几何的

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。

Their application of convex body and geometry probability is the important theory in integral geometry and convex geometry, One can study the geometric invariants and geometric probability and other issues.

它们在凸体和几何概率中的应用是积分几何和凸几何的重要理论，通过它们可以研究几何不变量和几何概率等相关问题。

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

In this paper, the Euclidean geometry from Non-Euclidean geometry to the development of roads, as well as the public starting from the fifth brief analysis of the Euclidean geometry and the similarities and differences Non-Euclidean geometry.

本文主要阐述从欧氏几何到非欧几何的发展道路，以及从第五公设出发简要分析了欧氏几何与非欧几何的异同。

More specifically, Gauss studied the geometry of surfaces based on the first fundamental form (also called "line element") of surfaces and generalized Euclidean geometry to "curved geometry" on surfaces.

局部微分几何的一个里程碑是 Gauss关于曲面的理论，他建立了基于曲面第一基本形式的几何，并把欧几里得几何推广到曲面上"弯曲"的几何。

In the fourth chapter, I analyze and contrast many architectural cases in history and modern times which ellipse were applied to, and explore the ellipse"s development in historic sense. The fifth chapter investigates the dynamic relationship between geometry and architecture based on ellipse"s geometric character, and analyzes ellipse architecture"s characters in symbolism, dualism, diversity and unity these four facets. In the sixthchapter, taking ellipse architecture as examples, I try to explore the relationship between the more general geometry"s purity and architecture"s complexity, and build the foundation for future exploration of geometry"s purity.

第四章从历史和现代两个方面展开了大量对椭圆形式在建筑中应用的个案和实例的研究与对比，探讨了椭圆形式在历史上意义的变迁；第五章以椭圆的几何特性为立足点，研究了椭圆几何--建筑之间的动态关系，从标志性，二元对立，多样和统一四个方面分析了椭圆建筑的特点；第六章以椭圆建筑为例，尝试探讨了更一般的几何的纯粹性与建筑的复杂性的关系，对几何纯粹性意义的挖掘为进一步的研究提供基础；第七章采用了类型对比的研究方法，分析了安藤忠雄和库哈斯两位设计哲学截然不同的建筑师对椭圆形式的使用；另外，以位置关系为线索，将椭圆和其他的几何形式结合起来，总结了一般情况下几何的纯粹性对建筑复杂性的作用。

After analyzing the problems of traditional geometry curriculum in junior high school, we can find that the key of innovation lies in two factors, reflecting the content and method of modern geometry and closing to the students real life at the same time.

我国的几何课程也正处在改革之中，通过对我国传统几何课程中的问题加以分析可以发现，如何让初中几反映出现代几何的内容和方法，同时尽量贴近学生的生活是我国几何课程改革的重点之所在。

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。

Therefore in the teaching students should be made to actuallyfeel that spherical geometry knowledge can be used to solve or explainsome real problems in both life and production, to reach the relatedconclusions about spherical geometry by comparing it with Euclideangeometry, and to have anidea of some non-Euclidean geometry models aswell as differences between flat geomtry models and spherical geometry ones.

是为对数学有兴趣和希望进一步提高数学素养的学生而设置，重点是培养学生空间想像和几何直观能力，教学中应使学生切实地感受到利用球面上的几何知识可以解决生活或生产中的一些实际问题；让学生通过欧氏几何和球面几何的类比，得到球面上的几何的相关结论；使学生了解一些非欧几何模型，从而思考平面几何模型与球面上的几何等非欧几何模型的差异。

Classical instruments allowed in geometric constructions are the compass and straightedge .

几何的方法问题，几何或机械手段被称为合成几何。

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。