几何学的

On this basis,the PDC bit's fivepoint survey theory is developed,and a series of formulas are derived,applying PDC bits' geometry and analytic space geometry.

在此基础上，运用PDC钻头几何学和空间解析几何学中的四点共面、行列式、坐标变换的知识，提出并推导出了PDC钻头的五点测绘理论及系列公式。

They include the fundamental concepts of jet bundle geometry needed in describing time-dependent mechanical systems, decomposition of jet bundles into a direct sum according to the constraints, horizontal distributions on constraint mainifolds, the global formulation of D'Alembert-Lagrange's equations and Chaplygin's equations, and nonholonomic mechanics on a Riemann-Cartan manifold. Meanwhile, the geometric significance of Chetaev's conditions and $\rd$-$\delta$ commutation relation are discussed in depth.

本文主要综述非完整约束系统几何动力学的外附型和内禀型Lagrange理论，包括非定常力学系统所需要的射丛几何学的基本概念、射丛按约束的直和分解、约束流形上的水平分布、 D'Alembert-Lagrange方程与Chaplygin方程的整体描述、以及Riemann-Cartan流形上的非完整力学，文中对Chetaev条件和d-δ交换关系的几何意义作了深入讨论。

During the course of the well-known "new mathematics" campaign, the status of Euclidean geometry was completely overthrown in I960" s. After deeply thought of "new mathematics", the standpoint that geometry curriculum should reflect the content and method of modern geometry and be in touch with the student" s real life was agreed on. Other countries have tried some significant attempts. We can find from some geometry textbooks that the methods of transform and vector have appeared as a normal part. Simultaneous, not only the new developments of geometry such as Topology have been referred , but also the connection between geometry and practice has been strengthened.In China, geometry curriculum is also in the during of innovation.

而学校几何课程在二千年的时间里一直没有多大的变化，直到二十世纪初"克莱因—培利运动"的第一次冲击，到60年代"新数学"运动的全盘改革，以及之后的深入反思，中学几何课程要反映现代几何学的内容和方法以及紧密联系于实践的观点已经受到普遍的重视，国外的几何课程已经在这方面做了不少有意义的尝试，从国外的一些几何教材中可以发现：变换、向量等工具已经作为正式的内容进入几何教学，拓扑学等几何的新发展也开始在教材中有所体现；几何课程与实践之间的联系更是在很大程度上得以加强。

The generalized fractal dimension model of openings perimeter in jointed rock mass is put forward. The relation between erecting parameters and generalized fraetal dimension of openings perimeter is analyzed. According to the fractal theory, the relation between overbreak as well as underbreak and generalized fractal dimension of openings perimeter is built.

块体理论是研究洞室超欠挖的重要工具，它是从拓扑几何学的角度来研究洞室中的关键块体，但关键块体与超挖块体之间存在区别，文中对超挖块体和关键块体之间的关系进行分析研究，应用块体理论和结构面网络模拟技术相结合的方法预测了洞室超挖块体的大小。

Similarly, Wiske (1990) concluded from her study of high school teachers who used Geometric Supposer that teachers need a deep and wide knowledge of their subject matter and a clear understanding of the process of building mathematical understanding to use the software effectively.

同样地， Wiske(1990)从她的中学老师老师需要建筑数学的理解有效地使用软件的他们的主题物质和程序的清楚理解的深和广泛知识二手的几何学的 Supposer 的研究总结。

In this paper, the effects of the rigid body motions and low frequency surface errors on the image quality were analyzed. Quadratic equations were used to build the mathematical model of the Wolter type I and II X-ray telescopes and reduce the computational complexity of ray tracing. With the help of a self-developed optical surface analysis code, the effects of the perturbations of the mirrors on the image quality was analyzed and the growth of the image spot formed by deformed telescopes was calculated, this is important for giving the reasonable fabrication tolerance.

在本篇文章中，详细分析了刚体运动误差和低频表面误差对成像质量的影响；使用空间解析几何学的二次曲面方程建立Wolter I、II型X射线掠入射望远镜镜片的数学模型，降低光线追踪的计算复杂度；借助自主开发的光学仿真软件分析了国内研制的X射线成像望远镜的刚体运动误差和低频表面误差对成像质量的影响，计算出像点艾里斑半径均方根值随误差变化的增长率，对工程上提出合理的制造公差的误差容限有重要的指导意义。

Crystals were aligned to follow the patters of sacred geometry - spiraling pyramidal energies.

依照神圣的几何学的急速的祈祷声排列的水晶--成螺旋状下降的金字塔形的能源。

For geometrical propositions are one and all apodeictic, that is, are bound up with the consciousness of their necessity; for instance, that space has only three dimensions.

因为几何学的定理全都是无可置疑的，亦即与它们的必然性的意识结合在一起的，例如空间只有三种量度；但这一类定理不可能是经验性的命题或经验判断，也不是从这些经验判断中推出来的。

Two years ago a study of another amazonian tribe , the piraha , reported that the ability of tribal adults to conceptualise numbers is no better than that of infants or even some animals

法国和美国的研究人员在最新一期的科学杂志上发表文章称，在亚马孙河丛林深处有一个部落群，即便他们没有用来表达几何学概念的语言也极具几何学天赋。

Two years ago a study of another amazonian tribe , the piraha , reported that the ability of tribal adults to conceptualise numbers is no better than that of infants or even some animals . the research suggested that without words for specific numbers , a number sense cannot develop

法国和美国的研究人员在最新一期的科学杂志上发表文章称，在亚马孙河丛林深处有一个部落群，即便他们没有用来表达几何学概念的语言也极具几何学天赋。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。