- Series: Undergraduate Texts in Mathematics
- Hardcover: 528 pages
- Publisher: Springer (September 28, 2005)
- Language: English
- ISBN-10: 0387986502
- ISBN-13: 978-0387986500
- Product Dimensions: 7 x 1.2 x 10 inches
- Shipping Weight: 2 pounds (View shipping rates and policies)
- Average Customer Review: 4.6 out of 5 stars See all reviews (14 customer reviews)
- Amazon Best Sellers Rank: #252,166 in Books (See Top 100 in Books)
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter your email address or mobile phone number.
Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
Use the Amazon App to scan ISBNs and compare prices.
Frequently Bought Together
Customers Who Bought This Item Also Bought
Browse our Teacher Supplies store, with everything teachers need to educate students and expand their learning.
More About the Author
Top Customer Reviews
Hartshorne's text overlaps mine in correcting Euclid's errors, developing rigorous foundations for Euclidean and Non-Euclidean geometries, and covering much history, presented delightfully. He gives a thorough discussion of area and the open problems in that theory. He concludes with a nice chapter on polyhedra.
Of course Harshorne proves that Euclid needed the parallel postulate, by exhibiting a non-Euclidean geometry. He gives a very pretty compass and straight-edge Euclidean theory of circles, which then turns into the Poincare plane model for hyperbolic geometry. He also proves that Euclid needed the method of exhaustion for volumes of solids: he gives the agreeably simple Dehn invariant proof that even a cube and a tetrahedron of equal volumes are not decomposable into congruent parts. It is a famous proof, rarely seen, and a beautiful use of the modern algebraic viewpoint in classical geometry. I had always supposed it must be hard but it is not.
Hartshorne also develops the contested "geometric algebra" of Euclid as a modern axiomatic algebra. Many commentators have shown it is wrong to think Euclid was doing "algebra" in the sense of a disguised theory of the roots of quadratic polynomials. But (unless and until Fowler's THE MATHEMATICS OF PLATO'S ACADEMY changes my mind) I think it is reasonable to say Euclid is doing algebra in this sense.
This is a really well written, expert, wonderfully enthusiastic book, about a great, absolutely classic topic, by a powerful world famous authority in geometry.
The organization assumes the student is reading euclid concurrently. then prof hartshorne explains the difficullties with euclids treatment and shows how to remedy them. e.g. he observes euclids proof of SAS uses a principle of superposition without stating it, then although he adopts the Hilbert option of making this an axiom, he also presents an alternative treatment in which the principle of superposition is an axiom, and SAS is then proved exactly as euclid does. this sort of thing shows very clearly that euclids proofs become correct, merely by clarifying his implicit assumptions.
i love this and think it enhances the subject enormously.
the exercises are so ambitious and far reaching I at first dismissed them as unrealistic, but soon became infected with dr hartshornes enthusiasm for putting the students in touch with their best abilities, and challenging them to reach as deeply as they can.
This book is a remarkable work of scholarship, with far more content than one course can use. The student has here a work that will repay years of study. again the price makes it a bargain compared to far inferior works at double the price.
I had read Professor Hartshorne's book Algebraic Geometry (Graduate Texts in Mathematics) before and arrived to the conclusion that this branch of mathematics is more an "algebraic" branch of mathematics than a "geometric" one. However, this book gave me the chance to see Professor Hartshorne as a geometer, not an algebrist as I had thought with the previous book. His style is excellent and conveys the geometric insight you want in a Geometry book.
Since I was told some years ago that Geometry could be Axiomatized, I had always hoped to see the structure being constructed. This book finally fulfilled my curiosity. I am indeed grateful with professor Hartshorne just for writing this book.
Most Recent Customer Reviews
I really don't have much more to say than has already been said. It's an excellent book. Not too well suited to the conformist as many proofs of known results have originality. Read morePublished 8 months ago by Paul A. Bonyak
It comes faster than I expect. No damages. I pretend buy other stuffs.Published 14 months ago by Lucas Moraes
This book is great and help me a lot. Im so thankfull for find it here.Published 15 months ago by Michele Lessa de Souza
The book begins with a quotation from Gauss that suggests the elegance of treating Geometry in the "pure spirit of geometry" i.e. without using real numbers. Read morePublished on July 15, 2009 by Daniel Álvarez
This is a great book, a mature and lively treatment of a familiar subject made new again. If I'd had a text like this as an undergraduate I'd likely still be in math. Read morePublished on October 10, 2007 by swimjay
I'm still working through this text but I should warn prospective buyers of one thing: The book's early chapters makes heavy references to Euclid's propositions in his books The... Read morePublished on September 22, 2007 by Timothy Reed
The book, like related literature, contends greater rigor in today's geometry or mathematics than in the time of Euclid. I challenge this and give some reasons why. Read morePublished on October 28, 2004 by Paul Vjecsner
This is without exception the hardest math course I have ever taken. Your understanding of the concepts is pertinent. Read morePublished on September 15, 2001 by mike rafter