# When Less Is More: Visualizing Basic Inequalities

### By Claudi Alsina and Roger B. Nelsen

Catalog Code: DOL-36
Print ISBN: 978-0-88385-342-9
Electronic ISBN: 978-1-61444-202-8
164 pp., Hardbound, 2009
List Price: $59.95 MAA Member:$48.95
Series: Dolciani Mathematical Expositions

The objective of this book is to illustrate how the use of visualization can be a powerful tool for better understanding of 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.

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
Solutions to the Challenges
Notation and symbols
References
Index