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Publisher:

Princeton University Press

Publication Date:

2014

Number of Pages:

160

Format:

Hardcover

Price:

24.95

ISBN:

9780691160603

Category:

General

[Reviewed by , on ]

Mark Hunacek

06/9/2014

Just as you can’t judge a book by its cover, sometimes you can’t accurately judge one by its title either. Based on the title of this book, I assumed it was going to be all about computing, and as a result kept passing up the chance to select it as a book to review. Finally, though, curiosity got the best of me and I looked up a description, and discovered that my assumption was unwarranted. While computers are relevant to the topics here, this is a book that can be read on a beach even if the nearest computer is miles away.

What we have here is a collection of independent chapters, each an essay on various topics in mathematics that have at least some relationship to computers or algorithms. Scattered throughout the chapters are challenge problems, the solutions to which appear in a chapter at the end of the book. The chapters are intended for a fairly general audience without extensive mathematical experience. Indeed, even intelligent high school students could read a reasonable amount of this book with profit, although the author does occasionally succumb to the temptation of using mathematical symbols without prior explanation, as for example with an integral sign on page 65. The mathematical topics are interesting and informative; if you teach at the college level, you are likely to find some interesting fodder for your courses here. You also may, as I did, learn some new things yourself.

As an illustration, consider chapter 2 (“Deceiving Arithmetic”). The author points out that in an episode of *The Simpsons* cartoon show (many of the writers of which are mathematically trained), the equation 1782^{12} + 1841^{12} = 1922^{12 }appears, and uses this as a springboard for a discussion of Fermat’s Last Theorem. Of course (as the author points out), one doesn’t need to know Fermat’s Last Theorem to know that this equation can’t possibly be correct; the left-hand side is odd and the right-hand side is even. However, if one computes the 12^{th} root of the left hand side, the answer, on many calculators, does indeed turn out to be 1922. This is, of course, attributable to round-off error; a more precise answer is 1921.99999996. Likewise, as is mentioned in the text, in another episode of *The Simpsons*, the similar-looking equation 3987^{12} + 4365^{12} = 4472^{12} appears; this is not quite as obviously false, but again exhibits a similar phenomenon when calculated. As it happens, I had only learned of this latter example a few months back (from Singh’s book *The Simpsons and their Mathematical Secrets*) and mentioned it in a number theory class I was teaching last semester; the students seemed to get a kick out of it.

There are a dozen chapters (each about eight to twelve pages long) that follow this one, and although considerations of space make it impracticable for me to describe each one, I can at least hit some high points.

Chapter 4 (“Infinite Detail”) introduces fractals by, among other things, creating Sierpinski’s triangle by successively iterating a photo of the singer Beyoncé. (This is not, by the way, her only appearance in the book; she shows up in chapter 3 as well, in a discussion of exponential growth.)

Euler’s formula V – E + F = 2 is introduced in chapter 6 via doodles: draw a random doodle on a page (i.e., a curve with possibly many intersection points); here V is the number of intersection points (counting the start and ending points), E is the number of segments between any two dots, and F is the number of enclosed areas. From here, the author switches gears momentarily for a look at the Traveling Salesman Problem (TSP), and then ties everything together with a discussion of how the TSP can be used to create art, which in turn (by Euler’s formula, using the fact that V = E and so F =2) can be used to create a maze, with a well-defined “inside” and “outside”. I had never heard of “TSP Art” before looking at this book, but I now see that there are tons of references to it on the internet.

The phrase “chocolate-covered pi” that appears in the subtitle of the book refers to chapter 8, which uses differently colored M&Ms to approximate the area under a curve (everything takes place within a suitably large rectangle, and different color M&Ms appear below and above the curve, so that the area under the curve can be determined by simple arithmetic operations and counting). Having discussed the principle in general, the author then uses this method to explain how the number π can be approximated.

The last (and most mathematically sophisticated) chapter applies linear algebra to a nice discussion of the Google page rank algorithm. This chapter should be of considerable interest to anybody who teaches undergraduate linear algebra, since it illustrates how eigenvectors (of Markov transition matrices) are relevant to this issue. (The phrase “Google bomb” that appears in the subtitle of the book refers to how things can be manipulated so as to produce certain webpages with high page rank; the book concludes by pointing out how in 2003 the official White House biography of George Bush was listed as the highest ranked webpage in response to the search request “miserable failure”.)

There’s more, of course (including determining March Madness brackets and the mathematics of facial recognition), but you get the idea. This book, which is filled with photos, drawings, and anecdotes, is a treasure trove of amusing mathematical vignettes. It makes for very pleasant summer reading.

Mark Hunacek (mhunacek@iastate.edu) teaches mathematics at Iowa State University.

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