Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics

If there is a better source of offbeat, interesting problems in applied mathematics, I have yet to see it. The closest is the similar book by Banks, Slicing Pizzas, Racing Turtles, and Further Adentures in Applied Mathematics. In this book, the first title problem concerns the engineering difficulties of towing icebergs from the polar regions to other locations in order to relieve water shortages. Complete in detail, it is a fascinating problem in engineering. The conclusion is that it can be done, and although it would be expensive, it does not involve any insurmountable problems. To me, the most amazing part was that the iceberg could be released several miles offshore and the inertia would allow it to literally coast to a stop in the desired location. Given the growing problems with the availability of fresh water, it appears that some day, we will see it happen. As a lifelong baseball fan, I found the chapter on the trajectory of baseballs fascinating. The table of the different pitches, their average speed and rate of rotation is one of the most informative collections of data that I have ever seen. In my youth, I struggled to throw curves, sliders and knuckle balls. I did occasionally get them to work, but seeing the required combination of velocity and spin explains a great deal as to why I failed so often. The chapter on the economic energy of a nation also held my interest. Using the formula for the kinetic energy of a particle as a model, Banks constructs a similar model based on the population and gross domestic product of a nation. The formula is E = ½ PG^2While there is clearly a bit of poetic license being applied in the chapter, it does have many valid points and when the formula is applied to several economic entities, the results seem quite reasonable. All teachers of mathematics are constantly in search of new problems to use in their courses. Students and instructors are collectively bored with the routine problems that seem to offer no new insights into what mathematics can be used for. In this book, you will find new uses for old mathematics that will make your creative hairs stand up straight.

Mathematics has been called the universal language. After reading Bank's book you might believe it's so. Banks takes the reader on a whirlwind tour of mathematical applications to a broad range of every-day events and phenomena. In doing so he exposes the reader not only to some fun and interesting mathematics but also to a better appreciation of analysis and how broadly it applies to our lives. As the title says, this is a book on applied mathematics. To read and enjoy it you need to understand basic integral calculus and solutions to differential equations. There's also a smattering of algebra, trigonometry, and geometry. One of the first things I noticed about the book is the breadth and scope of the topics. Banks does not live in a single corner of the world, but has obviously striven to sample a wide variety of mathematical applications in some remote corners of the world. There is, as the cover suggests, a mathematical treatment of towing icebergs, complete with cost and structural engineering analysis. This happens relatively close to the beginning of the book. Nearer the end of the book Banks has a chapter devoted to the science of waves in falling dominoes. In between is a wide selection of other topics, including quite a bit on exponential growth, both limited and unlimited, and its applications to lots of natural systems including alligator eggs, GNP, and deficit spending. Banks does more than simply describe physical problems and write down their differential equations. He also does a good job of explaining the phenomena. Nor do integrals and differential equations describe all the problems. A significant portion of the book, for example, is devoted to statistics and related things like curve fitting. And he does not forget the social sciences, either. Banks touches on such subjects as how to start a football game, a better way to score the Olympics, how to calculate the economic energy of a nation, and how to reduce the population. I found these subjects quite interesting, though I think the linear curve fit he used in the section on scoring the Olympics stretches my imagination. [To me, the data look pretty random. Indeed, the correlation coefficient is only slightly more than 0.5 (see figure 8.1 and correlation coefficient after equation (8.1)). Still, Banks (as if driven by a preconceived objective) presses on and applies a linear regression from which he later derives key results for his scoring method.]For the sports-minded among you Banks offers lots of examples of applied mathematics in the fields (pun intended) of baseball, golf, track, basketball, jumping rope, ski jumping, and the shot put. For example, did you know that a child jumping rope is swinging a curve called a troposkein? Furthermore, the troposkein is useful in vertical-axis wind turbines because the shape eliminates compression and bending forces. So the next time you see the kids jumping rope, tell