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. $31.10, fair condition, Sold by Book Culture Inc. rated 5.0 out of 5 stars, ships from New York, NY, UNITED STATES, published 1999 by American Mathematical Society.
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Fair. Obviously well-worn, but no text pages missing. May have highlighting and marginalia, but markings do not interfere with readability. Textbooks do not have accompanying CDs or access codes. Ships from an indie bookstore in NYC. Sewn binding. Cloth over boards. 357 p. Ams Chelsea Publishing, NO. 87.
Add this copy of Geometry and the Imagination Byhilbert to cart. $60.00, good condition, Sold by A Book Corner rated 5.0 out of 5 stars, ships from Beaverton, OR, UNITED STATES, published 1999 by American Mathematical Society.
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Hardback. No dust jacket. Solid blue covers. Cover edges and corners in good shape. Spine is tight. Pages are clean, no markings, notes or stains. Ships from Friends bookstore to benefit Beaverton (Oregon) library.
Add this copy of Geometry and the Imagination to cart. $65.15, Sold by BookDepart rated 5.0 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:
18373543591
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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; small amount of under lining and a few margin notes; fading to pages; in good condition with firm binding. No dust jacket.
Add this copy of Geometry and the Imagination (Ams Chelsea Publishing) to cart. $71.99, new condition, Sold by Academic US rated 5.0 out of 5 stars, ships from Piscataway, NJ, UNITED STATES, published 1957 by American Mathematical Society.
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Add this copy of Geometry and the Imagination (Ams Chelsea Publishing) to cart. $86.00, fair condition, Sold by SVFOL Bookstore rated 4.0 out of 5 stars, ships from SIERRA VISTA, AZ, UNITED STATES, published 1999 by American Mathematical Society.
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Fair. ACCEPTABLE-There is minor water damage to the bottom of the back cover near the spine LIKE NEW / VERY GOOD-No missing or damaged pages LIKE NEW / VERY GOOD-No text or writing on the pages or in the margins LIKE NEW / VERY GOOD-No underlining or highlighting of text VERY GOOD-Zero to Limited corner dings and/or curled corners All items shipped Monday-Friday, fast shipping! Proceeds support the Sierra Vista Public Library.
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