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.

    We all have a mental picture of ancient Egypt, but is it the right one? How much do we really know about this once great civilization?In this absorbing introduction, Ian Shaw, one of the foremost authorities on Ancient Egypt, describes how our current ideas about Egypt are based not only on the thrilling discoveries made by early Egyptologists but also on fascinating new kinds of evidence produced by modern scientific and linguistic analyses. He also explores the changing influences on our responses to these finds, by examining the impact of Egyptology on various aspects of popular culture such as literature, cinema, opera, and contemporary art. He considers all aspects of ancient Egyptian culture, from tombs and mummies to the discovery of artifacts and the decipherment of hieroglyphs, and from despotic pharaohs to animal-headed gods. From the general reader interested in Ancient Egypt, to students and teachers of ancient history and archaeology, to museum-goers, this Very Short Introduction will not disappoint.

    This book gives a succinct explanation of his metaphysical system, concentrating on the original aspects of his thought, which inspired many artists and thinkers including Nietzsche, Wagner, Freud, and Wittgenstein. Schopenhauer's central notion is that of the will--a blind, irrational force that he uses to interpret both the human mind and the whole of nature. Seeing human behavior as that of a natural organism governed by the will to life, Schopenhauer developed radical insights concerning the unconscious and sexuality which influenced both psychologists and philosophers

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.