Tales of impossibility : the 2000-year quest to solve the mathematical problems of antiquity / David S. Richeson

Format:

Book

Author/Creator:

Richeson, David S., author.

Language:

English

Subjects (All):

Mathematics, Ancient.

Physical Description:

1 online resource (451 pages)

Place of Publication:

Princeton, NJ : Princeton University Press, [2019]

Summary:

A comprehensive look at four of the most famous problems in mathematicsTales 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, Viète, 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.

Contents:

The four problems

Proving the impossible

Compass-and-straightedge constructions

The first mathematical crisis

Doubling the cube

The early history of pi

Quadratures

Archimedes's Number

The heptagon, the nonagon, and the other regular polygons

Neusis constructions

Curves

Getting by with less

The dawn of algebra

Viète's analytic art

Descartes's compass-and-straightedge arithmetic

Descartes and the problems of antiquity

Seventeenth-century quadratures of the circle

Complex numbers

Gauss's 17-gon

Pierre Wantzel

Irrational and transcendental numbers

Epilogue: Sirens or muses?

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Apr 2020)

ISBN:

9780691194233

0691194238

OCLC:

1110108642