A Mathematical History Of The Golden Number

Author : Roger Herz-Fischler
Publisher : Courier Corporation
ISBN 13 : 0486152324
Total Pages : 228 pages
Book Rating : 4.25/5 ( download)

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Download or read book A Mathematical History of the Golden Number written by Roger Herz-Fischler and published by Courier Corporation. This book was released on 2013-12-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Mario Livio
Publisher : Crown
ISBN 13 : 0307485528
Total Pages : 305 pages
Book Rating : 4.26/5 ( download)

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Download or read book The Golden Ratio written by Mario Livio and published by Crown. This book was released on 2008-11-12 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Roger Herz-Fischler
Publisher : Wilfrid Laurier Univ. Press
ISBN 13 : 0889201528
Total Pages : 208 pages
Book Rating : 4.21/5 ( download)

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Download or read book A Mathematical History of Division in Extreme and Mean Ratio written by Roger Herz-Fischler and published by Wilfrid Laurier Univ. Press. This book was released on 1987 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Gary B. Meisner
Publisher : Race Point Publishing
ISBN 13 : 163106486X
Total Pages : 227 pages
Book Rating : 4.69/5 ( download)

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Download or read book The Golden Ratio written by Gary B. Meisner and published by Race Point Publishing. This book was released on 2018-10-23 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 : 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 : Mario Livio
Publisher : Turtleback Books
ISBN 13 : 9781417616701
Total Pages : 304 pages
Book Rating : 4.09/5 ( download)

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Download or read book The Golden Ratio written by Mario Livio and published by Turtleback Books. This book was released on 2003-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: For use in schools and libraries only. Offers a look at phi, or "the golden ratio," discovered by Euclid more than two thousand years ago, examining the meaning of this remarkable mathematical proportion in terms of science, biology, philosophy, and other fields.

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 : Mathematical Association of America
Publisher : Cambridge University Press
ISBN 13 : 9780521531627
Total Pages : 572 pages
Book Rating : 4.24/5 ( download)

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Download or read book The Changing Shape of Geometry written by Mathematical Association of America and published by Cambridge University Press. This book was released on 2003-01-09 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of popular articles on geometry from distinguished mathematicians and educationalists.

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.