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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。
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。
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。
While, the most significance lies in the negation to the fifth postulate, that is, the birth of non Euclidean geometry. 而第五公设对数学发展的最大意义恰恰来自于对第五公设的否定即非欧几何的诞生。
Conventional flow mathematical models of coalbed methane are all based on Euclidean geometry. 摘要传统的煤层气渗流数学模型均是建立在欧几里德几何基础上的。
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。
This paper discusses how to transform the result which is about this problem in Euclidean geometry on the field to the rings. 本文探讨的是如何将域上欧氏几何中 ;关于这一问题的结果 ;有效的转到环上来 .
Growing process and shape of water tree in XLPE dielectric is random and branched which can not be described using Euclidean geometry. XL PE介质中水树枝的生长过程和形态表现出强烈的随机性和分叉趋势 ,且不能用传统的欧氏几何语言描述。基于局部介质击穿计算和分形几何原理 ,估计了水树枝发展形态的分叉趋势和分形维数。
In field Euclidean geometry, the problem of expressing orthogonal transformation as symmetrical product is one of the basic problems in geometry. 域上欧氏几何中 ,把正交变换表为对称之积的问题 ,是几何学中基本问题之一。
Euclidean geometry is not only the leader of the civilization of ancient Greek but also the brilliant achievements of axiomatic approach in mathematics. 以《几何原本》为代表的欧氏几何是古希腊文明的一个火车头;是古代数学公理化方法的一个辉煌成就.
They do so to high precision, showing that aside from the overall expansion, the universe obeys the laws of Euclidean geometry and must be very close to spatially flat. 他们高精密度的检测显示，除了整体的膨胀外，宇宙遵守欧几里得的几何定律，也具有几乎平坦的空间。
Euclidean geometry. 欧几里几何
In his early work on general relativity, Einstein realized that over cosmic distances space might not conform to the principles of Euclidean geometry - that is, the sum of the angles of a very large triangle might not equal exactly 180°. 爱因斯坦在早期研究广义相对论时就已认识到，在宇宙规模的距离上，空间是不可能符合欧几里得几何的原理的，这就是说，一个非常大的三角形的内角之和不可能正好等于180度。
The changes of the relations between the intuition and logic result from the development of non Euclidean geometry,from which is derives the method of the pattern and formalization in mathematics,and based on which the paradox is avoided. 研究表明 ,直观与逻辑矛盾的加剧源于非欧几何的发展 ,因而在数学中推出了模型方法与形式化并试图以此避开悖论
First of all,Euclidean geometry and its axiomatic approach are introduced in brief. Then,Euclidean geometry is analyzed from point of view of culture and its human value,aesthetic value and applied value are discussed. 文章简要介绍了欧氏几何及其公理化方法;并从文化的角度对其进行分析;探讨了欧氏几何的人文价值;美学价值和应用价值.
Firstly, this dissertation introduces the basic conceptions and relevant properties of projective geometry, affine geometry, metric geometry and Euclidean geometry used in computer vision, as well as the camera model with imaging principles. 本文首先介绍了计算机视觉中所用到的射影几何、仿射几何、度量几何和欧氏几何等各类几何学的基本概念和相关特性；概述了摄像机模型及成像原理；
At the same time,the duality propositions of the angular bisector,two perpendicular lines,the length of the line segment,the distance between a point and a line in Euclidean geometry,were also established. 在欧氏几何中建立起了角平分线,两条直线垂直、线段长度、点到直线的距离的对偶命题。
In this paper,we discuss the relation between the ordered affine geometry and the ordered affine geometry over the ordered division ring, them between the Euclidean geometry without continity and the Euclidean gemetry over the Pythagorean field. 本文讨论有序仿射几何与有序体上仿射几何之间的联系,以及无连续公理欧氏几何与pythagoras域上欧氏几何之间的联系。
The main results are: Assuming the camera undergoes two sets of translations, of which the corresponding rotation axes of camera are not parallel, then Euclidean geometry of a scene can be reconstructed linearly from four point correspondences. 当摄像机作两组平移运动时 ,若在两组平移运动之间摄像机具有不同的姿态 ,则从 4对图像对应点可以线性地重建场景的欧氏几何。
Yet the full nonline problem is difficult to solve by use of traditional Euclidean geometry method, even the numerical solution cannot be got, so it puzzled researcher nearly half century. 然而这些沉积生成的枝晶，其形貌上呈现出的极不规则、极其复杂的几何特征，这一非线性的生长问题用传统的欧氏几何来处理是十分困难的，甚至于无法获得数值解，所以在近半个世纪以来一直困扰着科学工作者。