Famous Problems of Geometry and How to Solve Them
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Numar articol:187837208
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Preț:57,00 Lei
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Anuntul a expirat la:22.12.2020, 14:57
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Specificatii
It took two millennia to prove the impossible; that is, to prove it
is not possible to solve some famous Greek problems in the Greek
way (using only straight edge and compasses). In the process of
trying to square the circle, trisect the angle and duplicate the
cube, other mathematical discoveries were made; for these seemingly
trivial diversions occupied some of history's great mathematical
minds. Why did Archimedes, Euclid, Newton, Fermat, Gauss, Descartes
among so many devote themselves to these conundrums? This book
brings readers actively into historical and modern procedures for
working the problems, and into the new mathematics that had to be
invented before they could be -solved.-The quest for the circle in
the square, the trisected angle, duplicated cube and other
straight-edge-compass constructions may be conveniently divided
into three periods: from the Greeks, to seventeenth-century
calculus and analytic geometry, to nineteenth-century
sophistication in irrational and transcendental numbers.
Mathematics teacher Benjamin Bold devotes a chapter to each
problem, with additional chapters on complex numbers and analytic
criteria for constructability. The author guides amateur
straight-edge puzzlists into these fascinating complexities with
commentary and sets of problems after each chapter. Some knowledge
of calculus will enable readers to follow the problems; full
solutions are given at the end of the book.Students of mathematics
and geometry, anyone who would like to challenge the Greeks at
their own game and simultaneously delve into the development of
modern mathematics, will appreciate this book. Find out how Gauss
decided to make mathematics his life work upon waking one morning
with a vision of a 17-sided polygon in his head; discover the
crucial significance of eπi = -1, -one of the most amazing formulas
in all of mathematics.- These famous problems, clearly explicated
and diagrammed, will amaze and edify curious students and math
connoisseurs.
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