Euclidean and Non-Euclidean Geometries: Development and History 4th Edition by Marvin Jay Greenberg (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I used this book in a course on geometric structures and found it to be a bit too dense for me. There is certainly a lot of material in the book and I would think it useful to keep a copy around for referencing different theorems and their proofs. However, that being said, proofs and theorems are written so closely together as to seem like one long paragraph. I also felt that, contrary to Greenberg’s opinion on the matter, there should be more diagrams in this book. Having one diagram that shows the result of a geometric proof that has 15 steps is too minimal for me.I gave this three stars mostly because the historical information in the book is quite interesting and well written. The proofs are well done (and frankly many are a bit beyond me) and for its reference value.

⭐I really enjoy this book! I’m taking a geometry course in college, and I find the theorems, projects, and proof exercises rather fun. You get to learn about the history of geometry, and more importantly, you get to try out some of the proofs on geometry itself. Great book if you want to learn on your own. Some topics might be advanced, but no worries, just study the other topics, and presto, you can come back and tackle the more advanced problems.

⭐This is the most comprehensive exposition of non-euclidean geometries, with an emphasis on hyperbolic geometry.Greenberg is didactic, clear, precise and gives here an illuminating treatment of those subjects, preceded by a very good review of both the euclidean background as well as the historical aspects.I really enjoyed reading this book and wish Greenberg would give us the same marvel on elliptic geometry, one day, even though I realize he is retired…

⭐Fascinating. The history is quite good. Very interesting.

⭐Great!!!

⭐good book

⭐I am in week 3 of a 12 week course and the pages are falling out of the binding. Not happy

⭐So my wife got this a while ago, and she got it for cheaper than what she would pay if she bought it from school. It was a good deal.

⭐O livro é um clássico muito bem escrito, porém a sua impressão é de baixa qualidade. Parece uma impressão à jato de tinta que borra se você estiver com as mãos um pouco suadas e apaga com a borracha escolar. As folhas não são costuradas ao miolo, mas sim coladas. Então o livro fica mais rígido e não para aberto sobre a mesa. Já li vários depoimentos de pessoas que compraram outros livros de Matemática e observaram o mesmo. Parece que muitos livros clássicos estão sendo reimpressos a baixo custo e vendidos a preços altíssimos. Alguns parecem até escaneados. Pelo preço que paguei esperava muito mais. É claro que devolvi o livro.

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