The Golden Section

Nature's Greatest Secret

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Author: Scott Olson

Publisher: Bloomsbury Publishing USA

ISBN: 0802715397

Category: Mathematics

Page: 58

View: 6354

Tells the story of the golden section, a line segment divided into two parts such that the ratio of the short portion to the longer portion is equal to the ratio of the longer portion to the whole, and its impact on civilization and the natural world.

The Golden Section

Nature's Greatest Secret

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Author: Scott Olsen

Publisher: Wooden

ISBN: 9781904263470

Category: Golden section

Page: 58

View: 6696

The Golden Section

Nature's Greatest Secret

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Author: Scott Olsen

Publisher: Wooden Books

ISBN: 1912706016

Category: Art

Page: 64

View: 5246

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. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Platonic & Archimedean Solids

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Author: Daud Sutton

Publisher: Bloomsbury Publishing USA

ISBN: 0802713866

Category: Mathematics

Page: 58

View: 8172

Looks at the relationship between the five Platonic and thirteen Archimedean solids.

Symmetry

The Ordering Principle

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Author: David Wade

Publisher: Wooden Books

ISBN: 1912706040

Category: Art

Page: 64

View: 1047

Why on earth do cars have the same symmetry as dragonflies? Is there really a beautiful swirling pattern lurking in every dripping tap? What do insect eggs have in common with planets, and why? In this exquisite book, the smallest and most concise ever produced, designer David Wade introduces the main principles of symmetry, and shows how, despite opinions over exactly what it is, symmetry can be found in almost every corner of science, nature and human culture. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Sacred Geometry

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Author: Miranda Lundy

Publisher: Bloomsbury Publishing USA

ISBN: 0802713823

Category: Mathematics

Page: 64

View: 2878

A unique introduction to this most ancient and timeless of universal sciences.

Harmonograph

A Visual Guide to the Mathematics of Music

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Author: Anthony Ashton

Publisher: Wooden Books

ISBN: 1912706059

Category: Music

Page: 64

View: 6137

Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

The Glorious Golden Ratio

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Author: Alfred S. Posamentier,Ingmar Lehmann

Publisher: Prometheus Books

ISBN: 1616144246

Category: Mathematics

Page: 363

View: 8098

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. From the Hardcover edition.

Sacred Number

The Secret Quality of Quantities

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Author: N.A

Publisher: Bloomsbury Publishing USA

ISBN: 0802714560

Category: Mathematics

Page: 64

View: 2957

Beautifully illustrated with many old engravings as well as contemporary imagery, "Sacred Number" covers basic counting systems and the widespread use of 20 important numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; and how numbers affect architecture.

Ruler and Compass

Practical Geometric Constructions

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Author: Andrew Sutton

Publisher: Bloomsbury Publishing USA

ISBN: 0802717764

Category: Mathematics

Page: 64

View: 5236

An introduction to geometry without measurements.

A Little Book of Coincidence

In the Solar System

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Author: John Martineau

Publisher: Wooden Books

ISBN: 1912706075

Category: Science

Page: 64

View: 4490

Venus draws a beautiful pentagram around Earth every eight years. Jupiter's two largest moons draw a perfect four-fold flower. The Planets grandly play out the slow Music of the Spheres. Is there a secret structure hidden in the Solar System? Packed with great illustrations and serious research from many sources, this internationally bestselling little book by cosmologist John Martineau will instantly retune your cosmological circuits to the extraordinary and primary patterns behind Life, the Universe and Everything. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Sun, Moon and Earth

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Author: Robin Heath

Publisher: Bloomsbury Publishing USA

ISBN: 0802713815

Category: Science

Page: 64

View: 3727

Every organism on Earth responds to four major cycles: the solar and lunar day, the synodic month and the year. We all dance to these primary rhythms. This book reveals the poetic cosmology that lies within the cycles of the Sun and Moon as seen from the Earth.

The Divine Proportion

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Author: H. E. Huntley

Publisher: Courier Corporation

ISBN: 0486131874

Category: Mathematics

Page: 208

View: 607

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 Golden Ratio and Fibonacci Numbers

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Author: Richard A Dunlap

Publisher: World Scientific

ISBN: 9814496944

Category: Mathematics

Page: 172

View: 4693

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. Contents:Basic Properties of the Golden RatioGeometric Problems in Two DimensionsGeometric Problems in Three DimensionsFibonacci NumbersLucas Numbers and Generalized Fibonacci NumbersContinued Fractions and Rational ApproximantsGeneralized Fibonacci Representation TheoremsOptimal Spacing and Search AlgorithmsCommensurate and Incommensurate ProjectionsPenrose TilingsQuasicrystallographyBiological ApplicationsConstruction of the Regular PentagonThe First 100 Fibonacci and Lucas NumbersRelationships Involving the Golden Ratio and Generalized Fibonacci Numbers Readership: Applied mathematicians. keywords:Golden Ratio;Fibonacci Numbers;Number Theory;Quasicrystallography;Tilings;Geometry;Optimization Algorithms;Numerical Sequences;Lucas Numbers;Continued Fractions;Aperiodicity;Incommensurate Structures "This attractive and carefully written book addresses the general reader with interest in mathematics and its application to the physical and biological sciences ... this one will make a valuable addition to academic and personal libraries." The Fibonacci Quarterly

The Golden Ratio

The Divine Beauty of Mathematics

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Author: Gary B. Meisner

Publisher: Race Point Publishing

ISBN: 9781631064869

Category: Mathematics

Page: 224

View: 364

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 features clear, entertaining, and enlightening 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. With its lush format and layflat dimensions that closely approximate the golden ratio, this is the ultimate coffee table book for math enthusiasts, architects, designers, and fans of sacred geometry.

Sciencia

Mathematics, Physics, Chemistry, Biology, and Astronomy for All

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Author: Matt Tweed,Matthew Watkins,Moff Betts

Publisher: Bloomsbury Publishing USA

ISBN: 0802778992

Category: Mathematics

Page: 416

View: 1877

Collects six short illustrated volumes covering topics in mathematics, physics, chemistry, biology, evolution, and astronomy.

Q.E.D.

Beauty in Mathematical Proof

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Author: Burkard Polster

Publisher: Bloomsbury Publishing USA

ISBN: 0802714315

Category: Mathematics

Page: 58

View: 1308

Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.

The Golden Ratio

The Story of PHI, the World's Most Astonishing Number

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Author: Mario Livio

Publisher: Broadway Books

ISBN: 9780307485526

Category: Mathematics

Page: 304

View: 3487

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. From the Hardcover edition.

The Golden Ratio

The Facts and the Myths

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Author: Francis D. Hauser, Ph.d.

Publisher: CreateSpace

ISBN: 9781517518776

Category:

Page: 56

View: 722

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.

Divine Proportion

Phi in Art, Nature, and Science

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Author: Priya Hemenway

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402735226

Category: Science

Page: 203

View: 5509

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.