Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on* the relationship between mathematical knots and DNA* how computers based on quantum logic can significantly speed up the factoring of large composite numbers* the relationship between four-dimensional geometry and physical theories of the nature of matter* the application of cellular automata models to social questions and the peregrinations of virtual ants* a novel mathematical model of quasicrystals based on decagon-shaped tilesBlazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    Poetry, patterns like Pascal's triangle, philosophy, psychology, music, and dozens of simple mathematical figures are enlisted to show that the "divine proportion" or "golden ratio" is a feature of geometry and analysis which awakes answering echoes in the human psyche. When we judge a work of art aesthetically satisfying, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures which forms the core of Professor Huntley's book.For the philosopher, scientist, poet, art historian, music listener, artist, as well as the general reader who wants to understand more about the fascinating properties of numbers, this is a beautifully written, exciting account of the search for a naturally manifested aesthetic that has occupied man since he first asked the question "why?""This is a delightful book to read. . . . It wanders here and there through some of the most attractive byways of simple mathematics, returning always to the oddities and pleasures of the golden section. This is a browser's book — a happy, untidy traveling or bedside book for those who know how to enjoy the charm of numbers and shapes." — Dr. J. Bronowski, The Salk Institute.

    It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers.

    And proves once and for all that maths isn't just for old men with white hair and beards who associate with elves.Maths has never been merrier.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    The author believes that there are such things as "The Mathematics of Life" and "The Mathematics of Art," and that the two coincide. Using simple mathematical formulas, most as basic as Pythagoras' theorem and requiring only a very limited knowledge of mathematics, Professor Ghyka shows the fascinating relationships between geometry, aesthetics, nature, and the human body.Beginning with ideas from Plato, Pythagoras, Archimedes, Ockham, Kepler, and others, the author explores the outlines of an abstract science of space, which includes a theory of proportions, an examination of "the golden section," a study of regular and semi-regular polyhedral, and the interlinking of these various shapes and forms. He then traces the transmission of this spatial science through the Pythagorean tradition and neo-Pythagorism, Greek, and Gothic canons of proportion, the Kabbala, Masonic traditions and symbols, and modern applications in architecture, painting, and decorative art. When we judge a work of art, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures both in art and nature that forms the core of Professor Ghyka's book. He also shows this geometry at work in living organisms. The ample illustrations and figures give concrete examples of the author's analysis: the Great Pyramid and tomb of Rameses IV, the Parthenon, Renaissance paintings and architecture, the work of Seurat, Le Corbusier, and flowers, shells, marine life, the human face, and much more.For the philosopher, scientist, archaeologist, art historian, biologist, poet, and artist as well as the general reader who wants to understand more about the fascinating properties of numbers and geometry, and their relationship to art and life, this is a thought-provoking book.

    The book has remained continuously in print through many editions and has some more than a quarter of a million copies. It is, as American Artist Magazine calls it, the "artist's bible," an invaluable reference for the painter, sculptor, and printmaker. During the past few years, however, new art movements and new research have led to many changes in the technology of artist's materials. With the assistance of Mayer's window, Bena, and his colleagues, Viking and Steven Sheehan, Director of the Ralph Mayer Center at Yale University, have prepared this latest revision of the book, which is now completely updated and expanded.

    Investigative reporters Laney Salisbury and Aly Sujo brilliantly recount the tale of a great con man and unforgettable villain, John Drewe, and his sometimes unwitting accomplices. Chief among those was the struggling artist John Myatt, a vulnerable single father who was manipulated by Drewe into becoming a prolific art forger. Once Myatt had painted the pieces, the real fraud began. Drewe managed to infiltrate the archives of the upper echelons of the British art world in order to fake the provenance of Myatt's forged pieces, hoping to irrevocably legitimize the fakes while effectively rewriting art history. The story stretches from London to Paris to New York, from tony Manhattan art galleries to the esteemed Giacometti and Dubuffet associations, to the archives at the Tate Gallery. This enormous swindle resulted in the introduction of at least two hundred forged paintings, some of them breathtakingly good and most of them selling for hundreds of thousands of dollars. Many of these fakes are still out in the world, considered genuine and hung prominently in private houses, large galleries, and prestigious museums. And the sacred archives, undermined by John Drewe, remain tainted to this day. Provenance reads like a well-plotted thriller, filled with unforgettable characters and told at a breakneck pace. But this is most certainly not fiction; Provenance is the meticulously researched and captivating account of one of the greatest cons in the history of art forgery.

    We make our homes in them. We go to school in them. We work in them. But why and how did people start making buildings? How did they learn to make them stronger, bigger, and more comfortable? Why did they start to decorate them in different ways? From the pyramid erected so that an Egyptian pharaoh would last forever to the dramatic, machine-like Pompidou Center designed by two young architects, Patrick Dillon’s stories of remarkable buildings — and the remarkable people who made them — celebrates the ingenuity of human creation. Stephen Biesty’s extraordinarily detailed illustrations take us inside famous buildings throughout history and demonstrate just how these marvelous structures fit together.

    Marina Abramovic: The Artist Is Present accompanies an exhibition at The Museum of Modern Art that documents approximately 50 of the artist's ephemeral time- and media-based works from throughout her career. The book also discusses a unique element of the Museum's retrospective, live performance: a new work created for the occasion, and performed by Abramovic herself; and re-creations of the artist's works by other performers-the first such to be undertaken in a museum setting. The book spans over four decades of Abramovic's early interventions and sound pieces, video works, installations, photographs, solo performances and collaborative performances made with the Dutch artist Ulay (Uwe Laysiepen). Essays by Klaus Biesenbach, Chief Curator of Media and performance art at MoMA, and four distinguished scholars examine Abramovic's ideas of time, duration and the reperformance of performance art as a way to extend it into posterity. The Artist Is Present also includes a CD with audio commentary by the artist that guides the reader through the publication. The artist is present not only in the exhibition but also in the experience of the book.Born in Belgrade just after the end of the Second World War, Marina Abramovic was raised in the Serbian Orthodox Church (her great uncle was a Patriarch and a canonized saint in the Church) and left Yugoslavia in 1976, having already established herself as a performance artist, living in Amsterdam and eventually New York, where she presently lives.

    Commissioned by the church and local nobility, El Greco produced dramatic paintings marked by distorted figures and vibrant color contrasted with subtle grays. Though his work was appreciated by his contemporaries, especially intellectuals, it wasn't until the 20th century that it was widely embraced and admired, influencing in particular the Expressionist movement.