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Math Trek: Adventures in the MathZone

Ivars Peterson and Nancy Henderson
Publication Date: 
Number of Pages: 
[Reviewed by
Mary Shepherd
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Math Trek is a children's book, suitable for children age 10 and older according to the publisher. It takes children through a variety of different mathematical ideas where kids can do some of the things mathematicians do. There is no formalism required. The book contains a series of readings and activities presented as amusement park activities to entice readers, especially young people, with some mathematical concepts. Each section includes at least one application of the particular mathematical idea. The hope is that in the process young readers may begin to learn why mathematicians enjoy their work so much.

Each chapter addresses one or two related concepts, explaining some simple problems, asking some questions and often giving one or more activities based on the concept. Most chapters give some historical perspective on the problem and/or a current use of the concept. There are answers to each question in the back of the book along with a glossary and a list of further readings including a web site where one can go for additional material. A brief tour of the site showed that it is easy to navigate and has links to many other web sites.

As an example of what you can expect in the book, let's look at the first chapter, entitled "Do Knot Enter." It discusses knots and unknots. The reader is asked to identify which of five "knots" is not a knot in order to enter the MathZone amusement park. To do this, the reader is given instructions for using a piece of string and tape to create knots or unknots. The reader may then create the various knots to figure out this initial problem, and, we hope, gets to see how similar knots, such as the granny knot and square knot are really different. There is also a page long account of how scientists are studying knots and unknots of DNA strands to learn how some viruses work.

Other chapters, with titles such as, "The MapZone," "The Crazy Roller Coaster," "Mersenne's Fun House," "The Fractal Pond Race," "Tilt-A-Whirl Madness," "Luck of the Boredwalk," "The Code-Locked Door," and "The Wild Game Hall," deal, respectively, with map coloring, twisted surfaces and topology, number theory and Mersenne primes, fractal shapes, chaos theory, probability theory using some "weird" dice, codes using binary numbers, and billiards using different shaped tables. The final chapter, "Way Out!" is a small "test" of what the reader encountered while in the park.

I had to become a kid again to read this book, which was a treat in itself. My favorite chapters were the ones on knots, map coloring, chaos theory and probability theory. I enjoyed the chapter on knots because of its discussion of the trefoil knot. Knot theory is not in my background and I was intrigued that the mirror image of the trefoil know is a different knot. I wonder how you could get this across to a 10 year old. In the map coloring chapter, I enjoyed the actual coloring activities. I could have spent several days with some of the challenges presented in this chapter. The chaos chapter gave the actual amusement park ride, the Tilt-A-Whirl, as an example of a mathematically chaotic system. That was my favorite ride as a child. In this chapter the reader can actually build his/her own chaotic system of a double pendulum with straws, string and clay. In the probability theory chapter, "weird" dice were introduced. These are dice with faces numbered differently from the standard one through six, but for which, when rolled in pairs, the sums of the faces have the same probabilities as with standard dice. I particularly enjoyed the discussion of how the strategy for the game Monopoly would change using these "weird" dice.

The chapter I found most difficult to accept was the one on twisted surfaces and topology. I had a hard time suspending my belief in the law of gravity so that Möbius strip roller coaster or slide would be possible. The recycling symbol as displayed in this chapter is not a Möbius strip, although the text says it is. This is the one error I noticed. (There is a note about this on the web site for the book.) This chapter also introduces the field of topology with the coffee cup to donut transformation, but left me wondering why a picture of the sculpture of a Costa surface was included.

I enjoyed the book, and I know I would have enjoyed it as a youth, also. It is not rigorous, but it is fun. It is appropriate both for the math literate and not so math literate young person. The cartoon-like illustrations and sometimes simplistic style make it truly a children's book, for young people generally aged 10 or so. I think it could be a potential resource for mathematical activity ideas for elementary and middle school teachers, and therefore it could also be used as supplemental reading in math content courses for future or in-service teachers. I think adults who have avoided math might enjoy the book also, especially if read and worked on with a young person. It is a rare chance for young people to enjoy mathematical activities.

Mary Shepherd, ( is Assistant Professor at SUNY College at Potsdam in Potsdam, New York. Her special interests are differential geometry and music.

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