## 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 10

Points

Points

**incident**with the same line are said to be collinear. ... There exists at least one line with exactly n + 1 (n > 1) distinct points**incident**with it. Side 12

Theorem P.2 (Dual of Axiom P3) Given two distinct lines, there is exactly one point

Theorem P.2 (Dual of Axiom P3) Given two distinct lines, there is exactly one point

**incident**with both of them. Theorem P3 (Dual of Axiom P4) Given two ... Side 13

Theorem P3 (Dual of Axiom P4) Given two distinct points, there is at least one line

Theorem P3 (Dual of Axiom P4) Given two distinct points, there is at least one line

**incident**with both of them. Theorem P.4 (Dual of Axiom P2) There exists ... Side 14

First, to make the proof less awkward, the phrase "is

First, to make the proof less awkward, the phrase "is

**incident**with" is frequently replaced by a variety of other familiar terms such as "is on," "contains ... Side 15

Theorem P.6 In a projective plane of order n, each line is

Theorem P.6 In a projective plane of order n, each line is

**incident**with exactly n + 1 points. Using these results, we can now determine the total number of ...### 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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