Euclidean and Non-Euclidean Geometries: Development and History | 
 enlarge | Author: Marvin J. Greenberg
Publisher: W. H. Freeman
Category: Book
Buy New: $68.42
New (26) Used (11) from $68.42
Rating:  17 reviews
Sales Rank: 169270
Media: Hardcover
Edition: 4th
Pages: 637
Number Of Items: 1
Shipping Weight (lbs): 2.4
Dimensions (in): 9.3 x 6 x 1.5
ISBN: 0716799480
Dewey Decimal Number: 516
EAN: 9780716799481
ASIN: 0716799480
Publication Date: September 28, 2007
Availability: Usually ships in 1-2 business days
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Condition: Brand New Hardcover US 4th Edition Free tracking Ref.172
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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.
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| Customer Reviews: Read 12 more reviews...
 an excellent and really untertaining book April 27, 2008
Eric Foucault (Blois, France)
There are already 16 reviews of this excellent and exciting book so i will only add that some people complained about the great number of results of the core text the reader is asked to search proofs as exercises. For a mathematically inclined reader this is not such a big trouble because most of these exercises have extended indications which math-inclined people can easily transform in a complete and sound proof. For myself i had almost no trouble with them.
So the difficulty is only for people who did not have a mathematical training as college junior. Even in this case they can learn a lot about the nature and purpose of pure mathematics and, if they are persistent and enduring, how to read and write mathematical proofs.
As a Frenchman i wonder why such a good book has not been translated in French, it really deserves it because books in French on geometry are so often unexciting and boring.
Quintessential Work on Non-Euclidean Geometry April 26, 2008
Robert Curtis (Cambridge, MA)
3 out of 3 found this review helpful
I had the pleasure of reading and studying the Second Edition of this text while in college. This course with this text was my favorite course during all of my undergraduate math courses.
Being a fan of the subject, I was eager to see the new Fourth Edition of the text. The Fourth Edition is quite expanded from earlier editions, going past the wonderful main story of the Parallel Postulate - told better by Greenberg than any other author, IMHO - and diving into the different non-Euclidean geometries that "open one's eyes" by setting aside the "obvious axiom of a unique parallel". The last chapters are greatly enhanced, with a superb presentation of the issue of straightedge and compass constructions in the Hyperbolic plane.
This presentation of Non-Euclidean geometry is more serious than the "popularized" books on advanced mathematical topics. If you're looking for a "light, fun" reading of this topic, this is not the book for you.
I feel that the real power of the story of the maturing of intellectual thought, so brilliantly portrayed in the story of the Parallel Postulate, must be experienced, through the effort (and often hard work) of actually **doing** geometry, rather than just reading lightly about it. If you want to dive in and actual experience geometry (and the consequent rewards), then this is the book for you. The explanations are magnificent, the problems are wonderful (and, at times, very challenging), all culminating in the "wow!" of modifying the Euclidean way of thinking to a new and beautiful alternate geometrical universe.
As other reviewers have noted, this text reads like a great novel - a drama involving geometry. If PBS/Nova ever make a "What does Parallel mean anyway?" show, this text will be the basis for that show.
I believe this Fourth Edition can be considered the quintessential text on this topic, on which all future discussion of the topics can be based, including both the introductory materials, as well as moving to the forefront of research on many topics in Hyperbolic geometry.
For a university course, weaker students will find this text quite challenging, and possibly too hard. For average students, this text will provide sufficient challenge and interest, and ample areas in the text that will not overwhelm. For advanced students, this text will certainly challenge in many different directions and interests, both in the later chapter discussions, and various problems throughout.
Greenberg's writing is meticulous - you will never find an error, a comma out of place, nor a sentence that is not perfect.
Euclidean and Non-Euclidean Geometries, Fourth Edition, by Marvin Jay Greenberg April 21, 2008
Philip Ehrlich
The Fourth Edition of M.J. Greenberg's textbook is a wonderful addition to the geometry textbook literature. No praise could be higher than to say that it is even better--indeed, a good deal better--than the highly regarded earlier editions. There are important revisions to each of the chapters and appendices, some of them extensive. As Greenberg aptly notes: "this book is a resource for a wide variety of students, from the naive to the sophisticated, from the non-mathematical-but-educated to the mathematical wizards." In this reviewer's opinion, Greenberg's fourth edition along with the Robin Hartshorne's mathematically more technical Geometry: Euclid and Beyond (2000)--a text to which Greenberg repeatedly makes reference--are far and away the most informed, up-to-date, and historically and philosophically sensitive geometry texts on the market today. No one with an interest in the foundations of geometry can afford to be without copies of these two great works.
 A very good book about Geometry April 8, 2008
Pablo Fernandez Sopuerta (Barcelona, Barcelona Spain)
1 out of 1 found this review helpful
This is a very good book about Euclidean and Non-Euclidean Geometries.
Well written, this book introduces to the lector in the historical context of the development of the Geometry.
I enjoyed very much.
Why is it so cheap, now (April, 2008) ? Because, this is the 3rd edition and exists a new 4th edition since September 28, 2007.
A Real Classic March 17, 2008
Steven G. Krantz
4 out of 4 found this review helpful
This is the fourth edition of a particularly fine text
by Marvin Jay Greenberg. If you want to learn about
Euclidean and non-Euclidean geometries---the great contributions
of Bolyai and Lobachevsky---this is the place to do it. The
book is authoritative but warm and inviting. It is full of
good history and full of good mathematics.
The fourth edition has a good deal of new material. Greenberg
explores some of the subtle logical issues, and also some
of the tricky points of geometry. He makes far-ranging
commentary on how non-Euclidean geometry fits into the modern
flow of mathematical thought. There is even some discussion
of Perelman's proof of the Poincare conjecture.
Even a reader without a strong mathematical background will get
a good deal from dipping into this book. It gives a great
sense of what the mathematical enterprise is all about, written
by a distinguished mathematician (who was also my teacher many
years ago). I consider this work to be one of the treasures on
my bookshelf.
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