Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

    These theories are not only untrue, it is not even science. It is fairy-tale physics: fantastical, bizarre and often outrageous, perhaps even confidence-trickery.This book provides a much-needed antidote. Informed, comprehensive, and balanced, it offers lay readers the latest ideas about the nature of physical reality while clearly distinguishing between fact and fantasy. With its engaging portraits of many central figures of modern physics, including Paul Davies, John Barrow, Brian Greene, Stephen Hawking, and Leonard Susskind, it promises to be essential reading for all readers interested in what we know and don't know about the nature of the universe and reality itself.

    From the early Greek influences to the Middle Ages and the Renaissance to the end of the 19th century, trace the fascinating foundation of mathematics as it developed through the ages. Aristotle, Galileo, Kepler, Newton: you know the names. Now here's what they really did, and the effect their discoveries had on our culture, all explained in a way the layperson can understand. Begin with the basis of arithmetic (Plato and the introduction of geometry), and discover why the use of Arabic numerals was critical to the development of both commerce and science. The development of calculus made space travel a reality, while the abacus prefigured the computer. The greats examined in depth include Leonardo da Vinci, a brilliant mathematician as well as artist; Pascal, who laid out the theory of probabilities; and Fermat, whose intriguing theory has only recently been solved.

    Like you, the elements have lives: personalities and attitudes, talents and shortcomings, stories rich with meaning. You may think of them as the inscrutable letters of the periodic table but you know them much better than you realise. Welcome to a dazzling tour through history and literature, science and art. Here you'll meet iron that rains from the heavens and noble gases that light the way to vice. You'll learn how lead can tell your future while zinc may one day line your coffin. You'll discover what connects the bones in your body with the Whitehouse in Washington, the glow of a streetlamp with the salt on your dinner table. From ancient civilisations to contemporary culture, from the oxygen of publicity to the phosphorus in your pee, the elements are near and far and all around us. Unlocking their astonishing secrets and colourful pasts, Periodic Tales will take you on a voyage of wonder and discovery, excitement and novelty, beauty and truth. Along the way, you'll find that their stories are our stories, and their lives are inextricable from our own.

    David Peat explains the development and meaning of this Superstring Theory in a thoroughly readable, dramatic manner accessible to lay readers with no knowledge of mathematics. The consequences of the Superstring Theory are nothing less than astonishing.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

     The eternal questions of science and religion were profoundly recast by Einstein's theory of relativity and its implications that time can be warped by motion and gravitation, and that it cannot be meaningfully divided into past, present, and future. In About Time, Paul Davies discusses the big bang theory, chaos theory, and the recent discovery that the universe appears to be younger than some of the objects in it, concluding that Einstein's theory provides only an incomplete understanding of the nature of time. Davies explores unanswered questions such as: * Does the universe have a beginning and an end? * Is the passage of time merely an illusion? * Is it possible to travel backward -- or forward -- in time? About Time weaves physics and metaphysics in a provocative contemplation of time and the universe.

    William H. Cropper vividly portrays the life and accomplishments of such giants as Galileo and Isaac Newton, Marie Curie and Ernest Rutherford, Albert Einstein and NielsBohr, right up to contemporary figures such as Richard Feynman, Murray Gell-Mann, and Stephen Hawking. We meet scientists--all geniuses--who could be gregarious, aloof, unpretentious, friendly, dogged, imperious, generous to colleagues or contentious rivals. As Cropper captures their personalities, he also offers vivid portraits of their great moments of discovery, their bitter feuds, their relations with family and friends, their religious beliefs and education. In addition, Cropper has grouped these biographies by discipline--mechanics, thermodynamics, particle physics, and others--eachsection beginning with a historical overview. Thus in the section on quantum mechanics, readers can see how the work of Max Planck influenced Niels Bohr, and how Bohr in turn influenced Werner Heisenberg.Our understanding of the physical world has increased dramatically in the last four centuries. With Great Physicists, readers can retrace the footsteps of the men and women who led the way.

    In this reader-friendly, unabridged edition of three of his best-selling books, renowned science writer Isaac Asimov demystifies physics, teaching the fundamentals in a manner easily understood by lay people. Including the complete text of Motion, Sound and Heat, Light, Magnetism and Electricity, and The Electron, Proton and Neutron, this volume will guide you through the evolution of physics from its early Greek beginnings up to the modern theories of the creation of time, space and matter. Each volume relates the tale of the human quest through the ages for answers to the fundamental questions of how the universe works. Told in its historical context, this quest for knowledge is a story of high drama and uncommon valor, when men put their very lives on the line for the sake of scientific truth.3 Volumes in One: Motion, Sound & Heat; Light, Magnetism & Electricity; The Electron, Proton & Neutron. 1993 Barnes & Noble reprint of three Isaac Asimov classics. Originally published in 1966.

    But in Art & Physics, Leonard Shlain tracks their breakthroughs side by side throughout history to reveal an astonishing correlation of visions.From teh classical Greek sculptors to Andy Warhol and Jasper Johns, and from Aristotle to Einstein, aritsts have foreshadowed the discoveries of scientists, such as when Money and Cezanne intuited the coming upheaval in physics that Einstein would initiate. In this lively and colorful narrative, Leonard Shlain explores how artistic breakthroughs could have prefigured the visionary insights of physicists on so many occasions throughtout history.Provacative and original, Art & Physics is a seamless integration of the romance of art and the drama of science...and exhilarating history of ideas.

    We're all looking for new ways of thinking that can bring about real solutions to modern problems, from the pursuit of inner serenity to solving world conflicts. In Do You QuantumThink? author Dianne Collins shares her ingenious discovery that reveals a critical missing link to make sense of our changing times. Her discovery provides us with the understanding and methodology to rise above problems of today by laying the foundation for an entirely new way to think.Part science, part philosophy, part spirituality, Do You QuantumThink? draws on a wide spectrum of sources, from cutting edge innovations in the sciences to the insights of the world's greatest spiritual leaders. This book will make you laugh, free you from limiting ideas, and introduce you to the most advanced principles and practical methods for living. Do You QuantumThink? will rock your world in the best of ways as you experience one revelation after another.