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A new and definitive reference for the Fibonacci numbers and the Golden Ratio. With Mondrian, Seurat, Toulouse-Lautrec, Tiwanaku, The Great Pyramid, Le Corbusier, Kepler, Penrose, quasicrystals, Pendry, green energy, and the latest light-based technologies, this maths and science book is written to be enjoyed. Explore Bohemian Paris - the capital of phi - in fresh analyses of art, architecture, and music. Lavishly illustrated, this book includes: the history of Fibonacci and Lucas numbers, spirals, sunflowers, pine cones, megaliths, and ornamental tilings. The Fibonacci Resonance discovery is revealed step by step from unique beginnings to abacus-bead visualizations. Comparisons are made with Silver Ratio Pell numbers, and a link is shown to perfect numbers and record-breaking Mersenne primes.
- Sales Rank: #4256523 in Books
- Published on: 2015-10-31
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x 1.38" w x 5.98" l, 2.24 pounds
- Binding: Hardcover
- 638 pages
From the Author
EXAMPLES ANALYSED INCLUDE
Seurat: "A Sunday Afternooon on the Island of La Grande Jatte" and "Circus Sideshow (Parade)".Toulouse-Lautrec: "Ambassadeurs, Aristide Bruant" and "Jane Avril" posters.Steinlen: "Chat Noir" poster.Mondrian: "Composition with Red, Blue, and Yellow 1930".Bartok: "MFSPC".Le Corbusier: "Villa Savoye" and "The Modulor"._________________________________________________________________________________
EMS BOOK REVIEW
"This is an encyclopedic work about the history, theory, and applications of the Golden Ratio and the Fibonacci numbers (and their companions, the Lucas numbers)."
. . . "A remarkable addition to this is the middle part of the book" �. . .
"the most original, most surprising, and most mathematical" . . .
"in which Menhinick develops a theory of Fibonacci resonance that is based on recursion formulas for Fibonacci and Lucas numbers expressing them as deviations from certain points on logarithmic spirals"
Professor Emeritus (KU Leuven) �Adhemar Bultheel---review of 'The Fibonacci Resonance' for The European Mathematical Society (EMS).
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TABLE OF CONTENTS
Preface . . . xiAcknowledgements . . . xiii
I BACKGROUNDChapter 1 Fibonacci numbers and the Golden Ratio . . . 1Chapter 2 Spirals . . . 35Chapter 3 In nature . . . 49Chapter 4 Music---Bartok . . . 61Chapter 5 Paris---capital of Phi . . . 67Chapter 6 Art---Seurat, Toulouse-Lautrec . . . 73Chapter 7 Art---Mondrian, gnomons, and megaliths . . . 89Chapter 8 Architecture---Le Corbusier . . . 123Chapter 9 Binet spirals, Debussy, and a black cat . . . 133
II LEADING TO A DISCOVERYChapter 10 Introducing Ori32 geometry . . . 159Chapter 11 The Ori32 Fibonacci circle . . . 167Chapter 12 Five Golden Powers . . . 175
III THE FIBONACCI RESONANCEChapter 13 The penny drops . . . 191Chapter 14 Proving the theorem . . . 201Chapter 15 Visualizing the effect . . . 207Chapter 16 Hearing it . . . 221Chapter 17 3D model . . . 225Chapter 18 Is it fractal? . . . 229Chapter 19 Fibonacci Resonance summary . . . 243
IV TO PELL AND BEYONDChapter 20 Generalization to Lucas Sequences . . . 251Chapter 21 Pell, Jacobsthal, and Mersenne . . . 265
V PHI IN SCIENCEChapter 22 Phi science introduction . . . 287Chapter 23 Phyllotaxis . . . 289Chapter 24 Phi in quantum mechanics . . . 297Chapter 25 Molecular Phi . . . 299Chapter 26 Penrose tiling . . . 309Chapter 27 Quasicrystals . . . 323Chapter 28 Islamic tiling . . . 343Chapter 29 Superlattices and metamaterials . . . 359Chapter 30 Quasicrystal 'onics' . . . 383
VI APPENDICESAppendix A Ori32 trigonometry . . . 401Appendix B Fibonacci hexads modulo 32 . . . 409Appendix C Continued fractions . . . 421Appendix D Powers of Phi: Golden Powers . . . 431Appendix E Binet from a generating function . . . 439Appendix F Inductive Binet, instant Binet . . . 443Appendix G Mersenne primes, Hilbert's 10th . . . 447Glossary . . . 451Symbols used . . . 459Collected formulae . . . 465References . . . 487About the author . . . 576List of Figures . . . 577Index . . . 591
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ABOUT THE AUTHOR
Clive N. Menhinick is a computer scientist, geometer, and research photographer, based in Cheshire, England. In 2005, he recognized that 'state-of-the-art' developments in DSLR camera technology---particularly the vast increase in colour resolution ('bit depth')---opened up a new frontier for research in natural science. Over a ten-year period he has conducted his own pioneering project, developing digital-photographic techniques and custom software. In his analysis he found that many results appeared to depend on a simple angle-based geometry that he named 'Ori32'. It was the study of this geometry that provided a clear path to the discovery of the Fibonacci Resonance. Clive read physics and mathematics at Liverpool University.
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