## Geometry and the Visual ArtsThis survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists, scientists, architects, philosophers, and others. In addition to profiles of Vitruvius, Albrecht Durer, and Leonardo da Vinci, it includes˙a survey of projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space. |

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### Contents

Chapter | 9 |

Preface | 11 |

Vitruvius | 15 |

Albrecht Diirer | 44 |

Leonardo da Vinci | 82 |

Form in Architecture | 102 |

The Optics of Euclid | 124 |

Euclids Elements of Geometry | 140 |

Cartesian and Projective Geometry | 173 |

Curves | 196 |

Space | 256 |

287 | |

289 | |

### Common terms and phrases

absolute geometry architect architecture artist axioms axis base-circle bisect called canvas cardioid century Chapter circle centre circumference co-ordinates compasses conic sections construction cube curve deﬁned deﬁnition Desargues Theorem diameter Diirer dimensions discussion distance distinct points draw a circle ellipse envelope equal equation equilateral triangle Euclid Euclidean ﬁgure ﬁnd ﬁrst ﬁve ﬁxed circle ﬁxed point given gives golden ratio Greek hyperbola illustrations inﬁnity inscribed intersect join Le Corbusier length Leonardo da Vinci limacon marked method mirror moves nephroid non-Euclidean geometry objects obtain Optics original painting parabola parallel pass perpendicular perspective drawing plane Plate Plato Platonic solids point Q Postulate Proclus produced projective geometry proof proportions Proposition prove Pythagoras radius rectangle reﬂected reﬂexion regular pentagon Renaissance right angles says sides solids space sphere spiral square straight line subtended symmetry tangent theory tion triangle ABC vanishing line vertex vertices Vitruvius