## Elementary GeometryThe geometry of two and three dimensional space has long been studied for its own sake, but its results also underlie modern developments in fields as diverse as linear algebra, quantum physics, and number theory. This text is a careful introduction to Euclidean geometry that emphasizes its connections with other subjects. Glimpses of more advanced topics in pure mathematics are balanced by a straightforward treatment of the geometry needed for mechanics and classical applied mathematics. The exposition is based on vector methods; an introductory chapter relates these methods to the more classical axiomatic approach. The text is suitable for undergraduate courses in geometry and will be useful supplementary reading for students of mechanics and mathematical methods. |

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### Contents

1 | 11 |

5 | 22 |

3 | 48 |

Euclidean geometry | 63 |

Coordinates and equations | 85 |

3 | 92 |

4 | 98 |

Plane geometry | 104 |

8 | 166 |

Area and volume | 192 |

Quadric surfaces | 223 |

Differential geometry of curves | 242 |

Differential geometry of surfaces | 266 |

Appendix A The trigonometric functions | 291 |

300 | |

303 | |

### Common terms and phrases

algebra angle axiom basis bounded calculate called centre Chapter circle complex conic consider constant contains coordinate system coordinates corresponding curvature curve defined definition denote derivative determinant differential dimensions direction distance ellipse equal equation Euclidean Example expression fact field Figure fixed follows formula four function geometry given gives idea integral intersection isometry length lies linear matrix means meet multiple Notice numbers obtained oriented origin orthogonal orthogonal matrix parallel parallelogram parameter parameterized perpendicular plane polygonal position vector possible problem Proof properties Proposition prove quadric rational region regular relative represented result root rotation rule scalar sides similar simple space sphere square straight line Suppose surface symmetric matrix tangent tangent vector theorem theory transformation triangle unit vector values write zero