Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics

by Robert B. Banks

Have you ever daydreamed about digging a hole to the other side of the world? Robert Banks not only entertains such ideas but, better yet, he supplies the mathematical know-how to turn fantasies into problem-solving adventures. In this sequel to the popular Towing Icebergs, Falling Dominoes (Princeton, 1998), Banks presents another collection of puzzles for readers interested in sharpening their thinking and mathematical skills. The problems range from the wondrous to the eminently practical. In one chapter, the author helps us determine the total number of people who have lived on earth; in another, he shows how an understanding of mathematical curves can help a thrifty lover, armed with construction paper and scissors, keep expenses down on Valentine's Day. In twenty-six chapters, Banks chooses topics that are fairly easy to analyze using relatively simple mathematics. The phenomena he describes are ones that we encounter in our daily lives or can visualize without much trouble. For example, how do you get the most pizza slices with the least number of cuts? To go from point A to point B in a downpour of rain, should you walk slowly, jog moderately, or run as fast as possible to get least wet? What is the length of the seam on a baseball? If all the ice in the world melted, what would happen to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides? Covering a broad range of fields, from geography and environmental studies to map- and flag-making, Banks uses basic algebra and geometry to solve problems. If famous scientists have also pondered these questions, the author shares the historical details with the reader. Designed to entertain and to stimulate thinking, this book can be read for sheer personal enjoyment.

Genres: Science, Mathematics, Nonfiction

304 pages, Kindle Edition

First published January 1, 1999

Reviews

[J. · Rating 2 out of 5]

I'm unsure who the intended audience for this is. This book assumes an unusually high level of background, so it's not really for the general audience. You'd need to have a pretty solid knowledge of calculus to follow most of the arguments, but one of its strengths is that it's written very casually and informally--an unusual mix. The problem mix is also weird, because some of the examples are great, interesting and approachable, the kinds of things that would make great class projects. But some of them are not very good problems--they seem arbitrary, rest on strange assumptions and simplifications, and are analyzed in an unclear manner.

The author shows a good sense of humor, and I did get a few chuckles out of the book. But he also makes some minor errors here and there, like confusing properties of irrational and transcendental numbers; a mistake undergraduate mathematics major shouldn't even make.

Overall, I really enjoyed some sections, but others I had to just skim. A strangely unwieldy book.

[Jim D'Ambrosia · Rating 2 out of 5]

Mixed feelings. There are fun and elementary (relatively) problems here, such as: what proportions of the American flag are red, white, and blue, respectively? Other problems seem more arcane, and some, contrived. Granted, beauty is in the eye of the beholder.

The book could have used some tighter editing and polishing. I ended up skipping over all the derivations; they weren't along the lines that I usually think -- again, eye of the beholder -- but still I thought some could have been reworked for clarity. Getting technical, there were little omissions here and there, and awkward here and there that made understanding harder. For example, where Banks uses the integration variable in the same sentence as an external variable, and says this: "... the radius r as it rotates from theta=0 to theta=theta is ...". Sure, I knew what he meant, but I had to work a little harder than I should have to figure it out.

[Andrianna Ayiotis · Rating 5 out of 5]

This is a book that has stayed with me from my days as a teen tentatively interested in mathematics all the way to pursuing a PhD in engineering. The whimsical inquiries and back-of-the-envelope calculations always have me reaching for a pen. The introductions to branches of math classically viewed as inaccessible are masterfully done. I look forward to passing my (admittedly worn) copy down one day to someone else who can get the same amount of joy out of it that I have.

[Maurizio Codogno · Rating 2 out of 5]

Con questo secondo libro di Robert Banks ho forse capito qual è la logica sottostante: un ossimoro, considerando che stavolta Banks era rimasto a corto di esempi prettamente fisici ed è dovuto affidarsi alla matematica per completare il testo. Più che un libro di divulgazione matematica, è infatti un libro per professori - a questo punto non saprei nemmeno definire a che livello, considerando che spesso è necessario un po' di calcolo differenziale - che vogliano presentare qualcosa di diverso ai propri studenti. Preso da questo punto di vista, il libro è in effetti interessante: allo stesso tempo, ciò però significa che non è poi il massimo da leggere se si ha voglia di scoprire qualcosa di divertente.

[Mark · Rating 4 out of 5]

This is not a book of math puzzles or math history. This is a book primarily about applied mathematics, or what "word problems" look like in the real world.

I slightly prefer the previous book Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics by this author. The author seems to have run a bit short on applied problems and adds in some standard topics (e.g. primes, Fibonacci) and some contrived problems (e.g. making a heart-like curve) to fill out the book. The exposition is still as good as the first book.

[Rosemary · Rating 2 out of 5]

We didn't finish this although some topics were quite interesting.