云非圆球,山非圆锥,闪电不走直线.大自然形状的复杂性有不同的种类,不仅仅是程度上的不同.为了描写这些形状,伯努瓦?B.芒德布罗设计和发展了一种新的几何学??分形几何学.他的工作对本书论及的许多不同的领域都很重要.现在,这样的领域因许多积极的研究者而大为扩充,芒德布罗展示了分形几何学的根源及其新应用的深入概述.本书的以前几个版本受到高度评价,但这一版有更广泛和深入的覆盖范围,以及更多插图.

本书是一本关于三维Euclid空间中光滑曲线与曲面一般几何理论的基础性专门学术著作。全书共9章，可划分为四个部分。第1章为第一部分，主要讲授三维矢量的代数与分析，是全书的理论基础。第2、3章为第二部分，属于三维Euclid空间的曲线论。第4～8章为第三部分，属于三维Euclid空间的曲面论。第9章为第四部分，深入详细地研究了包络现象。相对于既有文献，本书补充了新内容，对传统内容也往往采用新方法加以处理，对于同一问题有的还给出了不同的解法或证明，以例题的形式对工程中常见曲线、曲面的几何性质做了比较深入的定量研究讨论，还能够把其他数学分支的理论与方法自然地应用于经典微分几何的研究。本书思路清晰，推导过程详尽，论述深入浅出、直接明快，既不失作为数学著作的严谨与严格，又注意联系工程实际。

Credlts for Figures and Color Plates Much has changed in the world of fractals, computer graphics and modem mathematics since the first edition of Fractals Everywhere appeared. The company Iterated Systems, Inc., founded by Michael Barnsley and Alan Sloan, is now competing in the image compression field with both hardware and software products that use fractal geometry to compress images. Indeed, there is now a plethora of texts on subjects like fractals and chaos, and these terms are rapidly becoming "household words.

This volume of the Encyclopaedia contains two articles which give a survey of modern research into non-regular Riemannian geometry，carried out mostly by Russian mathematicians． The first article written by Reshetnyak is devoted to the theory of two—dimensional Riemannian manifolds of bounded curvature．Concepts of Riemannian geometry such as the area and integral curvature of a set and the length and integral curvature of a curve are also defined for these manifolds．Some fundamental results of Riemannian geometry like the Gauss．Bon formula are true in the more general case considered in the book． The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lieetween two giyen constants．The main result iS that these spaces are in fact Riemannian． This result has important applications in global Riemannian geometry． Both parts cover topics which have not yet been treated in monograph form．Hence the book will be immensely useful to

丢番图问题主要从代数几何进行考虑。书中涵盖了一些研究该课题的基础方法，如高度理论， Néron函数及其在一些经典定理中的应用，如Mordell-Weil 定理、关于积分点的西格尔定理、希尔伯特的不可约定理、Roth定理及其他。该书取代了 Diophantine Geometry,涵盖了许多重要的新资料，如Néron函数理论及Tate和 Silverman的研究结果。目次：值；值的恰当集

《立体几何中的三视图》共11讲,系统的讲述了直观图、三视图。内容包括作图的基本知识、常用的几何作图方法、基本几何体及其直观图的作法、正投影及三视图、点线面的投影、基本几何体的三视图、物体的表面交线、简单组合体三视图的画法、怎样由视图想象出其实物的形状、徒手画图、高考热点--三视图。 《立体几何中的三视图》取材适中，注重观察能力、形象思维能力和空间想象能力的培养，突出方法，结构紧凑，表述清楚，易教易学。 《立体几何中的三视图》可作为高等师范院校数学与应用数学专业教材及中学数学新课程教师培训教材，也可作为中学数学教师教学参考用书。对几何爱好者来讲，也同样是一本有益的读物。

《大学几何学》是一部久负盛名的欧氏几何学名著。 书中的部分强调作图问题，继之概括论述了相似和位似、三角形和四边形的性质，以及调和分割。随后的章节研究了包括反演点、正交圆、共轴圆及阿波罗尼斯圆等内容的圆的几何学。三角形几何学集中讨论了莱莫恩几何和布洛卡几何、等角共轭线、塔克圆以及垂极点，贯穿全书还给出了大量不同难度的习题。 《大学几何学》适合大、中学师生以及几何爱好者学习和研究。

19世纪下半叶至20世纪初，欧氏几何学经历了一场快速的复兴，期间发现了数以千百计的新定理。本书分十三个章节介绍了其中优美的一些珍宝。有一些构思精妙的定理在别的书中很难看到，如亚当斯圆，里格比点，春木定理等。 本书写的生动有趣，逻辑严谨，深入浅出。书中所列举的定理基本上都给出了详细的初等证明，书末附有习题解答。具有中学几何基本知识的读者就能看懂。

Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, ...) and objectives, in particular to understand certain classes of (pact) Riemannian manifolds defined by curvature conditions (constant or positive or curvature, ...). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields plement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysiy setting ambitious goals. It is the aim of thiook to be a systematic and prehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.