A Course in Modern Geometries - Rilegato

Cederberg, Judith

Rilegato

ISBN 10: 0387989722 ISBN 13: 9780387989723

Casa editrice: Springer, 2004

Riassunto

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".

Su questo libro

Recensione

Second Edition

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

Contenuti

1 Axiomatic Systems and Finite Geometries.- 2 Non-Euclidean Geometry.- 3 Geometric Transformations of the Euclidean Plane.- 4 Projective Geometry.- 5 Chaos to Symmetry: An Introduction to Fractal Geometry.- Appendices.- B Hilbert’s Axioms for Plane Geometry.- C Birkhoff’s Postulates for Euclidean Plane Geometry.- D The SMSG Postulates for Euclidean Geometry.- E Some SMSG Definitions for Euclidean Geometry.- F The ASA Theorem.- References.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 0387989722
• ISBN 13: 9780387989723
• Rilegatura: Copertina rigida
• Numero di pagine: 468
• Contatto del produttore: non disponibile
• Persona responsabile: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania