几何的

In 1943 - 1945, he worked in the Institute for Advanced Study at Princeton. Having arrived in the United States for two months, he finished his famous paper entitled "A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds", which inspired other differential geometers.

抵美两个月后，即完成其著名的论文──《闭曲面流形高斯--博内公式(Gauss-Bonnet Formula)的一个简单的内蕴证明》，对於后来微分几何的发展和微分几何学者的研究影响深远。

Based the new definition of double chord-power intergral which the pair of lines intersect the convex body in integral geometry, this paper studies the relationship of double chord-power intergral and chord-power intergral.

本文给出了积分几何中的最新定义：随机直线偶与凸体相交的双弦幂积分概念，利用积分几何的分析方法，研究了双弦幂积分的对称性，次可加性等性质及双弦幂积分与弦幂积分的相互关系。

In chapter 1, some examples of studying differential geometry's objects in the view of CAGD are introduced. The background and the results of the problem studied in this paper are also presented.

在第一章中，介绍了前人运用计算几何的观点来考察微分几何的研究对象的几个范例，并简要说明了本文的研究背景与研究结果。

Through studying some fundamental properties of the curved surface in differential geometry , a method of linear feature extraction based on differential geometry is introduced.

通过研究微分几何理论中曲面的一些基本性质，本文介绍了一种基于微分几何的线状地物提取方法，首先在局部区域内拟合一个二次曲面函数，然后通过该函数来估算灰度曲面的梯度和曲率，设定合适的梯度和曲率阈值来检测线状地物，最后进行后处理，消除许多噪声颗粒及小块区域。

Based on the source investigation and the comparative approach of history of mathematics,a historical background of Gauss' competition essay and its contribution to intrinsic differential geometry are discussed.

高斯(C.F.Gauss，1777-1855)研究微分几何的出发点是"我们是否可以从曲面本身的度量出发决定曲面在空间的形状"[1]，这就是所谓的内蕴微分几何。

Contemporary differential geometry is intrinsic , meaning that space is a manifold and structure is given by a Riemannian metric , or analogue, locally determining a geometry that is variable from point to point.

微分几何，这是简单的几何的曲率，已越来越重要，因为对数学物理的建议空间不是平坦的空间。

The authors' intention is that the reader should gain a new understanding of geometry from the process of reading this survey 2~In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geometry.

作者的意图是读者应该获得一个新的理解几何的阅读的过程中该调查2 ~在这本书中，作者给出了百科全书的主要领域和现代微分几何。

Part five discusses 3D model parametric representation, which includes 3D geometry parametrization and relative position relationship parametrization. In the former, the sweeping rules are further formalized, the concept of design parameters and modeling parameters is introduced. In the later, constraint transformation matrices of the position relationships between features are deduced, and the lost of model freedom resulted from the correspending constraint is analysed.

在特征几何参数化中，进一步规范化了特征几何的扫描生成规则，引入了设计参数和造型参数的概念，分析了造型参数向设计参数适时转化的必要性；在相对定位约束参数化中，推导了特征间一般位置约束关系的约束变换矩阵，拓宽了约束表示范围，并对约束的自由度亏损情况进行了分析。

Based on the features of spherical geometry, the writer thinks thatit is an effective way for students to learn spherical geometry wellby "practising mathematics" themselves.

鉴于球面上的几何内容的特点，笔者认为使学生切身体会"做数学"是学好球面上的几何的有效途径。

A method of computing certain inaccessible distances or heights based on similarity of geometric figures and attributed to Thales presaged more abstract approach to geometry taken by Euclid in his Elements , one of the most influential books ever written.

一种方法计算某些无法距离或高度相似性的基础上几何数字和归因于泰勒斯预示较抽象的做法所采取的欧几里得几何的元素，其中最具影响力的书籍写。

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。