• List Price: $64.95
  • Save: $25.86 (40%)
Rented from Campus Book Rentals
To Rent, select Shipping State from options above
Due Date: Dec 21, 2014
FREE return shipping at the end of the semester. Access codes and supplements are not guaranteed with rentals.
Used: Very Good | Details
Condition: Used: Very Good
Comment: Very Good - Standard used condition book with the text inside being clean and unmarked - Exterior of the book shows moderate signs of usage
Access codes and supplements are not guaranteed with used items.
Add to Cart
Qty:1
  • List Price: $64.95
  • Save: $15.37 (24%)
Only 11 left in stock (more on the way).
Ships from and sold by Amazon.com.
Gift-wrap available.
Add to Cart
Trade in your item
Get a $17.67
Gift Card.
Have one to sell? Sell on Amazon
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See all 2 images

Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics) Hardcover – September 28, 2005

ISBN-13: 978-0387986500 ISBN-10: 0387986502

Buy New
Price: $49.58
Rent
Price: $39.09
32 New from $45.00 38 Used from $35.25
Amazon Price New from Used from
Hardcover
"Please retry"
$49.58
$45.00 $35.25

Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student



Frequently Bought Together

Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics) + Euclid's Elements
Price for both: $67.87

Buy the selected items together
  • Euclid's Elements $18.29

Customers Who Bought This Item Also Bought

NO_CONTENT_IN_FEATURE

Up to 50% Off Select Statistics Titles
For a limited time, enjoy special savings on select statistics books from Springer. Learn more

Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 528 pages
  • Publisher: Springer (September 28, 2005)
  • Language: English
  • ISBN-10: 0387986502
  • ISBN-13: 978-0387986500
  • Product Dimensions: 1.5 x 7.1 x 10 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #284,559 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

4.5 out of 5 stars
5 star
8
4 star
1
3 star
1
2 star
1
1 star
0
See all 11 customer reviews
This book finally fulfilled my curiosity.
Rodrigo Hernandez-Gutierrez
Hartshorne is a leading mathematician known for work in rather abstract geometry (see his book ALGEBRAIC GEOMETRY).
Colin McLarty
This book is a remarkable work of scholarship, with far more content than one course can use.
mathwonk

Most Helpful Customer Reviews

80 of 82 people found the following review helpful By Marvin J. Greenberg on December 3, 2000
Format: Hardcover
Hartshorne is a famous algebraist and one main contribution of this text is to show fascinating interrelations between classical geometries and modern algebra (of course the book contains lots of pure geometry as well). Example 1: Many texts show the impossibility of the classical problems of constructibility by straightedge and compass (by observing that the coordinates of any point so constructed lie in the smallest extension field of the rationals Q closed under taking square roots of positive numbers). Hartshorne's is the only text that goes further, solving the analogous problem when the straightedge is marked (real roots of cubic and quartic equations must also be allowed); Archimedes observed that any angle can be trisected with these tools. Example 2. Dehn's solution to Hilbert's Third Problem is given, whereby any two polyhedra equivalent under dissection must have equal Dehn invariants, and it shown that a tetrahedron has different invariant than a cube. Example 3. In hyperbolic geometry, Hilbert's arithmetic of ends is developed and applied. Example 4. Pejas' algebraic classification of Hilbert planes is discussed.
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.
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
32 of 32 people found the following review helpful By Colin McLarty on July 14, 2001
Format: Hardcover Verified Purchase
Hartshorne is a leading mathematician known for work in rather abstract geometry (see his book ALGEBRAIC GEOMETRY). He takes Euclid's ELEMENTS as great mathematics, no mere genial precursor, and collates it with Hilbert's FOUNDATIONS OF GEOMETRY.
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.
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
22 of 23 people found the following review helpful By mathwonk on May 22, 2007
Format: Hardcover
This book reveals the love professor Hartshorne has for geometry and euclid. I became excited about the subject just reading the introduction. The book assumes the student knows high school geometry. which unfortunately eliminates many college students, but I am going to try to use it at least for the second part of my college course.

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.
1 Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
8 of 9 people found the following review helpful By Rodrigo Hernandez-Gutierrez on April 14, 2008
Format: Hardcover Verified Purchase
So this book answers one of the questions I always had. I had never had a complete reference of the axiomatization of geometry in my hands before.

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.
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again

Customer Images

Most Recent Customer Reviews

Search

What Other Items Do Customers Buy After Viewing This Item?