How to Fall Slower than Gravity

The book under review is a thematic sequel to the book In Praise of Simple Physics: The Science and Mathematics Behind Everyday Questions. Although the former book does not need to be read first in order to enjoy this current book, they both have the mission of presenting the power and utility of mathematics to analyze a variety of real world problems. Like the previous book, this one also contains a sequence of (mostly) independent mini-chapters that present a physical or mathematical issue. In each case either a solution is presented to the problem along with a challenge for the reader or a set of hints are provided to challenge the reader to solve the problem independently. Full solutions to all challenges are printed in the back of the text. The author also gives the reader full permission to skip to the solutions immediately if that helps you enjoy the book more. In other words, no need to feel any shame over not being able to solve every single problem.

There is a nice mix of theory, application, and simulation. In fact, I thought the problems that could be solved (approximately) via simulation were particularly nice to illustrate that sometimes a problem is just too messy to solve analytically, but that does not mean we should give up. While most chapters are directly inspired by real-world phenomena, there are also chapters that sneak in discussion of pure mathematics such as modular arithmetic, the Euclidean algorithm, Fourier series, and the Riemann zeta function.

While the title of the book intrigued me enough to read and review it, the corresponding chapter was not necessarily one of my favorites. I will highlight two problems that for various reasons were my favorites. One chapter discusses the possible existence of a material termed “NASTYGLASS,” a material that would cause intensely terrible visual distortion to the image on the other side. How terrible? Terrible enough to cause physical discomfort in the same way that audio distortion can cause pain to your ears when heard. With discussions of digital imagery, periodic functions, integration, and a bizarre application, the chapter should capture the interest and imaginations of many readers. My other favorite chapter was the final chapter, which discussed the problem of how to locate faults in long stretches of electrical cables, especially cables that are buried or stretch across the ocean and so are not easily accessible for spot-testing. I found the combination of history, circuit theory, practical application, and use of just the quadratic formula to be an engaging blend and a wonderful way to close out the book.

The potential audience for this book should be fairly large and go from highly talented high school students up through professionals in any STEM field. There is a lot of mathematical sophistication in the book, but it is well presented. The author suggests that the reader needs to have a minimal background at the level of AP Calculus. I would quibble to say that is only true if the student has taken a BC Calculus course. There are a number of uses of power series and basic properties of separable differential equations and difference equations that go beyond just an AB Calculus course, but on the other hand, those issues should not prevent enjoyment of large portions of the book.

Geoffrey Dietz is a Professor of Mathematics at Gannon University in Erie, PA. He is married and has six children.