The Golden Ratio

The Golden Ratio PDF
Author: Mario Livio
Publisher: Broadway
ISBN: 9780767908160
Size: 49.38 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 294
View: 2999

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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.

The Golden Ratio

The Golden Ratio PDF
Author: Gary B. Meisner
Publisher: Race Point Publishing
ISBN: 163106486X
Size: 70.67 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 224
View: 4465

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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 Golden Ratio

The Golden Ratio PDF
Author: IntroBooks
Publisher: Can Akdeniz
ISBN:
Size: 69.25 MB
Format: PDF, ePub
Category :
Languages : en
Pages : 40
View: 510

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The golden ratio is an irrational number and simultaneously an excellent technique that bestows a lot to those who are into the designing field. It helps in a number of things that are essential for the proper construction of architecture as well as designing. The golden ratio has a lot of names that are famous for the discrete tasks that can be performed by the golden ratio, and so accordingly it is named. The golden ratio was used by a number of distinguished mathematicians and artists who have also created some great masterpieces that are well known and famous worldwide. These masterpieces include the many architectural buildings, sculptures, images, paintings, designs, etc. The golden ratio is an amazing technique and probably the only technique that is present in a number of domains such as mathematics, physics, art, architecture, paintings, etc. The golden ratio is directly related to nature, which makes it more interesting and easygoing.

The Golden Ratio

The Golden Ratio PDF
Author: Mario Livio
Publisher: Headline Review
ISBN: 9780747249887
Size: 35.60 MB
Format: PDF, Kindle
Category : Algebraic fields
Languages : en
Pages : 294
View: 1677

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What do the Parthenon in Greece, crosses in graveyards, the ratio of the height of a woman's navel to a woman's height, sunflowers and Leonardo da Vinci's Mona Lisa have in common? The answer is that these disparate elements share a geometrical proportion of ancient origin commonly known as the golden ratio, or expressed numerically as phi. fractals and DNA on the way, the author takes us into the heart of this extraordinary number. He gives an account of the phi-obsessed individuals who devoted their lives to discovering its secrets - from the Pythagoreans who believed that the study of the Golden Ratio would reveal the hand of God, to the astronomer Johannes Kepler who felt that phi was the greatest treasure of geometry, to the modern day scientists who are discovering ever more remarkable ramifications of this strange, almost mystical, number.

The Golden Ratio And Fibonacci Numbers

The Golden Ratio and Fibonacci Numbers PDF
Author: R. A. Dunlap
Publisher: World Scientific
ISBN: 9789812386304
Size: 46.63 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 162
View: 2094

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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 Ratio; Geometric Problems in Two Dimensions; Geometric Problems in Three Dimensions; Fibonacci Numbers; Lucas Numbers and Generalized Fibonacci Numbers; Continued Fractions and Rational Approximants; Generalized Fibonacci Representation Theorems; Optimal Spacing and Search Algorithms; Commensurate and Incommensurate Projections; Penrose Tilings; Quasicrystallography; Biological Applications; Construction of the Regular Pentagon; The First 100 Fibonacci and Lucas Numbers; Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers. Readership: Applied mathematicians.

The Glorious Golden Ratio

The Glorious Golden Ratio PDF
Author: Alfred S. Posamentier
Publisher: Prometheus Books
ISBN: 1616144246
Size: 22.19 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 363
View: 7170

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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.

The Golden Section

The Golden Section PDF
Author: Scott Olson
Publisher: Bloomsbury Publishing USA
ISBN: 0802715397
Size: 32.50 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 58
View: 5252

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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 Ratio Fibonacci Sequence Golden Keys To Your Genius Health Wealth Excellence

The Golden Ratio   Fibonacci Sequence  Golden Keys to Your Genius  Health  Wealth   Excellence PDF
Author: Matthew K. Cross
Publisher: Hoshin Media
ISBN: 9781939623003
Size: 44.85 MB
Format: PDF
Category : Self-Help
Languages : en
Pages : 64
View: 3115

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It's been called the Secret of the Universe, a Most Precious Jewel, Nature's Path of Least Resistance and Maximum Performance and The Golden Key to the Cosmos. It is the Grand Pattern of Life, Growth and Success. It has fascinated and appears in the works of the world's greatest geniuses, including Leonardo Da Vinci, Albert Einstein, Walt Disney and Steve Jobs. Now, the open secret of the Golden Ratio and Fibonacci Sequence is revealed for your enjoyment and application. In this book you'll journey through Golden Ratio appearances and applications throughout Nature and the Universe and in all fields of human existence and endeavor, including: art, architecture, astronomy, beauty, business, culture, design, finance, health and longevity, geometry, mathematics, medicine, relationships, science and spirituality. This book presents a delightful cornucopia of Golden Ratio facts and facets, offering a bright window into its universality and power. The information presented is laser-like, with the ability to activate your unique genius and transform your consciousness. Universal wisdom will be at your fingertips once your Golden Doors of Perception are opened to the sacred design code of the Universe: The Golden Ratio & Fibonacci Sequence.

Divina Proportione

Divina proportione PDF
Author: Luca Pacioli
Publisher:
ISBN:
Size: 24.14 MB
Format: PDF
Category : Proportion (Art)
Languages : de
Pages : 365
View: 2579

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The Interesting Golden Ratio

The Interesting Golden Ratio PDF
Author: Vincent Siu
Publisher: Partridge Publishing Singapore
ISBN: 1482855437
Size: 54.13 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 158
View: 1347

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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.

The Golden Ratio

The Golden Ratio PDF
Author: Michael O'Mara Books
Publisher: Lark Books (NC)
ISBN: 9781454710226
Size: 47.44 MB
Format: PDF, ePub, Docs
Category : Art
Languages : en
Pages : 96
View: 7666

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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.

Divine Golden Ingenious

Divine  Golden  Ingenious PDF
Author: Oliver Götze
Publisher:
ISBN: 9783777426921
Size: 60.64 MB
Format: PDF, ePub
Category :
Languages : en
Pages : 192
View: 2743

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Does a mystic, divine formula lie behind everything that is beautiful? For centuries the golden mean has been a subject of endless fascination. The ratio of the proportion can be seen in Nature; it runs through artistic design processes and it affects our perception of our surroundings. But how much of this apparent "world formula" is true, and how much of it is myth? The history of the golden mean begins with Euclid in the 3rd century BC. But it was only in the 19th century that it was raised to the universal constant of beauty. From this point onwards the "golden section" was described in flora and fauna; the famous Fibonacci number. It determines the growth of the pineapple; and Le Corbusier optimised architecture by means of the Modulor. But does this art-historical phenomenon really play a universal role in the organisation of our world? Authors from all fields analyse the Golden Mean with regard to function, demonstrability and relevance, also by means of current examples from art and design as well as in comparison with the DIN and the tatami measurement.

The Golden Ratio Colouring Book

The Golden Ratio Colouring Book PDF
Author:
Publisher: LOM ART
ISBN: 9781910552643
Size: 26.52 MB
Format: PDF, Kindle
Category :
Languages : en
Pages : 96
View: 6866

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Everyone talks vaguely about the 'patterns' to be found in mathematics, but in this colouring book you will find them in all their inspirational glory.Many of the intricate waves, loops and geometrics that can be found in nature and art have their basis in maths - but you need no prior knowledge to admire and colour them. From mandalas to fractals, sunflowers to tiling, there is much to enjoy here and throughout the book you will also find short descriptions of particularly important curves, structures or geometric patterns to further your knowledge. Relax and enjoy the intricate patterns in this book and add colour to create stunning designs of your own. Who knows? You might begin to better understand the world too.

Matlab Guide To Fibonacci Numbers And The Golden Ratio

MATLAB Guide to Fibonacci Numbers and the Golden Ratio PDF
Author: Peter I. Kattan
Publisher: CreateSpace
ISBN: 9781466229877
Size: 11.81 MB
Format: PDF
Category :
Languages : en
Pages : 172
View: 2177

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This book is written for people who love MATLAB and Fibonacci numbers. One of the objectives of writing this book is to introduce MATLAB and Fibonacci numbers to students in high schools. The material presented is very easy and simple to understand -- written in a very simplified manner. The book is divided into two parts - A review of MATLAB is presented in the first part. This is followed by a presentation of Fibonacci numbers and the Golden Ratio in the second part. The topics covered in the book include symbolic computing with MATLAB, solving equations with MATLAB, MATLAB functions, graphs in MATLAB, Fibonacci numbers, The Golden Ratio, Properties of the Golden Ratio, Lucas numbers, Generalizations of Fibonacci numbers, and Random Fibonacci numbers. The book includes numerous M-files written specifically to compute different kinds of Fibonacci sequences and the Golden Ratio. The author has been using MATLAB for the past seventeen years and is the author of the best selling books "MATLAB for Beginners" and "MATLAB Guide to Finite Elements".

The Golden Ratio

The Golden Ratio PDF
Author: Francis D. Hauser, Ph.d.
Publisher: CreateSpace
ISBN: 9781517518776
Size: 51.88 MB
Format: PDF, ePub
Category :
Languages : en
Pages : 56
View: 5276

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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.