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Geometry and the Imagination (AMS Chelsea Publishing) Hardcover – October 1, 1999
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[This] superb introduction to modern geometry was co-authored by David Hilbert, one of the greatest mathematicians of the 20th century. --Steven Strogatz, Cornell University
A fascinating tour of the 20th century mathematical zoo ... Anyone who would like to see proof of the fact that a sphere with a hole can always be bent (no matter how small the hole), learn the theorems about Klein's bottle--a bottle with no edges, no inside, and no outside--and meet other strange creatures of modern geometry, will be delighted with Hilbert and Cohn-Vossen's book. --Scientific American
Original Language: German
Top Customer Reviews
It is beautiful geometry, beautifully described. Besides the relatively recent topics he handles classics like conic sections, ruled surfaces, crystal groups, and 3 dimensional polyhedra. In line with Hilbert's thinking, the results and the descriptions are beautiful because they are so clear.
More than that, this book is an accessible look at how Hilbert saw mathematics. In the preface he denounces "the superstition that mathematics is but a continuation ... of juggling with numbers". Ironically, some people today will tell you Hilbert thought math was precisely juggling with formal symbols. That is a misunderstanding of Hilbert's logical strategy of "formalism" which he created to avoid various criticisms of set theory. This book is the only written work where Hilbert actually applied that strategy by dividing proofs up into intuitive and infinitary/set-theoretic parts.Read more ›
Geometry is the study of relationships between shapes, and this book helps you see how shapes fit together. Ultimately, you must make the connections in your mind using your mind's eye. The illustrations and text help you make these connections. This is a book that requires effort and delivers rewards.
There Hilbert says "...In this book, it is our purpose to give a presentation of geometry, as it stands today, in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems of geometry, and beyond this, it is possible in many cases to depict the geometric outline ot the methods of investigation and proof, without necessarily entering into the details connected with the strict definitions of concepts and with the actual calculations."
A little further, he says "...This book was written to bring about a greater enjoyment of mathematics, by making it easier for the reader to penetrate to the essence of mathematics without having to weight himself down under a laborious course of studies."
As a reader of this book, I can say that the key words are "visual imagination" and "enjoyment of mathematics".
The purpose described by Hilbert is completely (and excellently) achieved.
The book is a masterpiece, written by one of the masters of Mathematics.
In an elegant and clear style, Hilbert explains the most beautiful geometrical concepts.
When reading it, you feel as if Hilbert was sit down besides you, just talking about geometry to you, (maybe with the aid of a sheet of paper and a pencil), and you can grasp the genius of the Göttingen Professor.
He does not use practically any formula or mathematical expression, however his prose is full of mathematical insights, geometrical facts, stimulating images and delicious "expository" proofs.Read more ›
On the other hand, how can one ignore the work of such a giant of mathematics who's willing to guide you into his imagination ?
However: The Preface states: "This book was written to bring about a greater enjoyment of mathematics, by making it easier for the reader to penetrate to the essence of mathematics without having to weight himself down under a laborious course of studies."
All I can say is that if you read this and find it "easy," then you have terrific mathematical talent! Yes, the drawings and the intuitive descriptions are helpful, but much of the book is so obscure that I have been told that one of the world's leading geometers is working on an annotated edition explaining what the authors were talking about. On topics which I had already studied elsewhere, I found the presentation illuminating.
I still recommend this book.
Most Recent Customer Reviews
I have no complaints about the written content of this book. It is lovely. The print quality, however, is abysmal. Read morePublished 1 month ago by Jacob Rus
Everyone acquainted with math knows this book's content and accessible style has made it a classic.
Anyone with a serious interest(occasional or consuming) in geometry... Read more
A pearl! Anyone interested in Geometry shouldn't miss the lucid presentation of the great Hilbert.Published on October 12, 2008 by Ioannis
This is a marvellous book. I will illustrate by one sample from each chapter (except chapter 1 on "the simplest curves and surfaces" which is the least exciting chapter). Read morePublished on January 11, 2007 by Viktor Blasjo