The Interesting Golden Ratio

Author : Gary B. Meisner
Publisher : Quarto Publishing Group USA
ISBN 13 : 076036026X
Total Pages : 227 pages
Book Rating : 4.62/5 ( download)

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Download or read book The Golden Ratio written by Gary B. Meisner and published by Quarto Publishing Group USA. This book was released on 2018-10-23 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alfred S. Posamentier
Publisher : Prometheus Books
ISBN 13 : 1616144246
Total Pages : 301 pages
Book Rating : 4.41/5 ( download)

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Download or read book The Glorious Golden Ratio written by Alfred S. Posamentier and published by Prometheus Books. This book was released on 2011-12-20 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vincent Siu
Publisher : Partridge Publishing Singapore
ISBN 13 : 1482855437
Total Pages : 158 pages
Book Rating : 4.32/5 ( download)

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Download or read book The Interesting Golden Ratio written by Vincent Siu and published by Partridge Publishing Singapore. This book was released on 2016-02-11 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard A Dunlap
Publisher : World Scientific
ISBN 13 : 9814496944
Total Pages : 172 pages
Book Rating : 4.40/5 ( download)

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Download or read book The Golden Ratio And Fibonacci Numbers written by Richard A Dunlap and published by World Scientific. This book was released on 1997-12-16 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Francis D. Hauser, Ph.d.
Publisher : CreateSpace
ISBN 13 : 9781517518776
Total Pages : 56 pages
Book Rating : 4.76/5 ( download)

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Download or read book The Golden Ratio written by Francis D. Hauser, Ph.d. and published by CreateSpace. This book was released on 2015-10-12 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Mario Livio
Publisher : Headline Review
ISBN 13 : 9780747249887
Total Pages : 294 pages
Book Rating : 4.81/5 ( download)

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Download or read book The Golden Ratio written by Mario Livio and published by Headline Review. This book was released on 2003 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Scott Olsen
Publisher : eBook Partnership
ISBN 13 : 1912706016
Total Pages : 64 pages
Book Rating : 4.13/5 ( download)

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Download or read book Golden Section written by Scott Olsen and published by eBook Partnership. This book was released on 2018-04-01 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Matthew K. Cross
Publisher : Hoshin Media
ISBN 13 : 9781939623003
Total Pages : 64 pages
Book Rating : 4.06/5 ( download)

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Download or read book The Golden Ratio & Fibonacci Sequence: Golden Keys to Your Genius, Health, Wealth & Excellence written by Matthew K. Cross and published by Hoshin Media. This book was released on 2013-04-18 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hans Walser
Publisher : American Mathematical Soc.
ISBN 13 : 1470457490
Total Pages : 142 pages
Book Rating : 4.95/5 ( download)

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Download or read book The Golden Section written by Hans Walser and published by American Mathematical Soc.. This book was released on 2020-08-03 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : H. E. Huntley
Publisher : Courier Corporation
ISBN 13 : 0486131874
Total Pages : 208 pages
Book Rating : 4.70/5 ( download)

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Download or read book The Divine Proportion written by H. E. Huntley and published by Courier Corporation. This book was released on 2012-06-08 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.