Curves are seductive. These smooth, organic lines and surfaces—like those of the human body—appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world—from our bodies to Salvador Dalí’s paintings and the space-time fabric of the universe itself. The book focuses on seven curves—the fold, cusp, swallowtail, and butterfly, plus the hyperbolic, elliptical, and parabolic “umbilics”—and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician René Thom. In an accessible discussion illustrated with many photographs of the human nude, McRobie introduces these curves and then describes their role in nature, science, engineering, architecture, art, and other areas. The reader learns how these curves play out in everything from the stability of oil rigs and the study of distant galaxies to rainbows, the patterns of light on pool floors, and even the shape of human genitals. The book also discusses the role of these curves in the work of such artists as David Hockney, Henry Moore, and Anish Kapoor, with particular attention given to the delicate sculptures of Naum Gabo and the final paintings of Dalí, who said that Thom’s theory “bewitched all of my atoms.” A unique introduction to the language of beautiful curves, this book may change the way you see the world.

Allan McRobie is a Reader in the Engineering Department at the University of Cambridge, where he teaches stability theory and structural engineering. He previously worked as an engineer in Australia, designing bridges and towers.

"I have never encountered anything quite like [The Seduction of Curves], which I view as genuinely sui generis. . . . The (excellent) prose descriptions are accompanied by lots of illustrations, both photographs and drawings, quite a few of which are in color. . . . An unusual and eclectic book, and one that taught me a lot of things that I did not know before."—Mark Hunacek, MAA Reviews

"To illustrate this little-known branch of mathematics, [Allan McRobie] draws on the art of David Hockney, Henry Moore and Salvador Dalí, as well as Helena Weightman's superb photographs of mountains, mushrooms, reflections on water and naked bodies."—Matthew Reisz, Times Higher Education

"Stunning. . . . The balance is such that it should appeal both to art lovers and those with a real interest in the mathematical basis."—Brian Clegg, Popular Science

"Marvelous."—Adhemar Bultheel, European Mathematical Society

"Can you find your own butterflies, swallowtails and wigwams? They are right there on your body: the geometrical figures that appear when smoothly curved surfaces are viewed from the right angle. Structural engineer Allan McRobie's The Seduction of Curves is your guide to these most intimate of mathematical objects."—Philip Ball, New Scientist

"A delightful journey beyond disciplines. . . . The book intends to lead readers to see the world differently and I believe that in many cases it will, linking subtle mathematical ideas to the world they are surrounded by."—Edmund O. Harriss, MathSciNet

"This book is a bold attempt at evoking multiple feelings towards curves. Allan McRobie deserves praise for sensually drawing parallels between the natural and constructed worlds."—Sudhirendar Sharma, Current Science

"Both immediate and analytical, beautiful and informative, The Seduction of Curves is a successful hybrid of art book, representation of descriptive geometry, and explanation of mathematical concepts . . . . a book that entertains and teaches, pleases and challenges in equal measure."—Hans J. Rindisbach, European Legacy

"Remarkable. . . . Successful . . . due to the erudition of the author plus the quality of the production both in the illustrations used and in the general elegance of the book itself. It would grace the grandest of coffee tables and provide the basis for interesting debates."—Phil Dyke, Leonardo Reviews

"This is what a book should be: startling, bold, and beautiful, idiosyncratic and yet universal. Only Allan McRobie could have written it. But all of us can enjoy it. He shows us how to look at ourselves, our bodies, and our world in a new way. After just a few minutes you'll feel like you're seeing everything for the first time. Brilliantly conceived, poetically written, and utterly original, The Seduction of Curves is a sinuous delight."—Steven Strogatz, author of The Joy of x: A Guided Tour of Math, from One to Infinity

"McRobie, a mathematician with a deep knowledge of the visual arts and the human body's curves, has written a startlingly original book. The Seduction of Curves is a probing exploration of the parallels between nature and the constructed world—and the most striking illustrated mathematics book I've ever seen."—Michael Harris, author of Mathematics without Apologies: Portrait of a Problematic Vocation

"This is a mathematics book, a science book, and an art book—a seductive and richly illustrated work of cultural synthesis, in which the visible and hidden folds and surfaces of our bodies are described by modern geometry and connected to engineering, optics, and other applications."—Michael Berry, University of Bristol