它不是门直观的学科.

He did not grant independent existence to the non-Euclidean geometries.

他不承认 非 欧几里德几何的独立存在性.

There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes.

有二种主要类型的虫孔: 洛伦兹虫孔和欧几里得虫孔.

The non-Euclidena geometries were in effect subordinated to Euclidean geometry.

非 欧几里德几何实际上是从属于欧几里德几何的.

Science should always try to use Euclidean geometry and vary the laws of physics where necessary.

科学应该永远试用欧几里德几何学,并在必要处改变物理定律.

The common conclusion was the uniqueness and necessity of Euclidean geometry.

欧几里德几何的唯一性与必要性已被公认.

It was this concept that Riemann generalized, thereby opening up new vistas in non-Euclidean geometry.

这个概念嗣后为Riemann所推广, 从而在 非 欧几里德几何学中开辟了新前景.

The euclidean norm of an n-vector x with real or complex components is defined as following.

凡具实数分量或复数分量的n - 维向量x的欧氏范数被定义如下.

All the process of clustering based on the Euclidean distance among data vectors.

聚类过程都是根据数据之间的Euclidean(欧几里得)距离.

We introduce some model to mimic the networks developing on the Euclidian space.

提出了确定性连接的演化的网络模型.