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Course in Modern Geometries

Course in Modern Geometries - 2nd edition

Course in Modern Geometries - 2nd edition

ISBN13: 9781441931931

ISBN10: 1441931937

Course in Modern Geometries by Judith N. Cederberg - ISBN 9781441931931
Edition: 2ND 10
Copyright: 2010
Publisher: Springer-Verlag New York
Published: 2010
International: No
Course in Modern Geometries by Judith N. Cederberg - ISBN 9781441931931

ISBN13: 9781441931931

ISBN10: 1441931937

Edition: 2ND 10

Summary

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 Poincar model, isometries, projectivities, conics and fractals. Parallel versions are available for ''Cabri Geometry'' and ''Geometers Sketchpad''.