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-which demonstrated 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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