Proofs Without Words II: More Exercises in Visual Thinking By: Roger B Nelsen

Author: Roger B. Nelsen

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:
geometry and algebra; trigonometry, calculus, and analytic geometry;
inequalities; integer sums, and infinite series; and linear algebra. 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.

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