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

Robert B. Banks (1922-2002) has written two marvelous books illustrating what applied mathematics really is about. The present one was the first to appear in 1998 and his Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics was a sequel that was published in 1999. This version is the first edition in paperback.

In 24 chapters the reader is bombarded by a firework of models and solutions for serious and amusing problems. The opening paragraph is typical giving all the data about the meteor that hit the earth some 50,000 years ago near Flagstaff (AZ). It induces a chapter on different units, which is useful for the rest of the book.

Although not in a particular order, one might recognize some recurrent themes in the different applications: things (large and small) falling from the sky (meteor, parachute, raindrops, etc.) but later also trajectories of basketballs, baseballs, water jets, and ski jumpers. Other applications are related to growth models (population, epidemic spread, national deficit, length of people, and world records running, etc). Some chapters deal with wave phenomena (traffic, water waves, and falling dominos), and others with statistics (monte carlo simulation) or curves (in architecture, jumping ropes and Darrieus wind turbines).

But this enumeration is far from complete. There are two chapters completely working out the economic project of towing icebergs from the Antarctic to North and South America, Africa, and Australia. This includes the computation of the energy needed, the optimal route to be followed, the thickness of the cables needed, the melting process, etc. And there are many other models for phenomena, I have not mentioned.

The models are sometimes derived, but in many occasions, they are mostly just given in the form of a differential equation (but also delay differential equations and integro-differential equations appear). It is indicated how to obtain solutions (often analytic, sometimes numerical), but intermediate steps are left to the reader to check. At several places also suggestions for assignments or extra problems to work out are included. Historical comments ad suggestions for further reading are often summarized. Hence teachers may find here inspiration for (if not ready-made examples of) exercises to give to their students.

The book stands out because the examples are all treated as real-life examples with real data, and taking into account all the complications that are usually left out in academic examples: the earth is not a perfect sphere, a baseball is rough because of its stitches, it is thrown with spin, there is resistance of the air, and the resistence differs with the height, etc. Even though, there is a lot of formulas and numbers, the reading is pleasant and smooth. It may be much harder if one wants to work out the details and/or the exercises for oneself.

The chapters can be used independently, although there are some forward or backward references, but these are not essential. One does however need some knowledge of differential equations (usually linear and first order but sometimes going beyond these), integrals are clearly needed (even elliptic integrals are used).

The edition is still the same as the original one. That means that references are still the older ones that have not been updated. Robert B. Banks has passed away some 10 years ago. If not, given his enthusiasm displayed in this book, I would have expected an update about the models for economic evolution, taking into account the banking problems in 2008 and the aftermath of the economic crisis that we are still living in, or perhaps also data about the tsunami that hit Japan in 2011 with the nuclear disaster of Fukushima as a consequence, or the impact and fall-out of the eruption of the Eyjafjallajökull vulcano in 2010. Perhaps someday, someone will add a third volume to these wonderful collections of applied problems.

**Submitted by Adhemar Bultheel |

**6 / Aug / 2013