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King of Infinite Space : Donald Coxeter, the Man Who Saved Geometry
"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." --Brian Greene, author of The Elegant Universe
The word "geometry" brings to mind an array of mathematical images: circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives--from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.
Many of the greatest names in intellectual history--Pythagoras, Plato, Archimedes, Euclid-- were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions--his famed Coxeter groups and Coxeter diagrams--have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.
Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesicdome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.
During the latter half of the 20th century, geometry largely fell out of favor within the mathematical community. As Canadian journalist Roberts so well describes in her first book, Donald Coxeter (1907-2003), a University of Toronto mathematician, almost singlehandedly preserved and advanced the discipline through hard work and acute insights. His impact has been felt in a wide variety of fields and acknowledged by the likes of Buckminster Fuller and M.C. Escher. Coxeter also helped transform mathematics education to bring geometry back into the mainstream. This change is critical because, as Roberts explains, a robust understanding of geometry is essential for progress in disciplines from crystallography to cosmology, and from video graphics to immunology. Given Coxeter's long life and career, his biography, in large part, tells the story of mathematics in the 20th century as well as a human portrait of a man who--despite his royal title--was a "humble, hands-on geometer." Roberts, who won a National Magazine Award for a Toronto Life profile of Coxeter, puts most of the technical material in appendixes, so the text is readily accessible to a general audience. 70 b&w photos and diagrams. (Sept.)
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September 19, 2009
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