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Proofs Without Words: Exercises in Visual Thinking

Proofs Without Words: Exercises in Visual Thinking

By Roger B. Nelsen

Catalog Code: PWW
Print ISBN: 978-0-88385-700-7
160 pp., Paperbound, 1993
List Price: $41.00
MAA Member: $30.75
Series: Classroom Resource Materials

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Proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus, and analytic geometry; inequalities; integer sums; sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Table of Contents

1. Geometry and Algebra
2. Trigonometry, Calculus & Analytic Geometry
3. Inequalities
4. Integer Sums
5. Sequences and Series
Index of Names

About the Author

Roger Nelsen received his BA in mathematics from DePauw University in 1964 and his PhD in mathematics from Duke University in 1969. Roger was elected to Phi Beta Kappa and Sigma Xi, and taught mathematics and statistics at Lewis & Clark College in Portland, Oregon for 40 years before his retirement in 2009. His other books include: An Introductions to Copulas, Springer, 1999 (2nd ed. 2006); Proofs Without Words II: More Exercises in Visual Thinking, MAA, 2000; Math Made Visual: Creating Images for Understanding Mathematics (with Claudi Alsina), MAA, 2006; When Less is More: Visualizine Basic Inequalities (with Claudi Alsina), MAA, 2009; The Calculus Collection: A Resource for AP and Beyond (with Caren Diefenderfer, editors), MAA, 2010; and Charming Proofs: A Journey Into Elegant Mathematics (with Claudi Alsina), MAA, 2010.

MAA Review

This slim collection of varied visual “proofs” (a term, it can be argued, loosely applied here) is entertaining and enlightening. I personally find such representations engaging and stimulating aids to that “aha!” moment when symbolic argument seems not to clarify. Since such pictures can be found sprinkled in the pages of many mathematics periodicals and even in the occasional textbook, others obviously feel the same way. A collection of a gross of them in a single volume is really a delight to peruse. Continued...