## 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 xiii

The

The

**relation**between Euclidean and non-Euclidean geometries became apparent with the development of projective geometry—a geometry with origins in artists' ... Side xv

... the

... the

**relationships**between mathematics and other liberal arts disciplines. ... to encourage student reading that further explores these**relationships**, ... Side 4

If the model is obtained by using interpretations that are objects and

If the model is obtained by using interpretations that are objects and

**relations**adapted from the real world, we say we have established absolute ... Side 8

... if there exists a one-to-one correspondence p from the set of points and lines of a onto the set of points and lines of 6 that preserves all

... if there exists a one-to-one correspondence p from the set of points and lines of a onto the set of points and lines of 6 that preserves all

**relations**. Side 25

This

This

**relation**involves points that do not lie on a line. Since the term "geometry" is usually reserved for structures in which each pair of points ...### 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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