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.
