As Frank Morgan says in the introduction to this book, Math Chat is a live call-in show, a column, and now a book. Readers and viewers of Math Chat are encouraged to send in questions, answers, and comments on anything math related. The column is basically a "Dear Abby" for mathematics; or (along a more contemporary line) an "Ask Marilyn" column for mathematics. This book gives some of the questions and answers from past columns and shows.
One description (from the MAA) of The Math Chat Book says, "This book makes no attempt to fit any mold." Indeed, it is aimed at as wide an audience as possible. Non-mathematicians will almost certainly find something of interest here. Partly because of the wide range of topics, but also because of the absence of any particularly technical mathematics. Professional mathematicians will find many of the topics interesting also, but may lament the lack of math. (As one colleague put it, the book provides answers to the questions, but not solutions.) Nonetheless, mathematicians can still enjoy this book, as it often provides a good starting point for doing math. (For example, I used Episode 11--Infinitely Many Ping-Pong Balls--to introduce the properties of infinite cardinals to my abstract algebra class. Interestingly, the question comes from an undergraduate math text for liberal arts students: The Heart of Mathematics.)
There are five parts (which the author calls stories) to the book: "Time," "Probabilities and Possibilities," Prime Numbers and Computing," "Geometry," and "Physics and the World". The stories are divided into chapters (which the author calls episodes), each of which deals with some specific problem or question.
The first story, "Time," deals with questions about time zones, leaps years, perfect calendars (where all of the months have the same number of days), and a little geometry (How can the sun appear at the same spot on the horizon of a planet for a whole 24-hour day?). The second, "Probabilities and Possibilities," is about just what the title says. Two examples of questions from this section:
(From Episode 6) Suppose every couple keeps having children until they have a girl and then stops. Assuming boys and girls are equally likely, will this produce more baby boys or baby girls?
(From Episode 15) Joan entered a 26.5-mile marathon, and she hoped to average under nine minutes per mile over the total distance. She has some of her friends time her over various mile segments of the course. For each mile that was measured, in fact for each possible mile that could have been measured (starting anywhere), her time was exactly nine minutes. Could she have met her goal of averaging under nine minutes per mile?
The third story, "Prime Numbers and Computing," deals with large prime numbers, writing positive integers using four 4s, powers of 5, quaternions, the census, and the nature of intelligence. The fourth story, "Geometry," is short (three episodes) but has a lot in it. Soap bubbles (see the front cover) and road networks are discussed here. The reader may be interested to learn which three U. S. states meet at three different points. The final story is "Physics and the World." The questions here range from the familiar
If you are in a falling elevator, can you survive the impact by jumping just before the elevator hits the ground?
to the strange,
Does an airplane get lighter when the passengers eat lunch?
to the challenging,
Why do mirrors reverse left and right, but not up and down?
Some of the more interesting topics occur in the later sections. Episode 23 deals with soap bubbles, and the most efficient way to enclose two adjacent volumes with a minimum of surface area. Episode 28 talks about Richard Feynman's Sprinkler. (For Feynman's humorous account of his experiment, read Surely You're Joking Mr. Feynman.) Episode 24 discusses the shortest road network connecting the vertices of a regular n-gon. As mentioned earlier, the answers are given here--not the solutions. I found the case of the square to be interesting, and wanted to see the justification for the answer; but no justification is given. However, my interest was piqued. And this seems to be the point of the book. As the author says, "Enjoy math. It's for everybody. "
And, for the most part, this book is for everybody... although it is ideally suited for people with little or no math background. It is a nice recreational introduction to some of the uses of mathematics. Junior high and high school math students should enjoy it. Undergraduate math students might have fun with it too. For the mathematician, the book can be enjoyed as light reading. And any school or organization which regularly gives out books of this type as awards for math competitions might find this a good prize.
Speaking of prizes, the book has a $1000 Quest hidden somewhere within. See here for details.
Donald L. Vestal is Assistant Professor of Mathematics at Missouri Western State College. His interests include number theory, combinatorics, reading, and listening to the music of Rush. He can be reached at firstname.lastname@example.org.