## 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

Topological Spaces: From

Topological Spaces: From

**Distance**to Neighborhood. Callahan: The Geometry of Spacetime: An Introduction to Special and General Relavitity. Side 21

**Distance**in this space is defined in terms of a function known as the Hamming**distance**. Definition The Hamming**distance**d(x, y) between two binary n-tuples ... Side 22

Definition The Hamming

Definition The Hamming

**distance**d(x, y) between two binary n-tuples x and y is the number of components by which the n-tuples differ. Side 23

These same binary 3-tuples are located at a

These same binary 3-tuples are located at a

**distance**2 from the other code word, 111. The vertex 111 is the center of a second 1-sphere consisting of all ... Side 24

Verify that any pair of coordinate vectors in the incidence table (Table 1.1) differ in exactly four components, that is, their Hamming

Verify that any pair of coordinate vectors in the incidence table (Table 1.1) differ in exactly four components, that is, their Hamming

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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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