## 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 x

Chapter 4: Several

Chapter 4: Several

**exercise**sets now include pointers to web-based instructions for carrying out specific**exercises**using dynamic geometry software. Side 8

The verification that all models of this system are isomorphic follows readily once the following theorem is verified (see

The verification that all models of this system are isomorphic follows readily once the following theorem is verified (see

**Exercises**5 and 6). Side 9

**Exercises**For**Exercises**1–4, consider the following axiomatic system: Axioms for Three-Point Geometry Undefined Terms. Point, line, on. Axiom 3P.1. Side 15

It is also possible to verify the existence of a line m that contains neither P nor Q (see

It is also possible to verify the existence of a line m that contains neither P nor Q (see

**Exercise**7). By case 1, Q is on exactly n + 1 lines m1, m2, ... Side 17

**Exercises**1. Which axioms for a finite projective plane are also valid in Euclidean geometry? Which are not? 2. Prove that the axiomatic system for finite ...### 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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