Non-Euclidean Geometry (Mathematical Association of America Textbooks) 6th Edition by H. S. M. Coxeter (PDF)

Description

This is a reissue of Professor Coxeter’s classic text on non-Euclidean geometry. It begins with a historical introductory chapter, and then devotes three chapters to surveying real projective geometry, and three to elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases of a more general ‘descriptive geometry’. This is essential reading for anybody with an interest in geometry.

User’s Reviews

Editorial Reviews: Review ‘No living geometer writes more clearly and beautifully about difficult topics than world famous Professor H. S. M. Coxeter. When non-Euclidean geometry was first developed, it seemed little more than a curiosity with no relevance to the real world. Then to everyone’s amazement, it turned out to be essential to Einstein’s general theory of relativity! Coxeter’s book has remained out of print for too long. Hats off to the MAA for making this classic available once more.’ Martin Gardner’Coxeter’s geometry books are a treasure that should not be lost. I am delighted to see Non-Euclidean Geometry back in print.’ Doris Schattschneider Book Description A reissue of Professor Coxeter’s classic text on non-euclidean geometry.

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

⭐An illuminating npresentation…a classic!

⭐A classic on the subject

⭐In my own geometry text, I only mentioned results in elliptic geometry in passing, because they did not fit in to Hilbert’s axiomatic approach, which is the closest in spirit to Euclid’s.Coxeter, by contrast, takes projective geometry as his starting point. The beginning of his book is devoted to that. When the additional structure of a distinguished non-degenerate conic C (the “absolute”) is assumed, one obtains real plane hyperbolic geometry if C is real or real plane elliptic geometry if C is imaginary. Thus a very pretty unification is achieved.In three dimensions, C is taken to be a non-degenerate quadric surface. Three dimensional elliptic space has the new phenomenon of Clifford parallel lines – difficult to visualize.

⭐Masterful treatment of Non-Euclidean concepts, including a rare “tour de force”, i.e. a comprehensive and in-depth treatment of both hyperbolic and elliptic geometries.But beware, the book is difficult, highly abstract, with almost no figures and spiced with some quaternions and tensors (which may be taken in a cursory manner…).So, it’s better to absorb first Coxeter’s “The Real Projective Plane” and Greenberg’s “Euclidean & Non-Euclidean Geometries” , and only then tackle this book.This book is part of Coxeter’s geometry SUM : Introduction to Geometry, The real Projective Plane, Projective Geometry, Geometry Revisited, Non-Euclidean Geometry… to be included in the collection of anyone interested in mathematics.

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