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The Golden Section

Author : Scott Olson
ISBN : 9780802715395
Genre : Mathematics
File Size : 51.20 MB
Format : PDF, Kindle
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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.
Category: Mathematics

The Golden Section

Author : Hans Walser
ISBN : 0883855348
Genre : Mathematics
File Size : 27.3 MB
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The Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. This book aims both to describe examples of the Golden Section, and to show some paths to further developments.
Category: Mathematics

Fibonacci And Lucas Numbers And The Golden Section

Author : Steven Vajda
ISBN : 9780486462769
Genre : Mathematics
File Size : 57.70 MB
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This survey of the use of Fibonacci and Lucas numbers and the ancient principle of the Golden Section covers areas relevant to operational research, statistics, and computational mathematics. 1989 edition.
Category: Mathematics

The Golden Section

Author : Garth E. Runion
ISBN : IND:30000009506639
Genre : Juvenile Nonfiction
File Size : 35.77 MB
Format : PDF
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Category: Juvenile Nonfiction

The Golden Ratio

Author : Mario Livio
ISBN : 0307485528
Genre : Mathematics
File Size : 29.29 MB
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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.
Category: Mathematics

The Glorious Golden Ratio

Author : Alfred S. Posamentier
ISBN : 9781616144241
Genre : Mathematics
File Size : 82.76 MB
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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. From the Hardcover edition.
Category: Mathematics

The Golden Section

Author : Steven L. Griffing
ISBN : 1462806449
Genre : Science
File Size : 73.37 MB
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This book contains a great deal of geometry regarding the golden section, including some discoveries of my own. It, also, contains some history of the golden section, as it was used in the art and architecture of the classical civilizations of Egypt and Greece. The golden section was used extensively in the art and architecture, during the classical civilizations of Egypt and Greece, and to some extent, later, in Europe. Its geometric basis can be found in the proportions of the bones of the human body, and of other animals.
Category: Science

The Golden Ratio And Fibonacci Numbers

Author : R. A. Dunlap
ISBN : 9812386300
Genre : Mathematics
File Size : 70.39 MB
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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.
Category: Mathematics

Math For Mystics

Author : Renna Shesso
ISBN : 1609252748
Genre : Body, Mind & Spirit
File Size : 73.8 MB
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Much of math history comes to us from early astrologers who needed to be able to describe and record what they saw in the night sky. Whether you were the king’s court astrologer or a farmer marking the best time for planting, timekeeping and numbers really mattered. Mistake a numerical pattern of petals and you could be poisoned. Lose the rhythm of a sacred dance or the meter of a ritually told story and the intricately woven threads that hold life together were spoiled. Ignore the celestial clock of equinoxes and solstices, and you’d risk being caught short of food for the winter. Shesso’s friendly tone and clear grasp of the information make the math “go down easy” in this marvelous book.
Category: Body, Mind & Spirit

The Golden Ratio

Author : Michael O'Mara Books
ISBN : 1454710225
Genre : Art
File Size : 31.1 MB
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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.
Category: Art