Famous Problems of Elementary Geometry: The Duplication of the Cube, the Trisection of an Angle, the Quadrature of the Circle

Cosimo, Inc.
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"This short book, first published in 1897, addresses three geometry puzzles that have been passed down from ancient times. Written for high school students, this book aims to show a younger audience why math should matter and to make the problems found in math intriguing. Klein presents for his readers an investigation of the possibility or impossibility of finding solutions for the following problems in light of mathematics available to him: duplication of the cube trisection of an angle quadrature of the circle Mathematicians and students of the history of math will find this an intriguing work. German mathematician FELIX KLEIN (1849 1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis and Elementary Mathematics from an Advanced Standpoint: Geometry."
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Additional Information

Publisher
Cosimo, Inc.
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Published on
May 1, 2007
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Pages
96
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ISBN
9781602064171
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Best For
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Language
English
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Genres
Mathematics / Geometry / General
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Content Protection
This content is DRM protected.
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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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