The Fibonacci Resonance and Other New Golden Ratio Discoveries PDF Download

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: 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: 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: 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: 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: G.E. Bergum
Publisher: Springer Science & Business Media
ISBN: 9401150206
Category : Mathematics
Languages : en
Pages : 500

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Book Description
Proceedings of `The Seventh International Research Conference on Fibonacci Numbers and Their Applications', Technische Universität, Graz, Austria, July 15-19, 1996

Author: E.M. Elsheik
Publisher: iUniverse
ISBN: 1491727187
Category : Science
Languages : en
Pages : 249

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Book Description
Everything you wanted to know about physics, biology, and the world at large becomes straightforward once you understand the life-organizing principle. Author E.M. Elsheikh, a mathematician and longtime professor, examines what the principle tells us about nature and life in this academic work. He proves that the secrets of our world reside in the quantum information contained in our DNA and genome. Discover the inner workings of life, and develop a better understanding of a maximum-action principle that explains self-organization, self-replication, and self-evolution. He also explores such topics as laws that describe phylogenetic evolution and ontogenetic development; little-known facts about genetics and evolution, including why Darwinian theory facilitates a more dynamic conception of human nature; extensions of quantum theory; and new foundations of knowledge. By challenging the notions of mainstream biology and physics and questioning assumptions about life being a physical rather than a supernatural phenomenon, youll stumble upon truths that few others know. Get ready to go on a fascinating journey that challenges paradigms and leads you to the Discovery of the Life-Organizing Principle.

Author: David D. Nolte
Publisher: Oxford University Press
ISBN: 0192528505
Category : Science
Languages : en
Pages : 384

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Book Description
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Author: Denis Barabe
Publisher: World Scientific
ISBN: 9814499153
Category : Science
Languages : en
Pages : 888

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Book Description
The book deals with biological, mathematical, descriptive, causal and systemic phyllotaxis. It aims at reflecting the widest possible range of ideas and research closely related to phyllotaxis and contains 30 well illustrated chapters.The book has three parts of equal importance. The first two parts concern data collecting, pattern recognition and pattern generation to which students of phyllotaxis are well accustomed. The third part is devoted to the problem of origins of phyllotactic patterns, giving the field of phyllotaxis the universality it requires to be fully understood.Phyllotaxis-like patterns are found in places where genes are not necessarily present. Part III concerns general comparative morphology, homologies with phyllotactic patterns, and recent trends on evolution that can help to understand phyllotaxis.The distinguished researchers who accepted to participate in the production of this book, strongly contributed to the field of phyllotaxis in the past and have devoted a lot of their time to the fascinating subject coming up with most valuable findings, or are newcomers with original ideas that may be very relevant for the future of the field. The book summarizes and updates their contributions, and promotes new avenues in the treatment of phyllotaxis.This book on mathematical and biological phyllotaxis is the first collective book ever. A landmark in the history of phyllotaxis.

Author: Nafish Sarwar Islam
Publisher:
ISBN:
Category :
Languages : en
Pages : 46

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Book Description
The frequency of appearance of the Golden Ratio in nature implies its importance as a cosmological constant and sign of being fundamental characteristic of the Universe. Except than Leonardo Da Vinci's Monalisa, it appears on the sunflower seed head, flower petals, pinecones, pineapple, tree branches, shell, hurricane, tornado, ocean wave, and bird's flight patterns. It is also very prominent on human body as it appears on human face, legs, arms, fingers, shoulder, height, eye-nose-lips, and all over DNA molecules and human brain as well. It is inevitable in ancient Egyptian pyramids and many of the proportions of the Greek Parthenon. But very few of us are aware of the fact that it is part and parcel for constituting black hole's entropy equations, black hole's specific heat change equation, also it appears at Komar's Mass equation of black holes and Schwarzschild-Kottler metric - for null-geodesics with maximal radial acceleration at the turning point of orbits. But here in this book the discussion is limited to the exhibition of mathematical aptitude of Golden Ratio - the Divine Proportion, the Cosmological Constant, and the Fundamental Constant of Nature.