The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.

About the Author

Claudi Alsina received his B.A. and Ph.D. in mathematics from the University of Barcelona. He did Post-doctoral studies at the University of Massachusetts, Amherst. Currently he is a Professor of mathematics at the Technical University of Catalonia. He participates in a a wide range of international activities, and has written several research papers and publications on mathematics and mathematics education.

Roger Nelsen received his B.A. in mathematics from DePauw University and a ; Ph.D. in mathematics from Duke University in 1969. He 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 ed. 2006); Proofs Without Words II: More Exercises in Visual Thinking, MAA, 2000.

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