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The Golden Ratio Phi Original Contributions New Discoveries
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Book Synopsis The Golden Ratio (Phi) – original contributions & new discoveries by : Andrei-Lucian Drăgoi
Download or read book The Golden Ratio (Phi) – original contributions & new discoveries written by Andrei-Lucian Drăgoi and published by Dr. Andrei-Lucian Drăgoi. This book was released on 2024-01-14 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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;
Book Synopsis The Golden Ratio by : Gary B. Meisner
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.
Book Synopsis The Mathematics of Harmony by : Alexey Stakhov
Download or read book The Mathematics of Harmony written by Alexey Stakhov and published by World Scientific. This book was released on 2009 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis A Mathematical History of the Golden Number by : Roger Herz-Fischler
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.
Book Synopsis Fibonacci’s Liber Abaci by : Laurence Sigler
Download or read book Fibonacci’s Liber Abaci written by Laurence Sigler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Is God a Mathematician? by : Mario Livio
Download or read book Is God a Mathematician? written by Mario Livio and published by Simon and Schuster. This book was released on 2011-02-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Book Synopsis A Mathematical History of Division in Extreme and Mean Ratio by : Roger Herz-Fischler
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:
Book Synopsis Alex's Adventures in Numberland by : Alex Bellos
Download or read book Alex's Adventures in Numberland written by Alex Bellos and published by A&C Black. This book was released on 2010-04-05 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: A tenth anniversary edition of the iconic book about the wonderful world of maths Sunday Times bestseller | Shortlisted for the BBC Samuel Johnson Prize 'Original and highly entertaining' Sunday Times 'A page turner about humanity's strange, never easy and, above all, never dull relationship with numbers' New Scientist 'Will leave you hooked on numbers' Daily Telegraph In this richly entertaining and accessible book, Alex Bellos explodes the myth that maths is best left to the geeks, and demonstrates the remarkable ways it's linked to our everyday lives. Alex explains the surprising geometry of the 50p piece, and the strategy of how best to gamble it in a casino. He shines a light on the mathematical patterns in nature, and on the peculiar predictability of random behaviour. He eats a potato crisp whose revolutionary shape was unpalatable to the ancient Greeks, and he shows the deep connections between maths, religion and philosophy. From the world's fastest mental calculators in Germany to numerologists in the US desert, from a startlingly numerate chimpanzee in Japan to venerable Hindu sages in India, these dispatches from 'Numberland' are an unlikely but exhilarating cocktail of history, reportage and mathematical proofs. The world of maths is a much friendlier and more colourful place than you might have imagined. This anniversary edition is fully revised and updated.
Book Synopsis The Divine Proportion by : H. E. Huntley
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.
Book Synopsis The Golden Ratio And Fibonacci Numbers by : Richard A Dunlap
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.
Download or read book Brilliant Blunders written by Mario Livio and published by Simon and Schuster. This book was released on 2014-05-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Drawing on the lives of five great scientists -- Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle and Albert Einstein -- scientist/author Mario Livio shows how even the greatest scientists made major mistakes and how science built on these errors to achieve breakthroughs, especially into the evolution of life and the universe"--
Download or read book Sophie's World written by Jostein Gaarder and published by Farrar, Straus and Giroux. This book was released on 2007-03-20 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: One day Sophie comes home from school to find two questions in her mail: "Who are you?" and "Where does the world come from?" Before she knows it she is enrolled in a correspondence course with a mysterious philosopher. Thus begins Jostein Gaarder's unique novel, which is not only a mystery, but also a complete and entertaining history of philosophy.
Book Synopsis Aesthetics of Interdisciplinarity: Art and Mathematics by : Kristóf Fenyvesi
Download or read book Aesthetics of Interdisciplinarity: Art and Mathematics written by Kristóf Fenyvesi and published by Birkhäuser. This book was released on 2017-11-28 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.
Book Synopsis The Golden Deer of Eurasia by : Joan Aruz
Download or read book The Golden Deer of Eurasia written by Joan Aruz and published by Metropolitan Museum of Art. This book was released on 2006 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Harmony of the World by : Johannes Kepler
Download or read book The Harmony of the World written by Johannes Kepler and published by American Philosophical Society. This book was released on 1997 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have presented and interpreted Johannes Kepler's Latin text to English readers by putting it into the kind of clear but earnest language they suppose Kepler would have used if he had been writing today.
Book Synopsis Cradle of Life by : J. William Schopf
Download or read book Cradle of Life written by J. William Schopf and published by Princeton University Press. This book was released on 2021-10-12 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the greatest mysteries in reconstructing the history of life on Earth has been the apparent absence of fossils dating back more than 550 million years. We have long known that fossils of sophisticated marine life-forms existed at the dawn of the Cambrian Period, but until recently scientists had found no traces of Precambrian fossils. The quest to find such traces began in earnest in the mid-1960s and culminated in one dramatic moment in 1993 when William Schopf identified fossilized microorganisms three and a half billion years old. This startling find opened up a vast period of time--some eighty-five percent of Earth's history--to new research and new ideas about life's beginnings. In this book, William Schopf, a pioneer of modern paleobiology, tells for the first time the exciting and fascinating story of the origins and earliest evolution of life and how that story has been unearthed. Gracefully blending his personal story of discovery with the basics needed to understand the astonishing science he describes, Schopf has produced an introduction to paleobiology for the interested reader as well as a primer for beginning students in the field. He considers such questions as how did primitive bacteria, pond scum, evolve into the complex life-forms found at the beginning of the Cambrian Period? How do scientists identify ancient microbes and what do these tiny creatures tell us about the environment of the early Earth? (And, in a related chapter, Schopf discusses his role in the controversy that swirls around recent claims of fossils in the famed meteorite from Mars.) Like all great teachers, Schopf teaches the non-specialist enough about his subject along the way that we can easily follow his descriptions of the geology, biology, and chemistry behind these discoveries. Anyone interested in the intriguing questions of the origins of life on Earth and how those origins have been discovered will find this story the best place to start.
Book Synopsis The Curves of Life by : Theodore Andrea Cook
Download or read book The Curves of Life written by Theodore Andrea Cook and published by . This book was released on 1914 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
