The Golden Ratio: The Divine Beauty of MathematicsThe Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book. Author Gary Meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life. The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet. Whoever you are, and whatever you may know about this topic, you’ll find something new, interesting, and informative in this book, and may find yourself challenged to see, apply, and share this unique number of mathematics and science in new ways. |
Contents
Introduction | 7 |
I GOLDEN GEOMETRY | 15 |
II PHI AND FIBONACCI | 37 |
III THE DIVINE PROPORTION | 55 |
IV GOLDEN ARCHITECTURE DESIGN | 91 |
V GOLDEN LIFE | 143 |
VI A GOLDEN UNIVERSE? | 181 |
APPENDICES | 207 |
Further Discussion | 208 |
Golden Constructions | 212 |
Notes Further Reading | 216 |
Acknowledgments | 221 |
| 222 | |
| 223 | |
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Common terms and phrases
align ancient appears architect architecture artist base width beauty black holes bottom Cathedral circle composition construction Corbusier Corbusier’s create cut in extreme digits dimensions distance Divina Proportione divine proportion dodecahedron Draw edge equation Euclid example extreme and mean facial feet Fibonacci numbers Fibonacci sequence fractal geometry Giza golden cut golden proportions golden ratio golden ratio point golden ratio proportions golden rectangle Golden Section golden spiral greater segment Greek grid height human face icosahedron illustration infinite number Johannes Kepler Kepler triangle Khufu Le Corbusier length Leonardo da Vinci logarithmic spirals logo Luca Pacioli mathematician mathematics mean ratio measurements Michelangelo Modulor nature orbits Pacioli painting Parthenon pattern pentagon pentagram percent perimeter phi-based PhiMatrix Platonic solids positions Pythagoras quasicrystal RAFAEL ARAUJO reflect the golden Renaissance rule of thirds Seurat shown side square structure symmetry unique universe vertical