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 Poincare model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".
Publisher: Springer-Verlag New York Inc.
Number of pages: 441
Weight: 1830 g
Dimensions: 235 x 155 x 25 mm
Edition: 2nd ed. 2001. Corr. 2nd printing 2004
J. N. Cederberg
A Course in Modern Geometries
"Cederberg's book has the virtue of exceptionally clear exposition and at the same time, it is brief enough not to exhaust one's patience . . . I have seen hundreds of college-level texts on geometry and this is one of the handful I like the most."
-THE UMAP JOURNAL