This text offers a vivid modern development of classical and non-Euclidean geometries. Intended for a first course that is concerned with firm foundations, the book presents abstract systems in an accessible style by means of models that are carefully integrated with the theory, enabling the reader to picture the ideas more clearly.

Klappentext

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. The 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.

Inhalt
Contents : Preliminary Notions.- Incidence and Metric Geometry.- Betweenness and Elementary Figures.- Plane Separation.- Angle Measure.- Neutral Geometry.- The Theory of Parallels.- Hyperbolic Geometry.- Euclidean Geometry.- Area.- The Theory of Isometries.- Bibliography.- Index.