用几何学

The analytical geometry is used to study the formulas of Moire fringes for the measurement of screen line, to analyze the geometric forms and their properties of Moire fringes , and further discusses the bases of theory for the measurement of screen line.

本文用解析几何学方法研究测量网线的莫尔条纹方程，分析莫尔条纹的几何形状与特性，并且进一步讨论网线测量的理论依据，旨在深刻地揭示测量网线的莫尔条纹原理。

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。

For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints.

例如，我们寻找一块领土，用各种各样的边界条件和各种各样的几何学限制条件减到最小或者使Laplace 操作者的规定的eigenvalue最大化。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

A man cannot tell whether Apelles, or Albert Durer, were the more trifler; whereof the one, would make a personage by geometrical proportions; the other, by taking the best parts out of divers faces, to make one excellent.

没有人能说阿佩勒斯和阿尔伯特两人谁更荒谬，他们一人用几何学的比例画人像，另一人将若干面容的优点抽出，集合在一起来画出一张精美绝伦的脸。

The elegancy and singularity of fractal pictures attract the attention of more and more fractal fans.Fractality is not only used for enjoyment,but also is a new research direction of geometry which is the research on anomalous geometry objects.

分形图形的优美与玄妙吸引着越来越多的分形爱好者，它不仅仅是用来欣赏的，而且代表着几何学的一个新的研究方向，即对非规整几何对象的研究［1］。

He took a geometry exercise-book written by his own hand, and drew his chair up with his leg.

他拿起他亲手写的几何学练习本，又用脚把安乐椅推了过来。

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。

Fuller invented the Geodesic dome coined the term synergetics, a "Geometry of Thinking," a metaphoric language for communicating experiences using geometric concepts, long before the term synergy became popular.

福勒发明了多面体球顶，创造了&协同几何学&这一词汇，提出&几何学的思维&，开创了用几何学的概念、使用隐喻语言沟通经验；很长时间以后，&协同&这一词语才流行起来。

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。