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The Golden Ratio

Author : Gary B. Meisner

Publisher : Quarto Publishing Group USA

Page : 227 pages

File Size : 22,42 MB

Release : 2018-10-23

Category : Mathematics

ISBN : 076036026X

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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.



The Divine Proportion

Author : H. E. Huntley

Publisher : Courier Corporation

Page : 212 pages

File Size : 47,81 MB

Release : 2012-06-08

Category : Mathematics

ISBN : 0486131874

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Book Description

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.



The Divine Proportions of Luca Pacioli

Author : W.A.W. Parker

Publisher : Barbera Foundation

Page : 214 pages

File Size : 18,79 MB

Release :

Category : Fiction

ISBN :

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Book Description

Luca Pacioli stood beside the great Leonardo da Vinci and gazed at The Last Supper. He saw immediately that something was terribly wrong. An orphan from a small town in Italy, Pacioli came of age during the Renaissance seemingly destined for a life of struggle and obscurity. But Pacioli had the good fortune of meeting mentors who recognized his uncanny ability with numbers and introduced him to renowned artists and philosophers, royalty, and popes. At a time when many still used Roman numerals and colleges didn’t even teach mathematics, Pacioli was determined to share his passion and make it accessible and understandable. Apprentice to an artist, but a terrible artist himself, he became a master at calculating mathematical perspective in paintings. Tasked with teaching mathematics with no textbook, he wrote his own—followed by books on double-entry bookkeeping, chess, and the divine proportion. In this way, Luca Pacioli, “the father of accounting,” still has something to teach us—not just about mathematics—but about how we account for setbacks in our lives and how we determine what our legacy will be.



Divine Proportion

Author : Priya Hemenway

Publisher : Sterling Publishing Company Incorporated

Page : 203 pages

File Size : 19,93 MB

Release : 2005

Category : Science

ISBN : 9781402735226

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Book Description

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.



Mystifying Square, Divine Proportions - Nature's Black Box

Author : Pauline Novak-Reich

Publisher : Pauline Reich

Page : 276 pages

File Size : 12,59 MB

Release : 2014-11-01

Category : Mathematics

ISBN : 9781742984810

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Book Description

This volume traces W.D. Gann's "Time Factor" and "Law of Vibration" back to the Chaldeans of 3000 BCE Sumer whose principal aspiration was to understand the motion of time. They divided time into years, months, weeks, days, hours, minutes and seconds and devised calendars which helped them predict, and therefore survive, their two rivers' ravaging floods. Inadvertently, their findings also solved the mystery behind the ups and down of money markets. From ancient Sumer to Egypt, ancient China to the native peoples of Central and North America, civilisations unlikely to have had contact with each other built remarkably similar monuments according to geometrical proportions designed to embody cosmic knowledge that would last for all time. Each deciphered time cycles, created calendars and made long term projections of natural phenomena. The Square-of-9 is a matrix embodying nature's cosmic clock. Pauline Novak-Reich takes the reader through ancient math, sacred geometry and lore demonstrating the extraordinary achievements of people who lived in tandem with nature. Each one of these civilisations discovered Nature's "Black Box." Gann often reiterated that: "Everything in existence is based on exact proportion and perfect relationship. There is no chance in nature; because mathematical principles of the highest order lie at the foundation of all things...Vibration is fundamental: nothing is exempt from this law. It is universal, therefore applicable to every class of phenomena on the globe."



Visual Harmony

Author : SendPoints

Publisher : Gingko Press Editions

Page : 0 pages

File Size : 18,29 MB

Release : 2016-03-07

Category : Commercial art

ISBN : 9781584236191

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Book Description

Effective visual communication is not an accidental occurrence, but rather is the result of serious intention on the part of the designer to balance all aspects of the design. This is often achieved through careful application of proportion based on guiding principles that are here detailed; the golden ratio, 'divine proportion' and the Fibonacci sequence. By way of 1200 full-colour illustrations, the way in which modern design is utilising these ancient principles is explored.



A Mathematical History of the Golden Number

Author : Roger Herz-Fischler

Publisher : Courier Corporation

Page : 228 pages

File Size : 48,5 MB

Release : 2013-12-31

Category : Mathematics

ISBN : 0486152324

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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.



The Golden Ratio

Author : Gary B. Meisner

Publisher : Race Point Publishing

Page : 227 pages

File Size : 39,81 MB

Release : 2018-10-23

Category : Mathematics

ISBN : 163106486X

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Book Description

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.



The Mathematics of Harmony

Author : Alexey Stakhov

Publisher : World Scientific

Page : 745 pages

File Size : 29,75 MB

Release : 2009

Category : Mathematics

ISBN : 9812775838

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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."



The Divine Equation

Author : Amir Tuchman

Publisher : Independently Published

Page : 218 pages

File Size : 23,38 MB

Release : 2017-12-28

Category : Religion

ISBN : 9781973114161

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Book Description

A series of startling and controversial discoveries reveal a previously unknown mathematical code encrypted in the Bible. The mysterious code was known to Noah and was implemented in the design of the Ark. About 1200 years later, the same code was utilized by Moses, who built the Ark of the Covenant, the Menorah, and the Altar. After another 480 years, the code was embedded into the Temple of Solomon, the decryption of which requires yet another encoded key. A 1000 years passed and the same mysterious code has once again echoed through the parables spoken by Jesus to his disciples. Since then, however, the knowledge of the code appeared to have been completely forgotten. Intriguingly, 1500 years later, during the Renaissance, the ancient "Biblical Code" has once again reappeared, but in the form of musical frequency, and today, is a standard for tuning musical instruments. Moreover, this mystical code serves as an underlying factor or constant for the modern economy and Stock Market. Nonetheless, the roots of this puzzling mystery go even deeper, for it rests within the very fundamental properties of matter and the building blocks of life itself. The question is, "what is the ultimate source of this enigma"?