## 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 xiii

It is no surprise that Mary Kantowski, in an article entitled "Impact of Computing on Geometry," has

It is no surprise that Mary Kantowski, in an article entitled "Impact of Computing on Geometry," has

**called**geometry "the most troubled and controversial ... Side xiv

... more general transformations

... more general transformations

**called**affinities. By using an axiomatic approach and generalizing the transformations of Xiv Preface to the First Edition. Side 2

Deductive reasoning takes place in the context of an organized logical structure

Deductive reasoning takes place in the context of an organized logical structure

**called**an axiomatic (or deductive) system. Such a system consists of the ... Side 3

... can be deduced or proved using the rules of inference of a system of logic (usually Aristotelian). These latter statements are

... can be deduced or proved using the rules of inference of a system of logic (usually Aristotelian). These latter statements are

**called**theorems. Side 10

Any set of points and lines satisfying these axioms is

Any set of points and lines satisfying these axioms is

**called**a projective plane of order n. Note that the word "incident" has been used in place of the ...### 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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