When Less is More: Visualizing Basic Inequalities

Dolciani Mathematical Expositions

by Claudi Alsina, Roger B. Nelsen

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.

Genres: Mathematics

199 pages, Hardcover

First published January 1, 2009

About the author

Claudi Alsina (Barcelona, 1952) es catedrático de matemáticas de la E.T.S. de Arquitectura de Barcelona en la Universidad Politécnica de Catalunya. Ha realizado una amplia labor de investigación matemática, de innovación educativa y de divulgación, tanto a nivel nacional como internacional. Autor de numerosas obras de popularización de las matemáticas, es un reconocido escritor y conferenciante. Resultado de sus viajes y de su forma de mirar el mundo es la presente guía. En Ariel ha publicado Vitaminas matemáticas y El club de la hipotenusa, Vitaminas matemáticas y Geometría para turistas.