Fragments of Infinity: A Kaleidoscope of Math and Art

Fragments of Infinity: A Kaleidoscope of Math and Art

by Ivars Peterson
     
 

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A visual journey to the intersection of math and imagination, guided by an award-winning author
Mathematics is right brain work, art left brain, right? Not so. This intriguing book shows how intertwined the disciplines are. Portraying the work of many contemporary artists in media from metals to glass to snow, Fragments of Infinity draws us into the mysteries of… See more details below

Overview

A visual journey to the intersection of math and imagination, guided by an award-winning author
Mathematics is right brain work, art left brain, right? Not so. This intriguing book shows how intertwined the disciplines are. 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. 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.
Ivars Peterson (Washington, DC) is the mathematics writer and online editor of Science News and the author of The Jungles of Randomness (Wiley: 0-471-16449-6), as well as four previous trade books.

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Editorial Reviews

Publishers Weekly
What do math equations look like when the numbers are translated into form and the form is rendered in, say, silk, or glass? In Fragments of Infinity: A Kaleidoscope of Math and Art, Ivars Peterson (The Jungles of Randomness), a writer and editor at Science News, studies sculpture inspired by abstract math. Many among this breed appear in plazas and subway stations; others get little visibility, being too minute or fragile. Quasicrystals and hypercubes rendered in glass and metal; lattices transformed into different geometric patterns; M?bius strips made of everything from ribbon to bronze; computer sculpture generators via numerous methods and media, the work examined explores "the beauty of embedded possibility." Helaman Ferguson, Harriet Brisson and William Webber are among the artists represented. 250-plus photos and illus. (Oct.) Copyright 2001 Cahners Business Information.

Product Details

ISBN-13:
9780470341124
Publisher:
Turner Publishing Company
Publication date:
05/02/2008
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
240
File size:
17 MB
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This product may take a few minutes to download.

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This book is about creativity and imagination at the intersection of mathematics and art. It portrays the work of several contemporary mathematicians who are also artists or whose mathematical thoughts have inspired others to create. It provides glimpses of artists enthralled by the unlimited possibilities offered by mathematically guided explorations of space and time. 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.

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. 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. 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.

Friedman'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. Many of the artists and mathematicians mentioned in this book belong to this peripatetic tribe of math and art enthusiasts. 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. The following chapters offer a glimpse of the ways in which we can stretch our minds to imagine and explore exotic geometric realms. They highlight the processes of creativity, invention, and discovery intrinsic to mathematical research and to artistic endeavor.

The book's title echoes thoughts of the Dutch graphic artist M. C. Escher, who sought to capture the notion of infinity in visual images. 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. '

"If only the plane on which [the tiles] fit into one another were infinitely large, then it would be possible to represent an infinite number of them," he continued. "However, we aren't playing an intellectual game here; we are aware that we live in a material, three-dimensional reality, and we cannot manufacture a plane that extends infinitely in all directions."

Escher's solution to his immediate artistic dilemma was to "bend the piece of paper on which this world of reptiles is represented fragmentarily and make a paper cylinder in such a way that the animal figures on its surface continue to fit together without interruptions while the tube revolves around its lengthwise axis." It was just one of many highly original schemes that Escher devised in his attempts to capture infinity visually. Other artists share this passion (or perhaps obsession) for visualizing creations of the mind, whether theorem or dream, and rendering them in concrete form, and they, too, must overcome limitations of their tools and their place in the natural world to present glimpses or fragments of these conceivable yet elusive realms.

Special thanks go to Helaman Ferguson and Nat Friedman, who introduced me to many of the people who and the ideas that inspired and encouraged my travels in the surprisingly wide and diverse world of mathematical art.

I also wish to thank the following persons for their help in explaining ideas, providing illustrations, or supplying other material for this book: Don Albers, Tom Banchoff, Bob Brill, Harriet Brisson, John Bruning, Donald Caspar, Davide Cervone, Benigna Chilla, Barry Cipra, Brent Collins, John Conway, H. S. M. Coxeter, Erik Demaine, Ben Dickins, Stewart Dickson, Doug Dunham, Claire Ferguson, Mike Field, Eric Fontano, George Francis, Martin Gardner, Bathsheba Grossman, George Hart, Linda Henderson, Paul Hildebrandt, Tom Hull, Robert Krawczyk, Robert Lang, Howard Levine, Cliff Long, Robert Longhurst, Shiela Morgan, Eleni Mylonas, Chris K. Palmer, Doug Peden, Roger Penrose, Charles Perry, Cliff Pickover, Tony Robbin, John Robinson, Carlo Roselli, John Safer, Reza Sarhangi, Doris Schattschneider, Dan Schwalbe, Marjorie Senechal, Carlo S�quin, John Sharp, Rhonda Roland Shearer, Arthur Silverman, John Sims, Clifford Singer, Arlene Stamp, Paul Steinhardt, John Sullivan, Keizo Ushio, Helena Verrill, Stan Wagon, William Webber, Jeff Weeks, and Elizabeth Whiteley. My apologies to anyone I have inadvertently failed to include in the list.

I am grateful to my editors at Science News, Joel Greenberg, Pat Young, and Julie Ann Miller, for allowing me to venture occasionally into topics that didn't always fit comfortably within the purview of newsworthy scientific and mathematical research advances. Some of the material in this book has appeared in a somewhat different form in Science News.

I wish to thank my wife, Nancy, for many helpful suggestions while reviewing the original manuscript. I greatly appreciate the efforts of everyone at Wiley who worked so hard to transform an unwieldy stack of manuscript pages and numerous illustrations in a wide variety of formats into the finished book.

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