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Sinopsis
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".
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Críticas
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
Reseña del editor
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".
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- EditorialSpringer
- Año de publicación2004
- ISBN 10 0387989722
- ISBN 13 9780387989723
- EncuadernaciónTapa dura
- IdiomaInglés
- Número de edición2
- Número de páginas468
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