The Value of Φ The Golden Ratio 240,000 Digits PDF Download

Author: Science Monkey
Publisher:
ISBN:
Category :
Languages : en
Pages : 300

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Book Description
Have fun with mathematics and discover the value of the square root of φ, the Golden Ratio in this book featuring about approximately 240,000 digits. Great gift for kids of all ages as well as adults, anyone with an appreciation for mathematics, logical equations, problem solving, aspiring scientists, math and science school teachers, physicists and more.

Author: Mario Livio
Publisher: Crown
ISBN: 0767908163
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.

Author: Syed K R
Publisher: Independently Published
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Get fascinated by the Golden Ratio and its magnanimity. Find out the the first 100000 digits of this unique irrational number.

Author:
Publisher:
ISBN: 9786500983234
Category : Mathematics
Languages : en
Pages : 0

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Book Description
Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Often symbolized as Phi (φ), is also expressed as one plus the square root of five, divided by two. The Golden Ratio has profoundly influenced both art and architecture, serving as a guiding principle for achieving balance and aesthetic beauty. Here we present that number printed, in his first two million digits, in a single volume.

Author: Joseph Tainter
Publisher: Cambridge University Press
ISBN: 9780521386739
Category : Social Science
Languages : en
Pages : 268

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Book Description
Dr Tainter describes nearly two dozen cases of collapse and reviews more than 2000 years of explanations. He then develops a new and far-reaching theory.

Author: Mats Danielson
Publisher: CRC Press
ISBN: 1000936899
Category : Education
Languages : en
Pages : 141

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Book Description
Have you ever experienced a decision situation that was hard to come to grips with? Did you ever feel a need to improve your decision-making skills? Is this something where you feel that you have not learned enough practical and useful methods? In that case, you are not alone! Even though decision-making is both considered and actually is a very important skill in modern work-life as well as in private life, these skills are not to any reasonable extent taught in schools at any level. No wonder many people do indeed feel the need to improve but have a hard time finding out how. This book is an attempt to remedy this shortcoming of our educational systems and possibly also of our common, partly intuition-based, decision culture. Intuition is not at all bad, quite the contrary, but it has to co-exist with rationality. We will show you how. Methods for decision-making should be of prime concern to any individual or organisation, even if the decision processes are not always explicitly or even consciously formulated. All kinds of organisations, as well as individuals, must continuously make decisions of the most varied nature in order to prosper and attain their objectives. A large part of the time spent in any organisation, not least at management levels, is spent gathering, processing, and compiling information for the purpose of making decisions supported by that information. The same interest has hitherto not been shown for individual decision-making, even though large gains would also be obtained at a personal level if important personal decisions were better deliberated. This book aims at changing that and thus attends to both categories of decision-makers. This book will take you through a journey starting with some history of decision-making and analysis and then go through easy-to-learn ways of structuring decision information and methods for analysing the decision situations, beginning with simple decision situations and then moving on to progressively harder ones, but never losing sight of the overarching goal that the reader should be able to follow the progression and being able to carry out similar decision analyses in real-life situations. The Open Access version of this book, available at www.taylorfrancis.com, has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.

Author: Gavin Towler
Publisher: Elsevier
ISBN: 0080966608
Category : Technology & Engineering
Languages : en
Pages : 1321

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Book Description
Chemical Engineering Design, Second Edition, deals with the application of chemical engineering principles to the design of chemical processes and equipment. Revised throughout, this edition has been specifically developed for the U.S. market. It provides the latest US codes and standards, including API, ASME and ISA design codes and ANSI standards. It contains new discussions of conceptual plant design, flowsheet development, and revamp design; extended coverage of capital cost estimation, process costing, and economics; and new chapters on equipment selection, reactor design, and solids handling processes. A rigorous pedagogy assists learning, with detailed worked examples, end of chapter exercises, plus supporting data, and Excel spreadsheet calculations, plus over 150 Patent References for downloading from the companion website. Extensive instructor resources, including 1170 lecture slides and a fully worked solutions manual are available to adopting instructors. This text is designed for chemical and biochemical engineering students (senior undergraduate year, plus appropriate for capstone design courses where taken, plus graduates) and lecturers/tutors, and professionals in industry (chemical process, biochemical, pharmaceutical, petrochemical sectors). New to this edition: Revised organization into Part I: Process Design, and Part II: Plant Design. The broad themes of Part I are flowsheet development, economic analysis, safety and environmental impact and optimization. Part II contains chapters on equipment design and selection that can be used as supplements to a lecture course or as essential references for students or practicing engineers working on design projects. New discussion of conceptual plant design, flowsheet development and revamp design Significantly increased coverage of capital cost estimation, process costing and economics New chapters on equipment selection, reactor design and solids handling processes New sections on fermentation, adsorption, membrane separations, ion exchange and chromatography Increased coverage of batch processing, food, pharmaceutical and biological processes All equipment chapters in Part II revised and updated with current information Updated throughout for latest US codes and standards, including API, ASME and ISA design codes and ANSI standards Additional worked examples and homework problems The most complete and up to date coverage of equipment selection 108 realistic commercial design projects from diverse industries A rigorous pedagogy assists learning, with detailed worked examples, end of chapter exercises, plus supporting data and Excel spreadsheet calculations plus over 150 Patent References, for downloading from the companion website Extensive instructor resources: 1170 lecture slides plus fully worked solutions manual available to adopting instructors

Author: Simon Benninga
Publisher: MIT Press
ISBN: 9780262024822
Category : Business & Economics
Languages : en
Pages : 648

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Book Description
Too often, finance courses stop short of making a connection between textbook finance and the problems of real-world business. "Financial Modeling" bridges this gap between theory and practice by providing a nuts-and-bolts guide to solving common financial problems with spreadsheets. The CD-ROM contains Excel* worksheets and solutions to end-of-chapter exercises. 634 illustrations.

Author: Gerard Cornuejols
Publisher: Cambridge University Press
ISBN: 9780521861700
Category : Mathematics
Languages : en
Pages : 358

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Book Description
Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Author: Walter Lewin
Publisher: Simon and Schuster
ISBN: 1439123543
Category : Science
Languages : en
Pages : 375

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Book Description
“YOU HAVE CHANGED MY LIFE” is a common refrain in the emails Walter Lewin receives daily from fans who have been enthralled by his world-famous video lectures about the wonders of physics. “I walk with a new spring in my step and I look at life through physics-colored eyes,” wrote one such fan. When Lewin’s lectures were made available online, he became an instant YouTube celebrity, and The New York Times declared, “Walter Lewin delivers his lectures with the panache of Julia Child bringing French cooking to amateurs and the zany theatricality of YouTube’s greatest hits.” For more than thirty years as a beloved professor at the Massachusetts Institute of Technology, Lewin honed his singular craft of making physics not only accessible but truly fun, whether putting his head in the path of a wrecking ball, supercharging himself with three hundred thousand volts of electricity, or demonstrating why the sky is blue and why clouds are white. Now, as Carl Sagan did for astronomy and Brian Green did for cosmology, Lewin takes readers on a marvelous journey in For the Love of Physics, opening our eyes as never before to the amazing beauty and power with which physics can reveal the hidden workings of the world all around us. “I introduce people to their own world,” writes Lewin, “the world they live in and are familiar with but don’t approach like a physicist—yet.” Could it be true that we are shorter standing up than lying down? Why can we snorkel no deeper than about one foot below the surface? Why are the colors of a rainbow always in the same order, and would it be possible to put our hand out and touch one? Whether introducing why the air smells so fresh after a lightning storm, why we briefly lose (and gain) weight when we ride in an elevator, or what the big bang would have sounded like had anyone existed to hear it, Lewin never ceases to surprise and delight with the extraordinary ability of physics to answer even the most elusive questions. Recounting his own exciting discoveries as a pioneer in the field of X-ray astronomy—arriving at MIT right at the start of an astonishing revolution in astronomy—he also brings to life the power of physics to reach into the vastness of space and unveil exotic uncharted territories, from the marvels of a supernova explosion in the Large Magellanic Cloud to the unseeable depths of black holes. “For me,” Lewin writes, “physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.” His wonderfully inventive and vivid ways of introducing us to the revelations of physics impart to us a new appreciation of the remarkable beauty and intricate harmonies of the forces that govern our lives.