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Geometric Inequalities

Nicholas Kazarinoff


Kazarinoff's Geometric Inequalities will appeal to those who are already inclined toward mathematics. It proves a number of interesting inequalities; for example, of all triangles with the same perimeter, the equilateral triangle has the greatest area; of all quadrilaterals with a given area, the square has least perimeter; and the famous Steiner theorem, the circle has more area than any other plane figure with the same perimeter. The writing is honest. The author labels difficult what is difficult and does not pretend that to the master mind (who is usually the author) all things are simple. The text suggests guessing, conjecturing and then proving. The author does not hesitate to offer a proof of his own which; he points out, he later found to be incorrect. The device of putting a proof of a general theorem in one column and a concrete case alongside could be more widely employed by others. — MAA Reviewer

Anybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students.

Electronic ISBN: 9780883859223

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