If only the plane on which fit into one another were infinitely large, then it would be possible to represent an infinite number of them, he continued. In 1959, in his essay Approaches to Infinity, Escher described the reasoning behind one of his intricately repeating designs, which featured a parade of reptiles, as follows: "Not yet true infinity but nevertheless a fragment of it a piece of ‘the universe of reptiles.’ Escher, who sought to capture the notion of infinity in visual images. The book’s title echoes thoughts of the Dutch graphic artist M. They highlight the processes of creativity, invention, and discovery intrinsic to mathematical research and to artistic endeavor. The following chapters offer a glimpse of the ways in which we can stretch our minds to imagine and explore exotic geometric realms. The tribe’s diversity of thought and custom, however, also brings to mind difficult questions of what constitutes mathematical art, what beauty means in that context, and what explicit role, if any, mathematics ought to play in the visual arts. Many of the artists and mathematicians mentioned in this book belong to this peripatetic tribe of math and art enthusiasts. One of my articles had focused on Helaman Ferguson, a sculptor and mathematician who not only works with computers but also carves marble and molds bronze into graceful, sensuous, mathematically inspired artworks.įriedman’s lively gathering introduced me to many more people who are fascinated by interactions between art and mathematics, and with them, I have attended and participated in subsequent meetings. My invitation to the pathbreaking meeting came about because of articles I had written for Science News highlighting the increasing use of visualization in mathematics, particularly the burgeoning role of computer graphics in illuminating and exploring mathematical ideas, from soap-film surfaces, fractals, and knots to chaos, hyperbolic space, and topological transformations. In 1992 I was invited to present the opening address at a remarkable meeting devoted to mathematics and art, organized by mathematician and sculptor Nat Friedman of the State University of New York at Albany. It delves into the endlessly fascinating mysteries of one-sided surfaces, four-dimensional spaces, self-similar structures, and other seemingly bizarre features of modern mathematics. It provides glimpses of artists enthralled by the unlimited possibilities offered by mathematically guided explorations of space and time. It portrays the work of several contemporary mathematicians who are also artists or whose mathematical thoughts have inspired others to create. This book is about creativity and imagination at the intersection of mathematics and art. Ivars Peterson (Washington, DC) is the mathematics writer and online editor of Science News and the author of The Jungles of Randomness (Wiley: 9-6), as well as four previous trade books. Featuring more than 250 beautiful illustrations and photographs of artworks ranging from sculptures both massive and minute to elaborate geometric tapestries and mosaics of startling complexity, this is an enthralling exploration of abstract shapes, space, and time made tangible. Portraying the work of many contemporary artists in media from metals to glass to snow, Fragments of Infinity draws us into the mysteries of one-sided surfaces, four-dimensional spaces, self-similar structures, and other bizarre or seemingly impossible features of modern mathematics as they are given visible expression. This intriguing book shows how intertwined the disciplines are. Mathematics is right brain work, art left brain, right? Not so. A visual journey to the intersection of math and imagination, guided by an award-winning author
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