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# Geometry from Euclid to Knots

This text covers topics appropriate for a geometry course geared to prospective teachers. It does so rather well. The treatment is axiomatic, although informality is sometimes used (and acknowledged). Stahl presents neutral geometry and shows how it gives rise to both Euclidean geometry and hyperbolic geometry. This is done in the context of presenting and discussing Euclid. In fact, Euclid is Stahl’s starting point.

The topics covered also include spherical geometry, perspective geometry, and some informal topology. Many exercises are provided. The low price of the paperback edition will help students who can ill afford high-priced texts.

A question occurred to me as I read the book: Is Euclid coming back into favour?

Dennis Lomas has studied computer science, mathematics, and philosophy.

Preface to the Dover Edition |

Preface |

1. Other Geometries: A Computational Introduction |

2. The Neutral Geometry of the Triangle |

3. Nonneutral Euclidean Geometry |

4. Circles and Regular Polygons |

5. Toward Projective Geometry |

6. Planar Symmetries |

7. Inversions |

8. Symmetry in Space |

9. Informal Topology |

10. Graphs |

11. Surfaces |

12. Knots and Links |

Appendix A: A Brief Introduction to the Geometer's Sketchpad |

Appendix B: Summary of Propositions |

Appendix C: George D. Birkhoff's Axiomatization of Euclidean Geometry |

Appendix D: The University of Chicago School Mathematics Project's Geometrical Axioms |

Appendix E: David Hilbert's Axiomization of Euclidean Geometry |

Appendix F: Permutations |

AppendixG: Modular Arithmetic |

Solutions and Hints to Selected Problems |

Bibliography |

Index |

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