## 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 vii

... Visual Geometry Project at Swarthmore College, and the Park City Regional Geometry Institute (now

... Visual Geometry Project at Swarthmore College, and the Park City Regional Geometry Institute (now

**known**as the IAS/Park City Math Institute) in Utah. Side 3

The statements that are accepted without proof are

The statements that are accepted without proof are

**known**as axioms. From the axioms, other statements can be deduced or proved using the rules of inference ... Side 5

These observations suggest that the construction of any model for four-point geometry must begin with the objects

These observations suggest that the construction of any model for four-point geometry must begin with the objects

**known**to exist, that is, four points. Side 10

this section we will consider an axiomatic system for an important collection offinite geometries

this section we will consider an axiomatic system for an important collection offinite geometries

**known**as finite projective planes. Side 18

An Application to Error-Correcting Codes The finite projective plane of order 2 illustrated in models P1 and P2 of the previous section is

An Application to Error-Correcting Codes The finite projective plane of order 2 illustrated in models P1 and P2 of the previous section is

**known**as a Fano ...### 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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