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LIKE NEW: This book is in excellent, like-new condition.
Product Details
From the back cover: “The objective of When Less Is More 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 can not only show two things as 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 a part of a course on inequalities.”
BRIEF 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. Additional topics
- Solutions to the Challenges
- Notation and symbols
- References
- Index
- About the Authors