The Golden Ratio PDF Download

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: Rochelle Pennington
Publisher: Pathways Press (Wi)
ISBN: 9780974081007
Category : Body, Mind & Spirit
Languages : en
Pages : 306

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Book Description
Learn how spiritual principles underlie all of life and are equations, formulas, and mathematical measures of cause and effect. By considering the observations within these pages - gathered from clergy, teachers, historical leaders, motivational speakers, newspaper columnists, best-selling authors, and therapists from around the world - you will become aware of the importance of a golden formula and discover how you can apply its wisdom to your own life in order to fill it with the blessings of love, peace, and plenty. By beginning from the inner places within your own heart, you can - and will - change your outer world and become rich in all the really matters in the end. Each of us has equal access to the choices that set these powers into motion for our good. Rochelle Pennington is a freelance author and newspaper columnist from Wisconsin whose work has been included in several best-selling series including Chicken Soup for the Soul, Don't Sweat the Small Stuff, and Stories for the Heart.

Author: Roger Herz-Fischler
Publisher: Courier Corporation
ISBN: 0486152324
Category : Mathematics
Languages : en
Pages : 228

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Book Description
This comprehensive study traces the historic development of division in extreme and mean ratio ("the golden number") from its first appearance in Euclid's Elements through the 18th century. Features numerous illustrations.

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: Laurence Sigler
Publisher: Springer Science & Business Media
ISBN: 1461300797
Category : Mathematics
Languages : en
Pages : 736

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Book Description
First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.

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: Ka-Kit Tung
Publisher: Princeton University Press
ISBN: 1400884055
Category : Mathematics
Languages : en
Pages : 319

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Book Description
Topics in Mathematical Modeling is an introductory textbook on mathematical modeling. The book teaches how simple mathematics can help formulate and solve real problems of current research interest in a wide range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. Yet the prerequisites are minimal: calculus and elementary differential equations. Among the many topics addressed are HIV; plant phyllotaxis; global warming; the World Wide Web; plant and animal vascular networks; social networks; chaos and fractals; marriage and divorce; and El Niño. Traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition are also included. Most chapters begin with the history of a problem, follow with a demonstration of how it can be modeled using various mathematical tools, and close with a discussion of its remaining unsolved aspects. Designed for a one-semester course, the book progresses from problems that can be solved with relatively simple mathematics to ones that require more sophisticated methods. The math techniques are taught as needed to solve the problem being addressed, and each chapter is designed to be largely independent to give teachers flexibility. The book, which can be used as an overview and introduction to applied mathematics, is particularly suitable for sophomore, junior, and senior students in math, science, and engineering.

Author: Doug Patt
Publisher: MIT Press
ISBN: 0262516993
Category : Architecture
Languages : en
Pages : 138

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Book Description
The basics of the profession and practice of architecture, presented in illustrated A-Z form. The word "architect" is a noun, but Doug Patt uses it as a verb—coining a term and making a point about using parts of speech and parts of buildings in new ways. Changing the function of a word, or a room, can produce surprise and meaning. In How to Architect, Patt—an architect and the creator of a series of wildly popular online videos about architecture—presents the basics of architecture in A-Z form, starting with "A is for Asymmetry" (as seen in Chartres Cathedral and Frank Gehry), detouring through "N is for Narrative," and ending with "Z is for Zeal" (a quality that successful architects tend to have, even in fiction—see The Fountainhead's architect-hero Howard Roark.) How to Architect is a book to guide you on the road to architecture. If you are just starting on that journey or thinking about becoming an architect, it is a place to begin. If you are already an architect and want to remind yourself of what drew you to the profession, it is a book of affirmation. And if you are just curious about what goes into the design and construction of buildings, this book tells you how architects think. Patt introduces each entry with a hand-drawn letter, and accompanies the text with illustrations that illuminate the concept discussed: a fallen Humpty Dumpty illustrates the perils of fragile egos; photographs of an X-Acto knife and other hand tools remind us of architecture's nondigital origins. How to Architect offers encouragement to aspiring architects but also mounts a defense of architecture as a profession—by calling out a defiant verb: architect!

Author: Rainer W. Schlegelmilch
Publisher: TeNeues
ISBN: 9783832769239
Category : Photography
Languages : en
Pages : 216

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Book Description
Few spectator sports generate such excitement as Formula 1. The name refers to the most advanced and competitive of the FIA's racing formulae. It's a raw combination of speed, skill, and that certain hint of daring. Journey back in time to the glory years of the 1960s. Marvel at the vintage cars, big-name champions and heart-stopping victories. All the big names are here: Jim Clark, Jacky Ickx, Jack Brabham--just to name a few. With Schlegelmilch's compelling photographs, this exceptional volume takes fans so close they can almost smell the burning rubber and hear the engines roar! Text in English, German, French, Spanish, and Italian AUTHOR: Rainer W. Schlegelmilch has been a motor sports photographer since 1962. His expert lens has covered all the great names in racing. His unique style captures the drama of this action-charged sport. SELLING POINTS: * An ideal gift for lovers of fine photography, fast cars and a fascinating decade * A worthy tribute to one of motor sports' most exciting eras 120 photographs

Author: Max Tegmark
Publisher: Vintage
ISBN: 0307744256
Category : Science
Languages : en
Pages : 434

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Book Description
Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.