里德

In Euclidean geometry, for example, such concepts as "point,""line," and " lie s on" are usually posited as primitive terms.

例如，在欧几里德几何中，「点」、「线」、「介于」都是基设名词。

In distance metric of similarity search,DTW that replaces the Euclidean distance metric could bring better performance.

采用动态时间弯曲距离度量方法克服了欧几里德距离度量方法自身的缺陷。

First, we measure similarity between different time-series data with Euclidean distance metric and dynamic time warping.

首先， 使用欧基里德距离量测法与动态时间扭曲法，测量出时间序列间的相似度。

"Two- and three-dimensional Euclidean spaces are metric spaces, as are inner product spaces, vector spaces, and certain topological spaces."

二维和三维的欧几里德空间是度量空间。另外，内乘空间、向量空间以及某些拓扑空间等也都是度量空间

Using colour systems such as is computationally prohibitive, but in practice it is adequate to use a Euclidean distance metric in components coded nonlinearly according to video practice.

使用如CIE L*u*v*或 L*a*b*的色度系统，计算是不允许的。但实际上，依据视频实践，在R'G'B'分量非线性编码时，使用欧机里德距离度量是适当的。

One way to think of the Euclidean plane is as a

有一种方法论把欧几里德平面看作满足可依据距离和角表达的特定联系的

Once the Euclidean plane has been described in this language, it is actually a simple matter to extend its concept to arbitrary dimensions.

一旦欧几里德平面用这种语言描述了，扩展它的概念到任意维度就是简单的事情了。

The first modestly skillful full-board chess program; the first checkers program, which defeated a regional champion; a program able to prove theorems in Euclidean plane geometry, which could pass the problem-solving section of a New York State high school regents examination; and serious research in both speech and character recognition were all part of the IBM Research playbook.

第一款水平一般的全棋盘象棋程序；第一款跳棋程序，它打败了区跳棋冠军；能证明欧几里德平面几何定理的程序，它能通过纽约高中入学考试；还有对语言和字符识别上的重要研究；这些都是IBM研究部打的算盘。

Based on the model of DLA, this paper simulates the process of aggregation's growth for random walk particles from local area on two-dimension Euclidean plane. The aggregation is confined to Euclidean circular plane for large enough particle walking area and far enough partial source distance. The centre of the Euclidean circular plane is on the line between the particle source's symmetric centre and the seed particle, and is more closer to the particle source than the seed particle. Though the rate of aggregation growth is different in different directions, the whole aggregation shows fractal structure.

以DLA模型为基础，模拟研究了在二维欧几里德平面上由局部区域内产生随机运动粒子的聚集生长过程，发现对于足够大的粒子运动区域和足够远的粒子源距离，凝聚集团大体上被限制在欧氏圆形面内，圆心在粒子源对称中心和种粒子的连线上，且比种粒子更加接近粒子源；凝聚集团朝各个方向的平均生长速率虽然不同，但整体仍呈分形结构。

The non-commutativity of two gen-erators in an algebra or a group can usually lead to a certain geometrical phase.whose magnitude is generally an area of a circuit(e.g.a triangle)in a certain space.such as the spherical surface or the Euclidean plane.

通常一个群或且一个代数中两个生成元的不对易性会导致某种几何相位。这种相位可能对应于球面或且欧几里德平面几何中某个闭合回路的面积。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。