Geometry

Intended as an introduction to Euclidean and non-Euclidean geometry, this book provides coverage of such topics as absolute geometry and the cut and reassemble theory of Bolyai. This second edition has been expanded to include a selection of expository exercises and 700 problems.

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"Geometry: A Metric Approach with Models", imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. Topics covered include the fundamentals of neutral (absolute) geometry; the theory of parallels; hyperbolic geometry; classical Euclidean geometry; proof of the existence of an area function; the cut and reassemble theory of Bolyai; and the classification of isometries of a neutral geometry. Over 700 problems and 250 figures are included in this revised second edition. This second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker. This textbook on geometry is intended for undergraduate students in mathematics.