# When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions)

## Claudi Alsina; Roger Nelsen

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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.

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.

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Book Description:

An introduction to basic inequalities in mathematics (including numbers, functions and geometry) motivated and illustrated by drawings that make it possible to 'see' the results in an elegant manner. Applications of the inequalities, historical details, and exercises for the reader (with solutions) are also included.

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 MatemÃƒÂ¡ticas 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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## 1.When Less is More: Visualizing Basic Inequalities (Hardback)

Editorial: Mathematical Association of America, United States (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
Librería
The Book Depository
(London, Reino Unido)
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Descripción Mathematical Association of America, United States, 2009. Hardback. Estado de conservación: New. UK ed.. Language: English . Brand New Book. 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. Nº de ref. de la librería AAA9780883853429

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## 2.When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions)

Editorial: The Mathematical Association of America
ISBN 10: 0883853426 ISBN 13: 9780883853429
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THE SAINT BOOKSTORE
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Descripción The Mathematical Association of America. Hardcover. Estado de conservación: New. New copy - Usually dispatched within 2 working days. Nº de ref. de la librería B9780883853429

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## 3.When Less is More: Visualizing Basic Inequalities (Hardback)

Editorial: Mathematical Association of America, United States (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción Mathematical Association of America, United States, 2009. Hardback. Estado de conservación: New. UK ed.. Language: English . Brand New Book. 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. Nº de ref. de la librería AAA9780883853429

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## 4.When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions)

Editorial: The Mathematical Association of America (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
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Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
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Descripción The Mathematical Association of America, 2009. Hardcover. Estado de conservación: New. Brand new. Clean, unmarked pages. Fine binding and cover. Hardcover. Ships daily. Nº de ref. de la librería 1603230135

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## 5.When Less is More: Visualizing Basic Inequalities

Editorial: Cambridge University Press (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
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Revaluation Books
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Descripción Cambridge University Press, 2009. Hardcover. Estado de conservación: Brand New. 1st edition. 250 pages. 9.25x6.25x0.75 inches. In Stock. Nº de ref. de la librería __0883853426

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## 6.When Less is More

ISBN 10: 0883853426 ISBN 13: 9780883853429
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Herb Tandree Philosophy Books
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Descripción 2009. Hardback. Estado de conservación: NEW. 9780883853429 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0483752

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## 7.When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions)

Editorial: The Mathematical Association of America (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
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Ergodebooks
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Descripción The Mathematical Association of America, 2009. Hardcover. Estado de conservación: New. 1. Nº de ref. de la librería DADAX0883853426

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## 8.When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions)

Editorial: The Mathematical Association of America (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
Nuevos Tapa dura Primera edición Cantidad: 1
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Irish Booksellers
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Descripción The Mathematical Association of America, 2009. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M0883853426

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## 9.When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions)

Editorial: The Mathematical Association o (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
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Murray Media
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Descripción The Mathematical Association o, 2009. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P110883853426

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## 10.When Less is More: Visualizing Basic Inequalities

Editorial: Cambridge University Press (2009)
ISBN 10: 0883853426 ISBN 13: 9780883853429
Librería
Revaluation Books
(Exeter, Reino Unido)
Valoración

Descripción Cambridge University Press, 2009. Hardcover. Estado de conservación: Brand New. 1st edition. 250 pages. 9.25x6.25x0.75 inches. In Stock. Nº de ref. de la librería zr0883853426

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