Introduction: Mathematics, Riddles and Humour

1. Exploding the Image

2. The Hidden Image

3. Crystals

4. Circles and Ellipses

5. Skeleton and Structure

6. Taking the Wider View

7. Invariants

8. Special Cases

9. Summing Up

10. Metaphors

11. One Problem. Many Solutions

12. Pictures into Numbers

13. A Point of Balance

14. Multiple Meanings

15. Matching problems

16. The Game of Algebra

17. Pattern and Illusion

18. Clarity, Proof and Certainty

Hints for Solutions to Problems

Solutions to Problems

"The topics and the writing are engaging, with a lighthearted edge that allows the book to be inviting and not intimidating. Overall the quality of writing is excellent. A fine general audience mathematics book, but one that I think is particularly well-suited to younger, curious readers who have a basic knowledge of geometry and a beginning understanding of algebra." ? Mathematical Association of America

Everything in mathematics has many meanings ? every diagram and every figure, every sum and every equation can be "seen" in different ways, just as every sentence in English or in algebra can be variously read and interpreted. This book explores mathematical topics by pointing out remarkable similarities and taking a fresh look at familiar items. Loaded with thought-provoking facts and surprises, it explores the relationships between mathematics and humor, shows how mathematicians use metaphors to name the nameless and to point to hidden connections, and presents a series of challenging puzzles that offer thought-provoking fun.
You don't have to be a mathematician to appreciate this playful approach to numbers, patterns, graphs, and pictures. Author David Wells focuses on insight and imagination rather than technique, emphasizing the mystery, intrigue, and other pleasurable aspects of mathematics. Hints for the captivating problems and puzzles appear at the end of the book, in addition to complete solutions.

David Wells is a retired Associate Professor of Mathematics at Penn State New Kensington.