$109.99

$3.99 delivery Tuesday, May 28. Details

Or fastest delivery May 21 - 24. Order within 1 hr 34 mins. Details

Select delivery location

Only 1 left in stock - order soon.

$$109.99 () Includes selected options. Includes initial monthly payment and selected options. Details

Ships from

Sun Moon & Stars

Ships from

Sun Moon & Stars

Sold by

Sun Moon & Stars

Sold by

Sun Moon & Stars

Returns

Eligible for Return, Refund or Replacement within 30 days of receipt

Returns

Eligible for Return, Refund or Replacement within 30 days of receipt

This item can be returned in its original condition for a full refund or replacement within 30 days of receipt. You may receive a partial or no refund on used, damaged or materially different returns.

Read full return policy

Payment

Secure transaction

Payment

Secure transaction

We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more

Details

$19.80

Get Fast, Free Shipping with Amazon Prime FREE Returns

Overall good condition. Wear on corner/edges. May contain markings. Ships direct from Amazon! Overall good condition. Wear on corner/edges. May contain markings. Ships direct from Amazon! See less

FREE delivery Thursday, May 30 on orders shipped by Amazon over $35

Select delivery location

Only 1 left in stock - order soon.

$$109.99 () Includes selected options. Includes initial monthly payment and selected options. Details

Access codes and supplements are not guaranteed with used items.

Enhancements you chose aren't available for this seller. Details

${cardName} not available for the seller you chose

${cardName} unavailable for quantities greater than ${maxQuantity}.

Sold by Opti Sales and Fulfilled by Amazon.

Other sellers on Amazon

New & Used (31) from $19.79 & FREE Shipping

Follow the author

Marvin J. Greenberg

+ Follow

More books from this author

Euclidean and Non-Euclidean Geometries: Development and History Third Edition

by Marvin Jay Greenberg (Author)

3.5 21 ratings

See all formats and editions

There is a newer edition of this item:

Euclidean and Non-Euclidean Geometries: Development and History
$194.99
(39)
Only 10 left in stock - order soon.

{"desktop_buybox_group_1":[{"displayPrice":"$109.99","priceAmount":109.99,"currencySymbol":"$","integerValue":"109","decimalSeparator":".","fractionalValue":"99","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"6A13lkgXTiyY3itBveY55rhWC3pD%2B%2F0XRN6MH5XFSgjcGfVhsj%2F3vmEiPidea3n6dyGkb2toNNWgh3dow6i3G2Sky7%2BVQRVd0xBEpirjRgN2oq%2BHNUPh0LHTTtjry%2BaXsw4Nrc2rBxEOyBTrTIgvvVqvOPjJrsh1ALqT%2Ff017obI73DWjDlbIg%3D%3D","locale":"en-US","buyingOptionType":"NEW","aapiBuyingOptionIndex":0}, {"displayPrice":"$19.80","priceAmount":19.80,"currencySymbol":"$","integerValue":"19","decimalSeparator":".","fractionalValue":"80","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"6A13lkgXTiyY3itBveY55rhWC3pD%2B%2F0XcgREMj4PogUNaSPO5BcbbnYbMGgHQRzBzcMo8GkhZ1s1AUfH%2Fcqpdgy9HZpjAISKht8DZTexrxBE%2BBPM0klnZck6MIuF6WG4iTt1gjibaCsSaELNbLI7%2FNQ%2F7GIIV2LJ4BXj6NtKW%2FN9%2BiUOgsRK%2Fu%2BxMYNXz%2FNI","locale":"en-US","buyingOptionType":"USED","aapiBuyingOptionIndex":1}]}

Purchase options and add-ons

This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.

Frequently bought together

$123.97

Get it as soon as Wednesday, May 29

Only 1 left in stock - order soon.

Sold by wisdom tree and ships from Amazon Fulfillment.

+

Mathematics: The Loss of Certainty (Galaxy Books)

$21.99

Get it as soon as Sunday, May 26

Only 13 left in stock - order soon.

Ships from and sold by Amazon.com.

Total price:

To see our price, add these items to your cart.

Try again!

Details

Added to Cart

One of these items ships sooner than the other.

Show details Hide details

Choose items to buy together.

Marvin Greenberg
39
Hardcover
36 offers from $43.00
Robin Hartshorne
46
Hardcover
24 offers from $19.73

Product details

Publisher ‏ : ‎ W. H. Freeman; Third edition (July 15, 1993)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 512 pages
ISBN-10 ‏ : ‎ 0716724464
ISBN-13 ‏ : ‎ 978-0716724469
Item Weight ‏ : ‎ 1.87 pounds
Dimensions ‏ : ‎ 6.4 x 1.11 x 9.3 inches

Best Sellers Rank: #1,751,277 in Books (See Top 100 in Books)
- #75 in Non-Euclidean Geometries (Books)
- #364 in Geometry
- #72,853 in Unknown

Customer Reviews:
3.5 21 ratings

Brief content visible, double tap to read full content.

Full content visible, double tap to read brief content.

Videos

Help others learn more about this product by uploading a video!

Upload your video

About the author

Follow authors to get new release updates, plus improved recommendations.

Marvin J. Greenberg

Brief content visible, double tap to read full content.

Full content visible, double tap to read brief content.

Discover more of the author’s books, see similar authors, read author blogs and more

Customer reviews

3.5 out of 5

21 global ratings

How customer reviews and ratings work

Sort reviews by

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

George C. Johnson

A wealth of knowledge of geometry

Reviewed in the United States on August 8, 2007

Verified Purchase

This text provides a wealth of knowledge about geometry. For me, with only a minimum of college level geometry previously studied, it was my first meeting with a rigorous development of any type of geometry, euclidean or noneuclidean. It was very exciting to see how this subject can be so carefully developed. Even though I was exposed to a meticulous construction of real analysis and algebra ,there is quite a difference in the techniques used to develop geometry, which you might anticipate.

Each time I have reviewed Dr.Greenberg's text, I am not only able to retain the material easier, but also to achieve a new level of understanding, which is kind of surprising.

This text is a treasure of knowledge of geometry, but the reader, if not much better prepared than me, needs to understand that digesting this text requires a bit of a committment , but it is well worth the effort. If you are a prior football player, like me, you will probably remember the coach mentioning it will take a 110% effort to win. This is a different way of indicating how tenacious, I feel, you will need to be.

I am really looking forward to reading Dr. Greenberg's most recent edition of this text, which is now available.

8 people found this helpful

Helpful

Paul Vjecsner

Another good textbook that does not recognize its pitfalls

Reviewed in the United States on November 16, 2004

Verified Purchase

It is a book that, as fashionable today, accuses Euclid of numerous flaws, while itself replete with them.

One can begin at the beginning of Euclid's Elements. He defined certain basic terms, which, it is now argued, should not be defined if to avoid "infinite regress" (p.11). Ironically, the accordingly undefined terms, and some additions to them, are said to be clarified, filling in gaps in Euclid's proofs (p.13).

"Infinite regress" is alleged because on defining terms by others, we can ask that the others be defined, and so on indefinitely. However, this is not how definition works. We speak and write volumes with barely a definition, because we already understand most of the language. If some of it is uncertain, we can clarify it with familiar words. And what we especially want to understand in discussions are key words as in the above.

Leaving terms undefined is motivated rather by wanting to arbitrarily "interpret" them for subjects like non-Euclidean geometries. This, as I noted elsewhere, commits the fallacy of equivocation. One cannot prove something by changing meanings of words involved.

As to gaps in Euclid's proofs, it is claimed he failed to supply axioms for conditions merely assumed (p.70). But it is axioms that are assumptions. In fact, they are said to (p.10) likewise avoid "infinite regress", by being accepted without proof. But the unstated conditions questioned, like betweenness (p.72), are of fundamental human knowledge gained by observation, the source of certainty even in logical principles, "not conceivable otherwise" and confirmable by diagrams. These conditions are like other words in the proofs tacitly understood, without making them explicit.

More specific to the author are other flaws. He misstates Euclid's 1st postulate, having it say that a unique (straight) line "exists" passing through any two distinct points. The uniqueness (or such as existence) is not stated in Euclid's postulate and is not an issue until Proposition 4.

Or, the author confuses his assertion (p.83) that every segment is congruent (equal) to itself (as usually part of Laws of Thought) with the 4th Common Notion, which states that things which coincide with one another are equal to one another. That Common Notion is referenced in again Proposition 4, and is about placing one shape over another whereupon they coincide and are equal in that sense.

Flaws in the book also enter elementary logic. It is e.g. stated (p.45) that "~[H > C]" ("H does not imply C") is the same as "H & ~C" ("[H and not-C] is true"). The statements are universal, and given the first one, the second can be false in particular cases. In another flaw (p.49) the Law of Excluded Middle is said to state that P implies P or not-P. What the law does state is merely that either P or not-P is true, without positing one of them.

The book contains many other flaws, not coverable within present limitations.

14 people found this helpful

Helpful

Mike

Great Book, Great Price (for older edition)

Reviewed in the United States on April 17, 2015

Verified Purchase

The sections on Hyperbolic Geometry serve as a great introduction, especially if you're (attempting) to learn this stuff on your own. The current edition's retail price is egregious! That's why I gave this older edition 5-stars - it's a great price!

6 people found this helpful

Helpful

B. McGovney

Great introduction to a challenging topic

Reviewed in the United States on April 13, 2002

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.

56 people found this helpful

Helpful