Geometry: A Comprehensive Course (Dover Books on Mathematics)
by Dan Pedoe
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Book Summary Information
Author: Dan PedoeEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1988-12-01
ISBN: 0486658120
Number of pages: 464
Publisher: Dover Publications
Book Reviews of Geometry: A Comprehensive Course (Dover Books on Mathematics)
Book Review: Clarity and Simplicity
Summary: 5 Stars
This text - comprised of detailed accounts of Euclidean, Affine, and Projective geometries, a thorough discussion of the Poincare model of hyperbolic geometry, and a motivating chapter on Algebraic geometry - is remarkable for its clarity and simplicity. Very little is initially expected of the reader - a sound knowledege of linear algebra, complex arithmetic and trigonometry - and the proof style is not too formal. Considering the level of detail of its treatment (it's a little more than twice the length of Coxeter's Geometry Revisited, which shares a similar selection of topics) it is ideal for undergraduates or those looking for a good, inexpensive text for self study.
Throughout the text the author emphasizes the use of basic algebraic techniques as an aid to finding clear and simple proofs. In more than one case a result is proved several times, each proof illustrating a different technique. In the first chapter, the utility of the vector approach is highlighted by using vector arithmetic, inner-products and exterior algebra to prove several classic theorems of plane geometry. In later chapters elementary group theory, Moebius transformations and linear algebra are used extensively in the discussions of the mappings of the Euclidean plane, of the mappings of the inversive plane, and of projective geometry respectively.
Basically, this is a good, detailed undergraduate introduction to geometry. It's perhaps a little less entertaining than Coxeter's introductory geometry books but it has a much friendlier price-tag.
Summary of Geometry: A Comprehensive Course (Dover Books on Mathematics)
Lucid, well-written introduction to elementary geometry usually included in undergraduate and first-year graduate courses in mathematics. Topics include vector algebra in the plane, circles and coaxial systems, mappings of the Euclidean plane, similitudes, isometries, mappings of the intensive plane, much more. Includes over 500 exercises.
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