When Less is More: Visualizing Basic Inequalities

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Brand new. We distribute directly for the publisher. Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too ... often, especially in secondary and collegiate mathematics, the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they don???t possess the richness and variety that one finds with inequalities.The objective of this book is to illustrate how the use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and the authors will convince you that the same is true when working with inequalities. They show how to produce figures in a systematic way for the illustration of inequalities and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument cannot only show two things unequal, but also help the observer see just how unequal they are.The concentration on geometric inequalities is partially motivated by the hope that secondary and collegiate teachers might use these pictures with their students. Teachers may wish to use one of the drawings when an inequality arises in the course. Alternatively, When Less Is More might serve as a guide for devoting some time to inequalities and problem solving techniques, or even as part of a course on inequalities. Read more Show Less

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2009 Hardcover New Book New and in stock. 4/9/2009. *****PLEASE NOTE: This item is shipping from an authorized seller in Europe. In the event that a return is necessary, you ... will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** Read more Show Less

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Overview

Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they don't possess the richness and variety that one finds with inequalities. The objective of this book is to illustrate how use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and we would like to convince you that the same is true when working with inequalities. We show how to produce figures in a systematic way for the illustration of inequalities; and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument can not only show two things unequal, but also help the observer see just how unequal they are.

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Product Details

  • ISBN-13: 9780883853429
  • Publisher: Mathematical Association of America
  • Publication date: 3/31/2009
  • Edition description: New Edition
  • Pages: 204
  • Product dimensions: 6.00 (w) x 9.10 (h) x 0.60 (d)

Meet the Author

Claudi Alsina received his B.A. and Ph.D. in mathematics from the University of Barcelona. His post-doctoral studies were at the University of Massachusetts, Amherst. He is Professor of Mathematics at the Technical University of Catalonia and has developed a wide range of international activities, research papers, publications and hundreds of lectures on mathematics and mathematics education. His latest books include Associative Functions: Triangular Norms and Copulas with M. J. Frank and B. Schweizer, WSP, 2006; Math Made Visual. Creating Images for Understanding Mathematics with Roger B. Nelsen, MAA, 2006; Vitaminas Matemáticas and El Club de la Hipotenusa, Ariel, 2008.

Roger B. Nelsen received his B.A. in mathematics from DePauw University in 1964 and his Ph.D. in mathematics from Duke University in 1969. Roger was elected to Phi Beta Kappa and Sigma Xi. His previous books include Proofs Without Words: Exercises in Visual Thinking, MAA 1993; An Introduction to Copulas, Springer, 1999 (2nd edition 2006); Proofs Without Words II: More Exercises in Visual Thinking, MAA, 2000; and Math Made Visual: Creating Images for Understanding Mathematics (with Claudi Alsina), MAA, 2006.

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Table of Contents

Preface; Introduction; 1. Representing positive numbers as lengths of segments; 2. Representing positive numbers as areas or volumes; 3. Inequalities and the existence of triangles; 4. Using incircles and circumcircles; 5. Using reflections; 6. Using rotations; 7. Employing non-isometric transformations; 8. Employing graphs of functions; 9. Additions topics; Solutions to the challenges; Selected open challenges for visualizing inequalities; Symbols and notation; References; Index.

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