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-even after more than half a century has passed! 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 ...
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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-even after more than half a century has passed! 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. It's also likely that you have heard those facts before, but surely 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 R3. 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: ?/4=1?1/3+1/5?1/7+?.... 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 G???ttingen 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.
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Add this copy of Geometry and the Imagination to cart. $69.70, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 1957 by MP-AMM American Mathematical.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of Geometry and the Imagination (Ams Chelsea Publishing) to cart. $61.00, very good condition, Sold by HPB-Emerald rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2020 by American Mathematical Society.
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Good. Shows minimal wear such as frayed or folded edges, minor rips and tears, and/or slightly worn binding. May have stickers and/or contain inscription on title page. No observed missing pages.
Add this copy of Geometry and the Imagination to cart. $72.15, Sold by BookDepart rated 4.0 out of 5 stars, ships from Shepherdstown, WV, UNITED STATES, published 1952 by Chelsea Publishing Company.
Edition:
1952, Chelsea Publishing Company
Hardcover
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Publisher:
Chelsea Publishing Company
Published:
1952
Alibris ID:
16705446340
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UsedGood. Hardcover; translated by P. Nemenyi; this work is an English translation of the famous Anschauliche Geometrie. Fading, scuffing, and shelf wear to ext erior; former owner's name written on front endpaper; fading to pages; in g ood condition with clean text, firm binding.
Add this copy of Geometry and the Imagination to cart. $116.88, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1952 by Chelsea Publishing House.
