Overview

A comprehensive look at four of the most famous problems in mathematics. Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems-squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle-have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs-demonstrating the impossibility of solving them using only a compass and straightedge-depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viete, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

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9780691218724

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Reviews

I greatly enjoyed Richeson's Tales of Impossibility. It deserves to become a classic and can be highly recommended. ---Robin Wilson, Times Higher Education Even if you never read a single proof through to its conclusion, you'll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school. ---Jim Stein, New Books in Mathematics The whole book, both informative and amusing, is a highly recommended read. ---Adhemar Bulteel, European Mathematical Society This book was a pleasure to read and I would recommend it for anybody who wants a lovely overview of many areas of the history of mathematics, with a focus on some very easy to understand problems. ---Jonathan Shock, Mathemafrica Richeson clearly explains what it means to be impossible to solve a problem, cites other impossibility results, goes into detail about geometric constructions with various instruments, and discusses the defective proofs and the cranks that have turned up along the way. * Mathematics Magazine * This fascinating text will appeal to all those interested in the history of mathematics, not leasy because of its helpful notes on each chapter and its two dozen pages of references for further reading ---Laurence E. Nicholas CMath FIMA, Mathematics Today

Richeson clearly explains what it means to be impossible to solve a problem, cites other impossibility results, goes into detail about geometric constructions with various instruments, and discusses the defective proofs and the cranks that have turned up along the way. * Mathematics Magazine * Even if you never read a single proof through to its conclusion, you'll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school. ---Jim Stein, New Books in Mathematics The whole book, both informative and amusing, is a highly recommended read. ---Adhemar Bulteel, European Mathematical Society This book was a pleasure to read and I would recommend it for anybody who wants a lovely overview of many areas of the history of mathematics, with a focus on some very easy to understand problems. ---Jonathan Shock, Mathemafrica I greatly enjoyed Richeson's Tales of Impossibility. It deserves to become a classic and can be highly recommended. ---Robin Wilson, Times Higher Education

Author Information

David S. Richeson is professor of mathematics and the John J. and Ann Curley Faculty Chair in the Liberal Arts at Dickinson College. He is the author of Euler's Gem: The Polyhedron Formula and the Birth of Topology (Princeton). Twitter @divbyzero

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