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A Course in Modern Geometries (Undergraduate Texts in Mathematics)by Judith N. Cederberg
Synopses & Reviews
Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".
This is a new edition of a highly accessible presentation on modern geometry. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. This second edition contains new material throughout, including a new chapter on chaos theory and fractal geometry. The book now includes pointers to the author's website, which contains guides for dynamic software explorations of many concepts, using both Cabri Geometry and Geometers Sketchpad.
Table of Contents
Axiomatic systems and finite geometries.- Non-Euclidean geometry.- Geometric transformations of the Euclidean plane.- Projective geometry.- Chaos to symmetry: an introduction to fractal geometry.
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