The Golden Ratio

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

Author: Mario Livio

Publisher: Broadway Books

ISBN: 9780307485526

Category: Mathematics

Page: 304

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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.
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The Golden Ratio

The Divine Beauty of Mathematics

Author: Gary B. Meisner

Publisher: Race Point Publishing

ISBN: 163106486X

Category: Mathematics

Page: 224

View: 9279

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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.
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Visual Marketing

From Attention to Action

Author: Michel Wedel,Rik Pieters

Publisher: Psychology Press

ISBN: 1136676481

Category: Business & Economics

Page: 328

View: 3114

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This comprehensive volume aims to further research and theory development in visual marketing. By bringing together leading researchers in the field, it strives to contribute to the establishment of visual marketing as a coherent discipline. The chapters represent an array of issues in visual marketing. They address three areas in theory: attention and perception, visual cognition and action and choice. The chapters go beyond what is known, and offer in many cases a more speculative and visionary account of the directions that visual marketing research could and should take. Rather than being confined to advertising only, this new volume shows how visual marketing permeates almost all consumer and marketing activities. It will be of interest to undergraduate and graduate students in marketing, management, industrial design, and consumer and social psychology. Professional practitioners, especially those involved with marketing communications, retail, and in store marketing and market research, will also benefit from the empirically based and innovative ideas put forth in this book.
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Cosmetic Medicine and Surgery, An Issue of Clinics in Plastic Surgery - E- Book

Author: Malcolm D. Paul,Raffi Hovsepian,Adam Rotunda

Publisher: Elsevier Health Sciences

ISBN: 1455709484

Category: Medical

Page: 232

View: 2814

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More and more plastic surgeons are turning to cosmetic medicine and minimally invasive surgery as a way to supplement their practices. This multidisciplinary issue, which includes dermatologists as well as plastic surgeons, gives detailed information on how to perform several procedures, including dermabrasion, botox injection, laser therapy, and thermage.
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Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 9955

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Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
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Education and Democracy in the 21st Century

Author: Nel Noddings

Publisher: Teachers College Press

ISBN: 0807772313

Category: Education

Page: 179

View: 6923

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"Educational philosopher Nel Noddings draws on John Dewey's foundational work to reimagine education's aims and curriculum for the 21st century. Noddings looks at education as a multi-aim enterprise in which schools must address needs in all three domains of life: home and family, occupational, and civic. She raises critical questions about the current enthusiasm for standardization, the search for 'one-best-way' solutions, and the practice of maintaining a sharp separation between the disciplines. Comprehensive in its scope, chapters examine the liberal arts curriculum, vocational education, restructuring secondary school, extracurricular activities, national and global citizenship, critical thinking, and moral education."--Back cover.
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DNA of Mathematics

Author: Dr. Mehran Basti

Publisher: FriesenPress

ISBN: 1460239563

Category: Religion

Page: 280

View: 7728

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For Dr. Basti, the explanation is straightforward though not simple: "Just as cells have dna, so mathematics has DNA in its structure." After years of research, he decided that his work had to contain a strong philosophical justification in order to stand the test of time. Part memoir and part manifesto, DNA of Mathematics introduces Mehran Basti's readers to both the research he has dedicated his career to and his personal background and beliefs which significantly impact his scientific work.
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The Fabulous Fibonacci Numbers

Author: Alfred S. Posamentier

Publisher: Prometheus Books

ISBN: 1615920226

Category: Mathematics

Page: N.A

View: 2372

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The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature-from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world.With admirable clarity, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. The authors begin with a brief history of their distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the golden ratio. And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.Alfred S. Posamentier (New York, NY) is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published over 40 books in the area of mathematics and mathematics education, including Pi: A Biography of the World's Most Mysterious Number and Math Charmers: Tantalizing Tidbits for the Mind.Ingmar Lehmann (Berlin, Germany) is on the mathematics faculty at Humboldt University in Berlin and the coauthor of Pi: A Biography of the World's Most Mysterious Number.
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Contemporary Authors

Author: Gale Group

Publisher: Gale Cengage

ISBN: 9780787666996

Category: Biography & Autobiography

Page: 446

View: 5193

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Your students and users will find biographical information on approximately 300 modern writers in this volume of Contemporary Authors® .
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