Proofs Without Words III: Further Exercises in Visual Thinking, by Roger B. Nelsen, The Mathematical Association of America, Washington, D. C., 2016. 187 pp., $50.00 (paper). ISBN 978-0-88385-790-8.
While some may quibble about whether these images are rigorous mathematical proofs, none can dispute their power and elegance. Nelsen has once again captured the essence of mathematics in a series of easy to understand, yet thorough diagrams illustrating fundamental mathematical concepts.
The proofs are organized into five categories. They are:
*) Geometry & Algebra
*) Trigonometry, Calculus & Analytic Geometry
*) Integers & Integer Sums
*) Infinite Series & Other Topics
Instructors of courses covering this content will most likely find a diagram that they can use to visually demonstrate a concept. This could be of enormous help to some students that are experiencing difficulties. Personally, I have had several math students that were struggling come to me and say that they are “visual learners.” Which is of course true, humans naturally understand images better than thoughts expressed in symbols.
This book was made available for free for review purposes.