## A Course in Modern GeometriesA Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3-4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. 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. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "Cabri Geometry" and "Geometer's Sketchpad". Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota. |

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Side ii

Edgar: Measure, Topology, and

Edgar: Measure, Topology, and

**Fractal**Geometry. Elaydi: An Introduction to Difference Equations. Second edition. Erdös/Surányi: Topics in the Theory of ... Side vi

In addition, Computer-produced high-speed Computations and high-resolution graphics played a major role in the development of chaos theory and

In addition, Computer-produced high-speed Computations and high-resolution graphics played a major role in the development of chaos theory and

**fractal**... Side vii

... a new chapter-length treatment of

... a new chapter-length treatment of

**fractal**geometry. These additions and changes are detailed below. 1. New geometric explorations The explorations offer ... Side viii

New

New

**fractal**geometry chapter Chaos theory and**fractal**geometry are significant areas of mathematical and scientific interest with many results recently ... Side ix

Viewed from this perspective,

Viewed from this perspective,

**fractal**geometry is an extension of the geometry covered in Chapter 3. And its study provides an exciting current event ...### Hva folk mener - Skriv en omtale

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### Innhold

1 | |

NonEuclidean Geometry | 33 |

Geometric Transformations of the Euclidean Plane | 99 |

Projective Geometry | 213 |

An Introduction | 315 |

Appendices | 389 |

References | 413 |

Index | 427 |

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