查询词典 projection geometry

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In this paper, a series of lunar map projection formulas are deduced including azimuthal projections, cylindrical projections and conical projections. The lunar map projections software is compiled. By caculating lunar map projection distortions, their projection distortion rules are found. Base on the lunar exploration mission, the lunar map projection scheme is given in this paper. The azimuthal conformal projection or the circumcenter perspective azimuthal projection is usually used in small areas, especially in two poles. When the whole map of the moon is needed, the azimuthal conformal projection or the circumcenter perspective azimuthal projection is used within 10° in the poles, and the traverse tangent cylindrical conformal projection or the normal secant conical conformal projection can be used in else areas, furthermore, band-division is necessary to reduce the projection distortion.

本文推导了基于月球参考球的各种投影公式，主要包括方位投影、圆柱投影和圆锥投影；编制了月球地图投影计算软件；对多种月球的投影变形进行了详细的计算，总结分析了各种月球投影的变形规律；结合月球探测的需要，给出了月球投影方案的建议：对于局部的面积较小的投影区域，建议使用等角方位投影或外心透视方位投影；如果绘制月面全图，在两极10°范围内采用等角方位投影或外心透视方位投影，其余区域可以采用等角横切圆柱投影和等角正割圆锥投影，并且要进行分带处理。

On the base of these, and the ideas of mathematical curriculum reform and the course of the reform of solid geometry, combining with educational reality and students" psychology, put forward some thoughts about solid geometry of middle school in future:(1) The arrangement of curriculum content should. give consideration to both the logical sequence of knowledge and the development of students" psychology, and make them united;(2) Paying great attention to the analogy of plane geometry and solid geometry;(3) Some respects remained to be strengthened about solid geometry in senior middle school;(4) Emphasizing the importance of conversion in solid geometry;(5) Stressing on the combination of solid geometry and algebra and other subjects;(6) The design of the content of solid geometry should have certain elasticity, and make solid geometry and modern education technology well combined.

在此基础上，又植根于近年来我国数学课程改革的理念和立体几何课程改革的进展，并结合我国的教育实际与学生心理，对未来中学立体几何课程的设胃提出若干思考：(1)课程内容的编排，要兼顾知识的逻辑顺序和学尘的心理发展相统一；(2)重视平面几何和立体几何的类比；(3)高中阶段立体几何有待加强的几个方面；(4)强调变换在立体几何中的重要性；(5)注意将立体几何和代数及其他学科相结合；(6)立体几何内容的设计要有一定的弹性，并注意与现代教育技术相结合。

As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。

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 first conductivity base board comprises: a base material, a first projection, a second projection and a light spacer; the first projection and the second projection are installed on the base material with central line symmetry, the second projection is the image structure of the first projection relative to the central line.

第一导电基板包括一底材、一第一凸块、一第二凸块及一光间隔物，第一凸块及第二凸块以对称于一中心线的方式设置于底材之上，第二凸块为第一凸块对应于此中心线的镜射结构。

The first section is descriptive geometry, including basic knowledge of cartography and projection, projections of point, beeline, plane and their interrelations, projection transformation, curve, curving plane, the projection of curving plane solids, line of section, line of intersection, section and segmentation, elevation projection, dimetric projection.

第一部分为画法几何：其中有制图基本知识，投影的基本知识，点、直线、平面的投影及它们之间的关系，投影变换，曲线、曲面及曲面立体的投影，截交线与相贯线，剖面图与断面图，标高投影，轴测投影等。

This paper studies and analyses the map projection transformation, using VC ++ programming language to realize three projection transformation: inclined position projection, Mercator projection and Gaussian M- Ke Lvge projection, and makes the application tests.

本文对地图投影变换做了尝试性的分析研究，利用VC++编程语言实现了斜轴等积方位投影、墨卡托投影和高斯-克吕格投影三种投影变换，并做了应用测试。

It respectively constructs quasi projection-separation facet sets of two convex polytopes while their orthogonal projection on the centerline overlap mutually. Afterward it judges the separation of two convex polytopes by confirming non-overlap in orthographic projection on the centerline or by finding out a projection-separation facet from two quasi projection-separation facet sets, otherwise a collision is judged.

该算法通过判断2个凸多面体在中心线上的正投影不相交，或者分别构造它们的准投影分离面集合，并从这2个集合中找到一个投影分离面，来判断2个凸多面体分离；否则，判断为相交。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

I was just taking her hand, to help her out of a car, and I knew it.

我只是握着她的手，扶她下车，但我知道这一切。

China and South Korea have excoriated Japan over its approval of new school books which they say whitewash the atrocities committed during Japanese occupation, and anti-Japanese protests have been held in Chinese cities. The lingering bitterness over Japan's past imperialism still threatens to mar relations between the big East Asian powers

中国和韩国强烈谴责日本通过新的中学历史教科书，他们认为这一教科书掩盖了日本在其占领期间所犯下的残酷暴行，反日抗议活动在中国数座城市发生，历史上日本帝国主义制造的痛楚无法被忘却，这有可能破坏东亚强国间的关系。