The Fibonacci Resonance and Other New Golden Ratio Discoveries PDF Download
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Author: Clive N Menhinick
Publisher:
ISBN: 9780993216602
Category : Mathematics
Languages : en
Pages : 638
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Book Description
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.
Author: Clive N Menhinick
Publisher:
ISBN: 9780993216602
Category : Mathematics
Languages : en
Pages : 638
Get Book Here
Book Description
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.
Author: Richard A Dunlap
Publisher: World Scientific
ISBN: 9814496944
Category : Mathematics
Languages : en
Pages : 170
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Book Description
In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.
Author: Scott Olsen
Publisher: eBook Partnership
ISBN: 1912706016
Category : Art
Languages : en
Pages : 64
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Book Description
What was the golden secret known to Leonardo da Vinci, Kepler, Plato and the ancient magicians? Can there really be a key to nature and life itself? In this small but compact volume internationally renowned divine proportion supersleuth Dr Olsen unravels perhaps the greatest mystery of all time, a code that seems to underly life, the universe and everything, a pattern we instinctively recognise as beautiful, and which nature herself uses at every scale. Designed for artists and scientists alike, this is the smallest, densest and most beautiful book on the golden section ever produced. WOODEN BOOKS are small but packed with information. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.
Author: R. A. Dunlap
Publisher:
ISBN:
Category : Fibonacci numbers
Languages : en
Pages :
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Book Description
Author: Gary B. Meisner
Publisher: Quarto Publishing Group USA
ISBN: 076036026X
Category : Mathematics
Languages : en
Pages : 227
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Book Description
This enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond. 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. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic.
Author: Krassimir T. Atanassov
Publisher: World Scientific
ISBN: 9789812381347
Category : Mathematics
Languages : en
Pages : 334
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Book Description
Discusses new ground on Fibonacci sequences and the well-known Fibonacci numbers. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.
Author: Alexey Stakhov
Publisher: World Scientific
ISBN: 9812775838
Category : Mathematics
Languages : en
Pages : 745
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Book Description
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."
Author: J. Wicherink
Publisher: Ontheemde Zielen Ontwaken
ISBN: 9081304720
Category :
Languages : en
Pages : 212
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Book Description
This book reunites science and spirituality after her roads separated 300 years ago. More and more scientists are discovering that both disciplines are only two sides of the same coin. We are on the verge of a major paradigm change in science where the immaterial subjective world of the mind can no longer be separated from the objective material world. This leap in human consciousness was already foreseen by the ancients and American indigenous people like the Maya, Hopi and Aztecs who prophesized that this transformation of consciousness would take place in our time. This book takes you on a journey from the ancient wisdom to the most modern scientific insights and demonstrates how both can be united.
Author: Leong Ying
Publisher:
ISBN: 9781983063800
Category :
Languages : en
Pages : 49
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Book Description
Euler's formula is used to derive a number theory that groups natural numbers into four distinct sets obeying twenty new arithmetic rules of addition and multiplication.All possible natural number sequences are calculated from seed values defined by the four group sets. Positive odd number bases are the roots to the Fibonacci sequence, and the only unique group function that can generate even and odd natural numbers. The remaining three groups generate only even numbers or unnatural ratios.The inter and intra ratios of the four group elements are evaluated. The inter-values determine that the Fibonacci sequence is the only function generating the full sets of natural numbers. The intra-ratio of all four groups asymptotically approaches the Golden ratio.From these deterministic evaluations of the natural number groups, it can be concluded that nature's natural tendency is to adopt the Fibonacci sequence as its preferred numbered building blocks, and that the ratio of its structures will naturally approach the Golden ratio.
Author: S. Vajda
Publisher:
ISBN:
Category : Fibonacci numbers
Languages : en
Pages : 202
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Book Description
