Proofs Without Words Ii. More Exercises In Visual Thinking

What are "proofs without words?" Many would argue that they are not really "proofs" (nor, for that matter, are many "without words," on account of equations which often accompany them). Like its predecessor Proofs Without Words, published by the MAA in 1993, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true, and also to see how one might begin to go about proving it true. The emphasis is on providing visual clues to the observer to stimulate mathematical thought. Proofs without words have been around for a long time. In this volume you find modern renditions of proofs without words from ancient China, tenth century Arabia, and Renaissance Italy. While the majority of the proofs without words in this book originally appeared in journals published by the MAA, others first appeared in journals published by other organizations in the US and abroad, and on the World Wide Web. The proofs in this collection are arranged by topic into five chapters. Although the proofs without words are presented primarily for the enjoyment of the reader, teachers will want to use them with students at many levels - in precalculus courses in high school, in college courses in calculus, number theory and combinatorics, and in pre-service and in-service classes for teachers.