欧几里德几何的唯一性与必要性已被公认。
The common conclusion was the uniqueness and necessity of Euclidean geometry.
非欧几里德几何实际上是从属于欧几里德几何的。
The non-euclidena geometries were in effect subordinated to euclidean geometry.
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。
Conventional flow mathematical models of coalbed methane are all based on Euclidean geometry.
欧几里德几何是一种数学系统归于希腊数学家欧几里德的亚历山大。
Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclidof Alexandria.
现象世界，也就是我们所感知的世界，必须符合欧几里德几何学的发现。
The phenomenal world, that is the world that we experience must, for example, satisfy the exhumes of Euclidean geometry.
它今天是众所周知的，因为他追加亚诺什“非欧几里德几何第一册纸。”
It is well-known today since he appended janos' paper on non-Euclidean geometry to the first volume.
欧几里德几何是对自然的高度抽象，分形几何则更为真实地反映了自然的形式结构。
Euclid geometry can be regarded as an abstraction of nature. Comparing to Euclid geometry's simpleness, Fractal geometry reflects natural contexture more veritably.
爱因斯坦12岁时开始自学欧几里德几何，对学校枯燥教学方式厌倦的他干脆自学起高等数学。
Einstein's 12-year-old self when the Euclidean geometry, boring teaching methods in schools, he simply fed up with higher math self-starting.
亚诺什继续反正今天是公认的，随着罗巴切夫斯基和高斯 ，非欧几里德几何的发现者之一；
Janos continued anyway and today is recognized, along with Lobachevsky and Gauss , as one of the discoverers of non-Euclidean geometry;
观察者B会做出这样的结论：在这种“力”和她发现的非欧几里德几何问题之间肯定存在有某种关系。
Observer B concludes that there must be some connection between this 'force' and the non-Euclidean geometry she finds.
看起来毕达哥拉斯的定理，似乎来自于欧几里德的三角形理论，从欧几里德几何学的发现中可以简单地推理出来。
It seems that the proof of Pythagoras's theorem comes pretty much from just consulting the ideas of Euclidean triangle, the exhume of Euclidean geometry and simply doing inferences from those.
通过引入对偶变量，将平面正交各向异性问题导入哈密顿体系，实现从欧几里德几何空间向辛几何空间的转换。
Based on the dual variables, the Hamiltonian system theory is introduced into plane orthotropy elasticity, the transformation from Euclidian space to symplectic space is realized.
她将看到和观察者A一样数量的尺子。所以同样的，将可以做出这样的结论：圆周和半径的比率将和欧几里德几何不一致。
She would see the same number of rulers involved as did observer a, and so would likewise conclude that the ratio of circumference to radius did not conform with Euclidean geometry.
半个世纪前，IBM的赫伯特·格勒恩特尔编写了一个程序，据称再现了欧几里德几何定理，但是，批评家们说它过于依赖程序员提供的规则。
Half a century ago, IBM's Herbert Gelernter authored a program that purportedly rediscovered Euclid's geometry theorems, but critics said it relied too much on programmer-supplied rules.
欧几里德正试图表达他的一个几何学观点。
Euclid was trying to convey his idea of a geometrical point.
阐述了欧几里德《几何原本》中译本的产生、基本内容结构及其在数字与人类文明史上的重要贡献。
This paper expounds the production of the Chinese version of Euclid's Geometry, its basic content structure and important contribution to Mathematics and the human civilized history.
科学和数学的著作，例如欧几里德的《几何原本》，是概述性的和代表性的。
Works of science and mathematics, such as Euclid's Elements, are generally not represented.
欧几里德从10个公理和假设中演绎出465个公理或命题，涉及了平面与立体几何图形各方面。
From 10 axioms and postulates, Euclid deduced 465 theorems, or propositions, concerning aspects of plane and solid geometric figures.
平面点集的(欧几里德)最小权三角剖分问题是计算几何和算法领域的一个长期悬而未决的公开问题。
The (Euclidean) minimum weight triangulation (MWT) of a planar point set is a long-standing open problem in the fields of computational geometry and algorithm design.
平面点集的(欧几里德)最小权三角剖分问题是计算几何和算法领域的一个长期悬而未决的公开问题。
The (Euclidean) minimum weight triangulation (MWT) of a planar point set is a long-standing open problem in the fields of computational geometry and algorithm design.
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