Geometry and the Imagination (AMS Chelsea Publishing)
| Author | : | |
| Rating | : | 4.75 (714 Votes) |
| Asin | : | 0821819984 |
| Format Type | : | paperback |
| Number of Pages | : | 357 Pages |
| Publish Date | : | 2014-08-27 |
| Language | : | English |
DESCRIPTION:
--Steven Strogatz, Cornell UniversityA 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. --Mathematical Association of AmericaThis superb introduction to modern geometry was co-authored by David Hilbert, one of the greatest mathematicians of the 20th century. --Scientific Ame
This is another example of a simple situation that leads to a rich geometry. It surely belongs in the "pantheon" of great mathematics books.. It is a joy to read, both for beginners and experienced mathematicians. 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. 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. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. In the section on lattices in three and more dimensions,
Great book, awful print quality I have no complaints about the written content of this book. It is lovely. The print quality, however, is abysmal.It’s apparently a printed-on-demand copy, perhaps printed by Amazon directly, and the text is blurry throughout. The images are filled with gray splotches. I recently bought several Springer books which had the same problem, so it seems to be a trend across purchases of new math books from Amazon.I decided to return the book and pick up a 50-year-old used copy instead and there is a night-and-day quality difference. The old book has crisp text a. A glimpse of mathematics as Hilbert saw it The leading mathematician of the 20th century, David Hilbert liked to quote "an old French mathematician" saying "A mathematical theory should not be considered complete until you have made it so clear that you can explain it to the first man you meet on the street". By that standard, this book by Hilbert was the first to complete several branches of geometry: for example, plane projective geometry and projective duality, regular polyhedra in A glimpse of mathematics as Hilbert saw it Colin McLarty The leading mathematician of the 20th century, David Hilbert liked to quote "an old French mathematician" saying "A mathematical theory should not be considered complete until you have made it so clear that you can explain it to the first man you meet on the street". By that standard, this book by Hilbert was the first to complete several branches of geometry: for example, plane projective geometry and projective duality, regular polyhedra in 4 dimensions, elliptic and hyperbolic non-Euclidean geometries, topology of surfaces, curves in space, Gaussian curvature . dimensions, elliptic and hyperbolic non-Euclidean geometries, topology of surfaces, curves in space, Gaussian curvature . Beautiful, Rewarding, and Deep. Peter Renz I have some 47 books in the geometry section of my shelves. If I had to discard 40 of these, Geometry and the Imagination would be among the 7 remaining.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.