The Divine Proportion PDF Download

Author: H. E. Huntley
Publisher: Courier Corporation
ISBN: 0486131874
Category : Mathematics
Languages : en
Pages : 212

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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.

Author: Gary B. Meisner
Publisher: Quarto Publishing Group USA
ISBN: 076036026X
Category : Mathematics
Languages : en
Pages : 227

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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.

Author: Priya Hemenway
Publisher: Sterling Publishing Company Incorporated
ISBN: 9781402735226
Category : Science
Languages : en
Pages : 203

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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.

Author: Norman John Wildberger
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 330

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Book Description
"... introduces a remarkable new approach to trigonometry and Euclidean geometry, with dramatic implications for mathematics teaching, industrial applications and the direction of mathematical research in geometry" -- p. vii.

Author: W.A.W. Parker
Publisher: Barbera Foundation
ISBN:
Category : Fiction
Languages : en
Pages : 214

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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.

Author: Alfred S. Posamentier
Publisher: Prometheus Books
ISBN: 1616144246
Category : Mathematics
Languages : en
Pages : 301

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Book Description
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: Steve Richards
Publisher: Union Square & Company
ISBN: 9781454710226
Category : Art
Languages : en
Pages : 0

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Book Description
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: Pauline Novak-Reich
Publisher: Pauline Reich
ISBN: 9781742984810
Category : Mathematics
Languages : en
Pages : 276

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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."

Author: Romeo D. Ty
Publisher:
ISBN: 9780985516819
Category :
Languages : en
Pages : 200

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Book Description
Architectural Details Sketchbook is about hand-sketches of details ranging from the Mediterranean to the American styles. It was purposely created to promote accuracy in creating details and to discourage the use of guesswork. Its main intent is to share creative ideas as well to architects, designers, students, and individuals alike based on its cultural heritage of style.

Author: Mario Livio
Publisher: Crown
ISBN: 0307485528
Category : Mathematics
Languages : en
Pages : 305

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Book Description
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.