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Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity

David S. Richeson

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Princeton University Press
01 October 2019
Mathematics & Sciences; Philosophy of mathematics; History of mathematics
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.
By:   David S. Richeson
Imprint:   Princeton University Press
Country of Publication:   United States
Dimensions:   Height: 235mm,  Width: 156mm, 
ISBN:   9780691192963
ISBN 10:   0691192960
Pages:   456
Publication Date:   01 October 2019
Audience:   College/higher education ,  Professional and scholarly ,  General/trade ,  Primary ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

David S. Richeson is professor of mathematics at Dickinson College and editor of Math Horizons. He is the author of Euler's Gem: The Polyhedron Formula and the Birth of Topology (Princeton). Twitter @divbyzero

Reviews for Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity

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


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