The Golden Ratio
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The Golden Ratio
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Author : Gary B. Meisner
language : en
Publisher: Race Point Publishing
Release Date : 2018-10-23
The Golden Ratio written by Gary B. Meisner and has been published by Race Point Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-23 with Mathematics categories.
The 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.
The Golden Ratio And Fibonacci Numbers
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Author : Richard A Dunlap
language : en
Publisher: World Scientific
Release Date : 1997-12-16
The Golden Ratio And Fibonacci Numbers written by Richard A Dunlap and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-16 with Mathematics categories.
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.
The Golden Section
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Author : Hans Walser
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-03
The Golden Section written by Hans Walser and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-03 with Mathematics categories.
The Golden Ratio
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Author : Mario Livio
language : en
Publisher: Crown
Release Date : 2008-11-12
The Golden Ratio written by Mario Livio and has been published by Crown this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-12 with Mathematics categories.
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 Fibonacci Sequence Golden Keys To Your Genius Health Wealth Excellence
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Author : Matthew K. Cross
language : en
Publisher: Hoshin Media
Release Date : 2013-04-18
The Golden Ratio Fibonacci Sequence Golden Keys To Your Genius Health Wealth Excellence written by Matthew K. Cross and has been published by Hoshin Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Self-Help categories.
It's been called the Secret of the Universe, a Most Precious Jewel, Nature's Path of Least Resistance and Maximum Performance and The Golden Key to the Cosmos. It is the Grand Pattern of Life, Growth and Success. It has fascinated and appears in the works of the world's greatest geniuses, including Leonardo Da Vinci, Albert Einstein, Walt Disney and Steve Jobs. Now, the open secret of the Golden Ratio and Fibonacci Sequence is revealed for your enjoyment and application. In this book you'll journey through Golden Ratio appearances and applications throughout Nature and the Universe and in all fields of human existence and endeavor, including: art, architecture, astronomy, beauty, business, culture, design, finance, health and longevity, geometry, mathematics, medicine, relationships, science and spirituality. This book presents a delightful cornucopia of Golden Ratio facts and facets, offering a bright window into its universality and power. The information presented is laser-like, with the ability to activate your unique genius and transform your consciousness. Universal wisdom will be at your fingertips once your Golden Doors of Perception are opened to the sacred design code of the Universe: The Golden Ratio & Fibonacci Sequence.
The Golden Ratio And Fibonacci Numbers
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Author : R. A. Dunlap
language : en
Publisher: World Scientific
Release Date : 1997
The Golden Ratio And Fibonacci Numbers written by R. A. Dunlap and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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. Contents: Basic Properties of the Golden Ratio; Geometric Problems in Two Dimensions; Geometric Problems in Three Dimensions; Fibonacci Numbers; Lucas Numbers and Generalized Fibonacci Numbers; Continued Fractions and Rational Approximants; Generalized Fibonacci Representation Theorems; Optimal Spacing and Search Algorithms; Commensurate and Incommensurate Projections; Penrose Tilings; Quasicrystallography; Biological Applications; Construction of the Regular Pentagon; The First 100 Fibonacci and Lucas Numbers; Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers. Readership: Applied mathematicians.
The Glorious Golden Ratio
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Author : Alfred S. Posamentier
language : en
Publisher: Prometheus Books
Release Date : 2011-12-20
The Glorious Golden Ratio written by Alfred S. Posamentier and has been published by Prometheus Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-20 with Mathematics categories.
What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.
The Golden Ratio
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Author : Francis D. Hauser, Ph.d.
language : en
Publisher: CreateSpace
Release Date : 2015-10-12
The Golden Ratio written by Francis D. Hauser, Ph.d. and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with categories.
Euclid's masterpiece textbook, The Elements, was written twenty-three hundred years ago. It is primarily about geometry and contains dozens of figures. Five of these are constructed using a line that "is cut in extreme and mean ratio." Today this is called the golden ratio and is often referred to by the symbol Φ. Many myths have grown up around this ratio. This book was written to learn about them. They arise from the pyramids, the Pythagorean Brotherhood, the platonic solids, the Fibonacci numbers, sea shells, and others. There is a common thread among these myths. Φ is an irrational number (a number whose digits after the decimal point go on forever and never form a repeating pattern). Φ can be used to draw pleasing figures. But its numerical value cannot be written down using integers and fractions, which were the only numbers used in Euclid's time. Mathematicians before Euclid knew that irrational numbers existed. But to many people, a number that can't be written down was absurd. For centuries, many scientists and engineers believed that Φ was godlike. This book discusses the myths from an engineering viewpoint. The last chapter of the book shows how Euclid handled irrational numbers; how Euclid did algebra using geometry; and a simple visual proof of why there are only five platonic solids.
The Golden Ratio Phi Original Contributions New Discoveries
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Author : Andrei-Lucian Drăgoi
language : en
Publisher: Dr. Andrei-Lucian Drăgoi
Release Date : 2024-01-14
The Golden Ratio Phi Original Contributions New Discoveries written by Andrei-Lucian Drăgoi and has been published by Dr. Andrei-Lucian Drăgoi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-14 with Education categories.
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 Interesting Golden Ratio
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Author : Vincent Siu
language : en
Publisher: Partridge Publishing Singapore
Release Date : 2016-02-11
The Interesting Golden Ratio written by Vincent Siu and has been published by Partridge Publishing Singapore this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Mathematics categories.
This book uses simple geometry, trigonometry and algebra to explain how to construct and calculate the golden ratio. Starting from Euclids propositions in The Elements, the golden ratio and its related geometry such as the pentagon, pentagram and Vesica Piscis are constructed and determined graphically. Then the value of the ratio is solved by quadratic equations, and depending on the initial assumptions, two values are found. It is proposed that the ratio can be obtained easily by applying the Pythagoras theorem. Common terms like golden triangle, golden rhombus, golden spiral and golden angle are deduced and explained. The connections between the golden ratio and Fibonacci numbers, continued fractions, fractals, chaos and tiling are also introduced. The conclusion is that it is mathematics and not the golden ratio that is fascinating.