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Publisher:

Mathematical Association of America

Publication Date:

2001

Number of Pages:

232

Format:

Paperback

Series:

Classroom Resource Materials

Price:

32.95

ISBN:

088385-717-0

Category:

General

[Reviewed by , on ]

Herbert E. Kasube

12/27/2001

This book is different! Most "problem books" contain many difficult and thought-provoking problems that are usually tackled with pencil and paper. The problems contained in such books tend to be at the level of the Mathematics Olympiad. As an example of such a text I refer you to Mathematical Olympiad Challenges by Andreescu and Gelca (Birkhäuser, 2000). As the subtitle of the book under review indicates, the problems in this book are more activity-oriented. Some use pencil and paper, but most require that the students actually move around.

For example, an activity labeled "Laundry Math" involves the topological aspects of turning a shirt or pair of pants inside out. This kind of problem is not to be found in most texts. Another activity called "Get Knotted" presents three activities referred to as "party tricks". We even see photographs of students performing these "tricks".

Before you get the wrong idea, be aware that there is serious mathematics being presented here. In addition to the laundry quandary mentioned above, topology shows up in some Möbius constructions, slicing a bagel and coloring a map on a torus We also encounter probability questions along the way. Chapter 25 is entitled *Weird Lotteries* and certainly lives up to that title. Graph theory appears in a few places, including Chapter 30 on *Chessboard Maneuvers*.

The book is full of photographs of students actually taking part in these activities. What a nice touch! Instead of merely describing the problem in words we actually see people riding bicycles (Chapter 9), turning pants inside out (Chapter 17) and blowing bubbles (Chapter 21).

The author has kindly included extensive hints and solutions in Part II of the book. These are clearly written and very informative.

If you are looking for a book to help students prepare for the Mathematical Olympiad or the Putnam Exam, this one is **not** for you. If, on the other hand, you want a book with a bounty of activities that you could use in your mathematics classroom or as part of a mathematics club try this one. We as mathematicians are always looking for ways to stimulate interest in mathematics in others. In particular, if one were to visit a high school mathematics classroom and want to show the students that mathematics can actually be FUN, look to this book for some wonderful ideas.

**Herbert E. Kasube** (hkasube@hilltop.bradley.edu) is associate professor of mathematics at Bradley University. His mathematical interests include number theory, discrete mathematics and the history of mathematics. When not doing mathematics he can often be found jogging around the streets of Peoria.

Part I: Activities and Problem Statements

1. Distribution Dilemmas

2. Weird Shapes

3. Counting the Odds…and Evens

4. Dicing, Slicing and Avoiding the Bad Bits

5. "Impossible" Paper Tricks

6. Tiling Challenges

7. Things that Won't Fall Down

8. Mobius Madness: Tortuous Twists on a Classic Theme

9. The Infamous Bicycle Problem

10. Making Surfaces in 3- and 4-Dimensional Space

11. Paradoxes in Probability Theory

12. Don't Turn Around Just Once!

13. It's All in a Square

14. Bagel Math

15. Capturing Chaos

16. Who Has the Advantage?

17. Laundry Math

18. Get Knotted!

19. Tiling and Walking

20. Automata Antics

21. Bubble Trouble

22. Halves and Doubles

23. Playing with Playing Cards

24. Map Mechanics

25. Weird Lotteries

26. Flipped Out

27. Parts That Do Not Add to Their Whole

28. Making the Sacrifice

29. Problems in Parity

30. Chessboard Maneuvers

Part II: Hints, Solutions and Further Thoughts

Part III: Solutions and Discussions

References

Index

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