-PDF Download- The Fibonacci Resonance And Other New Golden Ratio Discoveries EBOOK

The Fibonacci Resonance and Other New Golden Ratio Discoveries

Author: Clive N Menhinick

Publisher:

Published: 2015-05

Total Pages: 638

ISBN-13: 9780993216602

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.

The Golden Ratio

Author: Mario Livio

Publisher: Crown

Published: 2008-11-12

Total Pages: 305

ISBN-13: 0307485528

DOWNLOAD EBOOK →

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

The Golden Ratio (Phi) – original contributions & new discoveries

Author: Andrei-Lucian Drăgoi

Publisher: Dr. Andrei-Lucian Drăgoi

Published: 2024-01-14

Total Pages: 32

ISBN-13:

DOWNLOAD EBOOK →

The Golden Ratio (PHI) (aka “golden mean”, “golden section” or “divine section”: standardly denoted with the capital Greek letter PHI) is the only positive (irrational) quadratic solution of the (minimal polynomial) equation x^2-x-1=0, so that PHI=[sqrt(5)+1]/2. The purpose of this paper is to demonstrate some aspects recently discovered by the author of this paper: (1) a recursive geometrical method for constructing PHI (inspired by the Taoist religious iconography) which is more simple and elegant than Odom’s method; (2) an occurrence of PHI in the water molecule geometry; (3) a quasi-Pythagorean property of the (PHI, e, PI) triad; (4) some other interesting quasi-exact relations between the elements of the (PHI, e, PI) triad; (5) the tendency of the human systolic/diastolic blood pressure different (combinational) ratios to stabilize (with age) to values close to PHI;

The Golden Ratio

Author: Gary B. Meisner

Publisher: Quarto Publishing Group USA

Published: 2018-10-23

Total Pages: 227

ISBN-13: 076036026X

DOWNLOAD EBOOK →

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.

The Golden Ratio And Fibonacci Numbers

Author: Richard A Dunlap

Publisher: World Scientific

Published: 1997-12-16

Total Pages: 172

ISBN-13: 9814496944

DOWNLOAD EBOOK →

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.

Golden Section

Author: Scott Olsen

Publisher: eBook Partnership

Published: 2018-04-01

Total Pages: 64

ISBN-13: 1912706016

DOWNLOAD EBOOK →

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.

Applications of Fibonacci Numbers

Author: G.E. Bergum

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 500

ISBN-13: 9401150206

DOWNLOAD EBOOK →

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

Discovery of the Life-Organizing Principle

Author: E. M. Elsheik

Publisher: iUniverse

Published: 2014-03

Total Pages: 251

ISBN-13: 1491727179

DOWNLOAD EBOOK →

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, you'll 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.

The Golden Section

Author: Scott Olsen

Publisher: Bloomsbury Publishing USA

Published: 2006-10-17

Total Pages: 68

ISBN-13: 0802715397

DOWNLOAD EBOOK →

Tells the story of the golden section, a line segment divided into two parts such that the ratio of the short portion to the longer portion is equal to the ratio of the longer portion to the whole, and its impact on civilization and the natural world.

The Golden Ratio and Fibonacci Numbers

Author: R. A. Dunlap

Publisher:

Published: 1997

Total Pages:

ISBN-13:

DOWNLOAD EBOOK →