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| Preface | |
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| To the Student | |
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| To the Instructor | |
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| Acknowledgments | |
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| About The Author | |
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| Music of the Spheres | |
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| Pythagoras and the Pythagoreans | |
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| Profile: Pythagoras | |
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| Ratio and Proportion | |
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| Pythagoras and the Musical Ratios | |
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| Sequences, Series, and Means | |
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| Plato and the Musical Ratios | |
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| Profile: Plato | |
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| The Musical Ratios in Architecture | |
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| Profile: Vitruvius | |
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| Profile | |
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| Profile | |
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| Summary | |
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| The Golden Ratio | |
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| The Golden Ratio | |
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| Profile: Euclid | |
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| The Fibonacci Numbers and the Golden Ratio | |
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| Profile | |
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| The Golden Ratio in Architecture | |
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| Profile | |
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| Summary | |
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| The Triangle | |
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| Angles Between Lines | |
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| Triangles | |
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| Right Triangles | |
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| Congruence, Symmetry, Isometry, and Similarity | |
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| Summary | |
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| Ad Quadratum and the Sacred Cut | |
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| The Square | |
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| The Rectangle | |
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| Other Quadrilaterals | |
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| The Rectangular Format in Painting | |
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| Profile | |
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| Profile | |
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| Architectural Proportions Based on the Square and the Rectangle | |
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| The Earthly and the Mundane | |
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| Summary | |
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| Polygons, Tilings, and Sacred Geometry | |
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| Polygons | |
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| Pentagons and Pentagrams | |
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| Profile | |
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| Other Polygons | |
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| Tilings with Polygons | |
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| Summary | |
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| The Circle | |
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| Geometry of the Circle | |
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| Radians | |
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| Lines Intersecting a Circle | |
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| The Round Format in Art | |
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| Profile: The Della Robbia Family | |
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| The Circle as a Symbol in Art | |
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| Summary | |
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| Circular Designs in Architecture | |
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| More Circle Geometry | |
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| The Circle in Gothic Architecture | |
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| Round Windows | |
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| Circular Ornamentation in Walls and Pavements | |
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| Arches and Vaults | |
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| The Vesica | |
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| Summary | |
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| Squaring the Circle | |
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| The Geometry of Squaring the Circle | |
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| Squaring the Circle in the Great Pyramid | |
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| Other Examples from Art and Architecture | |
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| Summary | |
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| The Ellipse and the Spiral | |
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| The Ellipse | |
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| Profile: Apollonius Of Perga | |
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| Graphing the Ellipse | |
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| Profile: Ren+ Descartes | |
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| The Spiral | |
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| The Spiral in Art and Architecture | |
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| Summary | |
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| The Solids | |
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| Surfaces and Solids | |
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| The Polyhedra | |
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| Cylinders and Cones | |
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| Similar Solids | |
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| The Platonic Solids | |
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| Profile: Archimedes | |
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| The Creation-by Geometry? | |
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| Polyhedra in the Renaissance | |
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| Profile: Piero Della Francesca | |
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| Profile: Luca Pacioli | |
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| Polyhedra as Art Motifs | |
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| Summary | |
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| The Sphere and Celestial Themes in Art and Architecture | |
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| The Sphere | |
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| The Dome | |
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| The Terrestrial Sphere | |
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| The Celestial Sphere | |
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| Profile: Johannes Kepler | |
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| Time | |
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| The Sphere and the Heavens as Art Motifs | |
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| Profile: Maurits Cornelius Escher | |
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| Profile: Dante Alighieri | |
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| Profile: Galileo Galilei | |
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| Summary | |
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| Brunelleschi's Peepshow and the Origins of Perspective | |
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| What Is Perspective? | |
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| A Perspective Primer | |
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| Paintings Before Perspective | |
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| Setting the Stage | |
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| Brunelleschi and Alberti | |
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| Profile | |
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| Three Renaissance Artists | |
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| Profile | |
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| Profile | |
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| Profile | |
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| Later Developments | |
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| Profile | |
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| Summary | |
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| Fractals | |
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| Dimension | |
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| Profile | |
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| Self-Similarity | |
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| How to Create a Fractal | |
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| Fractal-Related Art | |
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| Summary | |
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| Appendices | |
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| The Art-Math Tourist | |
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| Biographical Profiles | |
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| Listin | |