The Golden Ratio

Author : Gary B. Meisner
Publisher : Quarto Publishing Group USA
Page : 227 pages
File Size : 51,8 Mb
Release : 2018-10-23
Category : Mathematics
ISBN : 9780760360262

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The Golden Ratio by Gary B. Meisner Pdf

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 : Richard A Dunlap
Publisher : World Scientific
Page : 172 pages
File Size : 53,6 Mb
Release : 1997-12-16
Category : Mathematics
ISBN : 9789814496940

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The Golden Ratio And Fibonacci Numbers by Richard A Dunlap Pdf

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 : A. C. McKay,R. A. Thompson
Publisher : Wentworth Press
Page : 252 pages
File Size : 49,5 Mb
Release : 2016-08-26
Category : History
ISBN : 1362401757

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Euclid's Elements by A. C. McKay,R. A. Thompson Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Scott Olsen
Publisher : eBook Partnership
Page : 64 pages
File Size : 48,6 Mb
Release : 2018-04-01
Category : Art
ISBN : 9781912706013

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Golden Section by Scott Olsen Pdf

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 : Steve Richards
Publisher : Union Square & Company
Page : 0 pages
File Size : 40,8 Mb
Release : 2016-11
Category : Art
ISBN : 1454710225

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The Golden Ratio by Steve Richards Pdf

The elegance of mathematics meets the creativity of art in this unique coloring book. The golden ratio is the mathematical equation that describes what many consider the "divine proportion," and it's found throughout nature, as well as in art and architecture. This stunning coloring book showcases the beauty of Fibonacci's most famous formula, exploring the many ways numbers and beauty combine. Logical and creative minds alike will enjoy filling in the spirals and designs in these remarkable images.

Author : Alfred S. Posamentier,Ingmar Lehmann
Publisher : Prometheus Books
Page : 301 pages
File Size : 46,9 Mb
Release : 2011-12-20
Category : Mathematics
ISBN : 9781616144241

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The Glorious Golden Ratio by Alfred S. Posamentier,Ingmar Lehmann Pdf

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.

Author : Lieselotte Kugler,Oliver Götze
Publisher : Hirmer Verlag GmbH
Page : 232 pages
File Size : 45,5 Mb
Release : 2016
Category : Art
ISBN : UCSD:31822042171405

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Divine, Golden, Ingenious by Lieselotte Kugler,Oliver Götze Pdf

Does a mystic, divine formula lie behind everything that is beautiful? For centuries the golden mean has been a subject of endless fascination. The ratio of the proportion can be seen in Nature; it runs through artistic design processes and it affects our perception of our surroundings. But how much of this apparent 'world formula' is true, and how much of it is myth? The history of the golden mean begins with Euclid in the 3rd century BC. But it was only in the 19th century that it was raised to the universal constant of beauty. From this point onwards the 'golden section' was described in flora and fauna; the famous Fibonacci number. It determines the growth of the pineapple; and Le Corbusier optimised architecture by means of the Modulor. But does this art-historical phenomenon really play a universal role in the organisation of our world? Authors from all fields analyse the Golden Mean with regard to function, demonstrability and relevance, also by means of current examples from art and design as well as in comparison with the DIN and the tatami measurement. Exhibition: Museum für Kommunikation, Berlin, Germany (08.09.2016-28.02.2017) / Museum für Kommunikation, rankfurt, Germany (17.03.-27.08.2017). Essays by W. Beinert, A. Beutelspacher, M. Braun, W. Busch, C. Erbar, K. Fendius, J. Fingerhut, H. Fladt, O. Götze, P. Hirschmiller, H. Höge, B. Högner, M.-L. Kinne, M. Kuhn, P. Leins, M. Lauer, D. Lordick, T. Niemeyer, K. Schillinger, F. Schütz, E. Spiekermann, P. Zizka

Author : Mario Livio
Publisher : Headline Review
Page : 294 pages
File Size : 45,9 Mb
Release : 2003
Category : Algebraic fields
ISBN : 0747249881

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The Golden Ratio by Mario Livio Pdf

What do the Parthenon in Greece, crosses in graveyards, the ratio of the height of a woman's navel to a woman's height, sunflowers and Leonardo da Vinci's Mona Lisa have in common? The answer is that these disparate elements share a geometrical proportion of ancient origin commonly known as the golden ratio, or expressed numerically as phi. fractals and DNA on the way, the author takes us into the heart of this extraordinary number. He gives an account of the phi-obsessed individuals who devoted their lives to discovering its secrets - from the Pythagoreans who believed that the study of the Golden Ratio would reveal the hand of God, to the astronomer Johannes Kepler who felt that phi was the greatest treasure of geometry, to the modern day scientists who are discovering ever more remarkable ramifications of this strange, almost mystical, number.

Author : Roger Herz-Fischler
Publisher : Courier Corporation
Page : 228 pages
File Size : 47,5 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9780486152325

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A Mathematical History of the Golden Number by Roger Herz-Fischler Pdf

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 : Lucienne Roberts,Rebecca Wright,Alex Bellos
Publisher : Unknown
Page : 279 pages
File Size : 55,9 Mb
Release : 2014-02
Category : Golden section
ISBN : 0957238118

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Golden Meaning by Lucienne Roberts,Rebecca Wright,Alex Bellos Pdf

Author : David Berlinski
Publisher : Vintage
Page : 353 pages
File Size : 42,8 Mb
Release : 2011-04-27
Category : Mathematics
ISBN : 9780307789730

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A Tour of the Calculus by David Berlinski Pdf

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review

Author : Priya Hemenway
Publisher : Sterling Publishing Company Incorporated
Page : 203 pages
File Size : 42,9 Mb
Release : 2005
Category : Science
ISBN : 1402735227

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Divine Proportion by Priya Hemenway Pdf

The number Phi, simply defined, is one plus the square root of five, all divided by two. But its myriad occurrences in art, nature, and science have been a source of speculation and wonder for thousands of years. Divine Proportion draws upon both religion and science to tell the story of Phi and to explore its manifestations in such diverse places as the structure of the inner ear, the spiral of a hurricane, the majesty of the Parthenon, and the elusive perfection of the Mona Lisa. A universal key to harmony, regeneration, and balance, Phi is at the heart of a tantalizing story begun on clay tablets in ancient Babylon, and which will continue to be written for centuries to come.

Author : Alexey Stakhov
Publisher : World Scientific
Page : 745 pages
File Size : 47,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812775832

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The Mathematics of Harmony by Alexey Stakhov Pdf

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 : Adrian Bejan,J. Peder Zane
Publisher : Anchor
Page : 306 pages
File Size : 42,9 Mb
Release : 2013-01-08
Category : Science
ISBN : 9780307744340

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Design in Nature by Adrian Bejan,J. Peder Zane Pdf

In this groundbreaking book, Adrian Bejan takes the recurring patterns in nature—trees, tributaries, air passages, neural networks, and lightning bolts—and reveals how a single principle of physics, the constructal law, accounts for the evolution of these and many other designs in our world. Everything—from biological life to inanimate systems—generates shape and structure and evolves in a sequence of ever-improving designs in order to facilitate flow. River basins, cardiovascular systems, and bolts of lightning are very efficient flow systems to move a current—of water, blood, or electricity. Likewise, the more complex architecture of animals evolve to cover greater distance per unit of useful energy, or increase their flow across the land. Such designs also appear in human organizations, like the hierarchical “flowcharts” or reporting structures in corporations and political bodies. All are governed by the same principle, known as the constructal law, and configure and reconfigure themselves over time to flow more efficiently. Written in an easy style that achieves clarity without sacrificing complexity, Design in Nature is a paradigm-shifting book that will fundamentally transform our understanding of the world around us.

Author : Jane Dunn
Publisher : Random House
Page : 335 pages
File Size : 46,9 Mb
Release : 2021-08-05
Category : Cooking
ISBN : 9781473590847

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Jane’s Patisserie by Jane Dunn Pdf

The fastest selling baking book of all time, from social media sensation Jane's Patisserie 'This will be the most-loved baking book in your stash!' - Zoë Sugg 'The Mary Berry of the Instagram age' - The Times Life is what you bake it - so bake it sweet! Discover how to make life sweet with 100 delicious bakes, cakes and treats from baking blogger, Jane. Jane's recipes are loved for being easy, customisable, and packed with your favourite flavours. Covering everything from gooey cookies and celebration cakes with a dreamy drip finish, to fluffy cupcakes and creamy no-bake cheesecakes, Jane' Patisserie is easy baking for everyone. Whether you're looking for a salted caramel fix, or a spicy biscoff bake, this book has everything you need to create iconic bakes and become a star baker. Includes new and exclusive recipes requested by her followers and the most popular classics from her blog - NYC Cookies, No-Bake Biscoff Cheesecake, Salted Caramel Drip Cake and more!