“a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance”
Is it possible to create mathematical drawings that help students understand mathematical ideas, proofs and arguments? We are convinced that the answer is yes and our objective in this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest.
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.” Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books and on the WorldWide Web. Popularizing this genre was the motivation for the second author of this book in publishing the collections [Nelsen, 1993 and 2000].
The first author became interested in creating proofs without words some years ago and more recently began a systematic study on how to teach others to design such pictures. This led him to organize and present many workshops on the topic devoted to secondary and university teachers. Consequently, we decided to join forces and prepare this book, extending a mathematical collaboration that goes back many years.
Often times, a person encountering a “proof without words” may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of exceptional ingenuity on the part of the picture's creator.
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