## 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 xiv

Also, since algebraic techniques are frequently used, this study

Also, since algebraic techniques are frequently used, this study

**demonstrates**the interaction of several areas of mathematics and serves to develop ... Side xv

... Chapter 4 offers an introduction to projective geometry and

... Chapter 4 offers an introduction to projective geometry and

**demonstrates**that this geometry provides a general framework within which the geometries of ... Side 1

... were developed in the late nineteenth century, in part to

... were developed in the late nineteenth century, in part to

**demonstrate**and test the axiomatic properties of Completeness, consistency, and independence. Side 4

In this second case, we say we have

In this second case, we say we have

**demonstrated**relative consistency of the first axiomatic system. Because of the number of elements in many axiomatic ... Side 6

A with a negation of A. Thus, to

A with a negation of A. Thus, to

**demonstrate**that a system consisting of n axioms ... for four-point geometry is**demonstrated**by the following three models, ...### 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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