## 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 v

As a result, the

As a result, the

**geometric**content of several NSF school curriculum projects includes coverage of transformations and symmetry (for example, ... Side vi

Furthermore, they require that university-level mathematics curricula include appropriate

Furthermore, they require that university-level mathematics curricula include appropriate

**geometric**education for future teachers of secondary mathematics. Side vii

Renewed interest in

Renewed interest in

**geometry**by mathematicians and scientists led NSF to fund several other**geometry**-related projects. These included the**Geometry**Center (a ... Side viii

**Geometric**Explorations Title Location Exploring Dynamic**Geometry**Software (DGS) Web Exploring the Hyperbolic Plane with DGS Web Exploring the Double ... Side ix

Viewed from this perspective, fractal

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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