- Hardcover: 637 pages
- Publisher: W.H. Freeman & Company; 4 edition (Sep 1 2007)
- Language: English
- ISBN-10: 0716799480
- ISBN-13: 978-0716799481
- Product Dimensions: 23.6 x 16.3 x 3.6 cm
- Shipping Weight: 1.1 Kg
- Average Customer Review: 4.4 out of 5 stars See all reviews (5 customer reviews)
-
Amazon Bestsellers Rank:
#595,642 in Books (See Top 100 in Books)
- #13 in Books > Science > Mathematics > Geometry & Topology > Non-Euclidean Geometries
- #35 in Books > Science > History & Philosophy > History of Mathematics
- See Complete Table of Contents
|
||||||||||||||||||
|
||||||||||||||||||
|
||||||||||||||||||
| ||||||||||||||||||
Product Details |
Product Description
Product Description
This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.
Tag this product(What's this?)Think of a tag as a keyword or label you consider is strongly related to this product.
Tags will help all customers organize and find favorite items. |
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most helpful customer reviews
5.0 out of 5 stars
A real mind stretcher.,
By
This review is from: Euclidean & Non-Eucl Geometry 3e (Hardcover)
The first edition of this book is the one that I learned Non-Euclidean geometry from and I have always had fond memories of the course. I took it as an independent study, and chose to do all I could on my own, seeking help only when absolutely necessary. It was a time of fascination, as I was often astonished at the results and how they can be applied to the fundamental structure of the universe. The material on the geometry of physical space inspired me to go to the library searching for additional reading material.This edition is even better than the first, it has many more exercises and projects and the sections on the history of the parallel postulate have been expanded and updated. There is more than enough material for a one-semester course, although you would have to be very selective when culling material, as nearly every page is an element of an essential progression. I took geometry in high school and found it dull and uninspiring. However, with this book I found my college geometry course to be the most interesting math course that I have ever had, and that is saying a lot. It is an excellent text for learning an essential but often neglected subject. Published in the recreational mathematics e-mail newsletter, reprinted with permission.
4.0 out of 5 stars
Great introduction to a challenging topic,
By
This review is from: Euclidean & Non-Eucl Geometry 3e (Hardcover)
This is a full-fledged math text that I picked up on discount back when I was working at Bay Tree Bookstore in Santa Cruz. Yes, it's taken me over ten years to finally getting around to reading it. What finally worked for me is the realization that, since I'm not taking it for a class, I don't have to do the problems at the end of each chapter. That finally allowed me to read the book in comfort, as if I were auditing a class.This book starts with Euclid's first axioms and leads you through the whys and whos of the development of non-Euclidean geometry. First, you get a complete re-introduction to Euclidean geometry itself, which is very handy and leads you directly to later developments. The unprovability of the Parallel Postulate (Euclid's Axiom V) reminded me of the Ultraviolet Catastrophe in physics/chemistry history, and Greenberg shows the motivating effect this had on the mathematics community. Unfortunately, the problem wasn't solved in a matter of decades, as with the Catastrophe, and mathematicians poked at the Parallel Postulate as if it were a sore tooth for hundreds of years before they realized that the REALLY interesting results happened when you discarded the Postulate altogether. In fact, one of the most heartbreaking sections of the book is Greenberg's description of Girolamo Saccheri's work in the 17th century. Saccheri had discovered a type of quadrilateral that seemed able to have acute summit angles and right base angles at the same time. These are perfectly possible in what's now known as hyperbolic geometry, but the only geometry known in Saccheri's time, Euclidean geometry, made no allowances for such a strange creature. Instead of realizing what he was looking at, Saccheri abandoned this line of inquiry in disgust. "It is as if a man had discovered a rare diamond," Greenberg writes, "but, unable to believe what he saw, announced it was glass." The axioms of hyperbolic geometry are well-presented; I understood them quite well even though it's been 17 years since I took geometry. Klein's and Poincare's models of the hyperbolic plane are presented in an interesting fashion and fleshed out with several excercises and examples. I'm ashamed to say that the book started to pull away from me like an Astin Martin from a Yugo in the final two chapters. Aside from the very advanced nature of the proofs in these chapters, Greenberg's definition of ideal points is not what it could be (sets of rays?), and some of the text relies on results from previous chapters exercises. Someday I might come back to this to do the exercises as well.
5.0 out of 5 stars
A Modern Classic,
By
This review is from: Euclidean & Non-Eucl Geometry 3e (Hardcover)
By a classic I mean to warn people that it isn't very up to date in Non-Euclidean geometry, but it is the best I have been able to find on the subject. I have an even older book by by a Spanish scholar who doesn't do anywhere near as well. If you need this "jive geometry" for your understanding of physics and relativity, this is a very good place to start.
Share your thoughts with other customers: Create your own review
Want to see more reviews on this item?
|
Most recent customer reviews |
Listmania!
Look for similar items by category
Look for similar items by subject
Feedback
Would you like to update product info or give feedback on images?
|
