## 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

Daepp/Gorkin: Reading, Writing, and

Daepp/Gorkin: Reading, Writing, and

**Proving**: A Closer Look at Mathematics. Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory. Second edition. Side vi

(Results suggested by inductive approaches should be

(Results suggested by inductive approaches should be

**proved**.) • Recent developments in geometry should be included. • A wide variety of computer ... Side 3

Furthermore, it is impossible to

Furthermore, it is impossible to

**prove**all statements constructed from the ... From the axioms, other statements can be deduced or**proved**using the rules of ... Side 4

... cannot ascertain whether or not lines exist until theorems verifying this are

... cannot ascertain whether or not lines exist until theorems verifying this are

**proved**, since there is no axiom that explicitly insures their existence. Side 6

Definition 1.2 An axiom in an axiomatic system is independent if it cannot be

Definition 1.2 An axiom in an axiomatic system is independent if it cannot be

**proved**from the other axioms. If each axiom of a system is independent, ...### 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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