Geometry and the Imagination pdf epub mobi txt 电子书 下载 2024


Geometry and the Imagination

简体网页||繁体网页
David Hilbert
American Mathematical Society
1999-10-1
357
USD 41.00
Hardcover
AMS Chelsea Publishing
9780821819982

图书标签: 几何  数学  希尔伯特  科普  geometry  Hilbert  Mathematics  Math   


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发表于2024-12-23

Geometry and the Imagination epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Geometry and the Imagination epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Geometry and the Imagination pdf epub mobi txt 电子书 下载 2024



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This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer--after more than half a century! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians.

"Hilbert and Cohn-Vossen" is full of interesting facts, many of which you wish you had known before, or had wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $pi/4 = 1 - 1/3 + 1/5 - 1/7 + - ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem.

One of the most remarkable chapters is "Projective Configurations". In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader.

A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained!

The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry.

It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the "pantheon" of great mathematics books.

Geometry and the Imagination 下载 mobi epub pdf txt 电子书

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Geometry and the Imagination pdf epub mobi txt 电子书 下载
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用户评价

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中文译名<直观几何>。只读了微分几何一章,配图超级多----这个大赞!个人感觉适合初学者。

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非常棒

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粗读,净跟着图走了

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粗读,净跟着图走了

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希爾伯特簡直是一百年前的3Blue1Brown啊,強烈推薦給高中生和低年級本科生培養幾何直觀。

读后感

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是五个月前看的 书的特点:1极丰富的几何知识,不同几何领域的联系。 2书中提许多问题,引导读者自然思考,更难能可贵的是还 提到许多没有解决的自然提出问题,使得感到分外贴切(例如说到了菲尔茨第一届的主道格拉斯的托普拉问题直观说明,在第四章微分几何中有关极...  

评分

是五个月前看的 书的特点:1极丰富的几何知识,不同几何领域的联系。 2书中提许多问题,引导读者自然思考,更难能可贵的是还 提到许多没有解决的自然提出问题,使得感到分外贴切(例如说到了菲尔茨第一届的主道格拉斯的托普拉问题直观说明,在第四章微分几何中有关极...  

评分

是五个月前看的 书的特点:1极丰富的几何知识,不同几何领域的联系。 2书中提许多问题,引导读者自然思考,更难能可贵的是还 提到许多没有解决的自然提出问题,使得感到分外贴切(例如说到了菲尔茨第一届的主道格拉斯的托普拉问题直观说明,在第四章微分几何中有关极...  

评分

有本数学书,我一直有所偏爱:希尔伯特的《直观几何》。这本出自大师之手的小册子,中译本仅薄薄的上下两册,封面很朴素,但插图极精美。那些立体感很强的几何图形,以粗细变化有致的线条,准确地表现出物体在空间的透视关系,给人以审美的欣喜。"拓扑学"一章麦比乌斯带和克莱...

评分

是五个月前看的 书的特点:1极丰富的几何知识,不同几何领域的联系。 2书中提许多问题,引导读者自然思考,更难能可贵的是还 提到许多没有解决的自然提出问题,使得感到分外贴切(例如说到了菲尔茨第一届的主道格拉斯的托普拉问题直观说明,在第四章微分几何中有关极...  

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