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.

    Describes how fractals were discovered, explains their unique properties, and discusses the mathematical foundation of fractals.

    First published in 1937.

    Full page B&W photos

    This book offers the opportunity to truly comprehend the workings of one of humanity's greatest minds. Acclaimed by Einstein himself, it is among the clearest, most readable expositions of relativity theory. It explains the problems Einstein faced, the experiments that led to his theories, and what his findings reveal about the forces that govern the universe. The concepts of relativity and the fourth dimension unfold with all the vivid excitement of research into the unknown, in language anyone can readily understand.

    . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald TribuneOne of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader.He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system.In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations.Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature

    In The Rebirth of Nature, Sheldrake urges us to move beyond the centuries-old mechanistic view of nature, explaining why we can no longer regard the world as inanimate and purposeless. Sheldrake shows how recent developments in science itself have brought us to the threshold of a new synthesis in which traditional wisdom, intuitive experience, and scientific insight can be mutually enriching.

    So, why do we perceive a flow of time? Is the future “already there”, and is the past “still there”, even though we are only aware of a single moment of time? Drawing on the latest ideas from both relativity and quantum theory, award-winning science writer John Gribbin (In Search of Schrödinger’s Cat) addresses the questions that have baffled philosophers since antiquity and Zeno’s arrow paradox. Along the way, we find that in the quantum world it is literally true that a watched pot never boils, and learn how physicists have come to terms with the idea of the four-dimensional block universe as an explanation of the distinction between past, present and future. Why do eggs break when we drop them, but never unbreak? The Universe as we know it began in a Big Bang, which in some sense marks the beginning of time. Is it possible that we need to invoke the Big Bang to explain why we never see unbroken eggs? This idea glories in the name “the past hypothesis”, but many physicists regard it as no more than an attempt to sweep the problem of the arrow of time under the rug. Read The Time Illusion and see if you agree!

    From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons.

    Enjoy a thrilling intergalactic tour as Andrew Thomas redefines the force of gravity and introduces a brave new view of the universe!

    This unique selection of illustrations with commentaries and source texts guides us on a fascinating journey through the representations of the secret arts.

    With his own research as well as that of some of the most distinguished scientists of our time, Schäfer moves us from a reality of Darwinian competition to cooperation, a meaningless universe to a meaningful one, and a disconnected, isolated existence to an interconnected one. In so doing, he shows us that our potential is infinite and calls us to live in accordance with the order of the universe, creating a society based on the cosmic principle of connection, emphasizing cooperation and community.

    By linking research ranging from the ancient Greek "dream temples" and modern experiments in telepathy, REM, and lucid dreaming to his own research on human consciousness, he theorizes that dreaming is the basis for consciousness, and that it is through dreaming that we are able to manifest a sense of ourselves.

    A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how today's theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, the book describes the majestic sweep and accomplishments of twentieth-century physics. In the end, we stand in awe before the grand vision of modern physics--one of the greatest chapters in the intellectual history of humankind.

    Alex Grey's reflections combine his extensive knowledge of art history and his own first-hand experiences in creating art on the boundaries of consciousness. Included are practical techniques and exercises that can be used to explore the spiritual dimension of art. Challenging and thought-provoking, The Mission of Art will be enjoyed by everyone who has ever contemplated the deeper purpose of artistic expression.