John Adam is starting to make quite a splash with his books on mathematics in nature. A few years ago, he penned the informative and lively Mathematics in Nature: Modeling Patterns in the Natural World which explored nature in great detail and with engaging prose and analyses.

Now Adam has written a terrific book that takes his earlier work a step further. This is, again, a mathematical treatment of nature but his approach is fun and enticing. This book asks the reader to journey with the author on his many walks. The author walks outside, looks at what is around him, and asks questions — 96 to be precise. The questions are sometimes simple, sometimes not so simple. But with the questions we find answers based a model (sometimes simplified but still useful) with diagrams, equations, and explanations that give the reader insight to the answers. What’s more, the derivations are well presented so that readers will want to explore the topics on their own.

Let’s look at some examples.

Question 17: *The Grand Canyon — How long to fill it with sand?* There are other “simplistic” questions like this one and we find here the idea of using our intuition with some (gross) approximations to derive an educated guess. It is reminiscent of Archimedes’s estimate of the number of poppy seeds to fill the universe. (See Archimedes: What Did He Do Besides Cry Eureka?)

Question 31: *Can you infer fence post (or bridge) “shapes” just by walking past them?* This question looks at an inverse problem. Adam begins his answer with a model of a fence made of either flat posts or round posts. He develops the model to show how light would appear through both sorts of fences as a function of the viewing angle. The treatment is methodical and explained in equations, text, diagrams, and graphs. (The answer is that you *can* tell the shapes by passing by the fence.)

There are some obvious questions with answers that are not always obvious, such as:

Question 45: *Why is the sky blue?* and others about rainbows, mirages, and bubbles with rainbows. Some of this material is a repeat of parts of his earlier book, but I welcomed their inclusion in the context of this book. And I was happy to relearn the material.

Sunrises and sunsets play a large role in the questions, as you would expect, but where I met a surprise is the role of ice in the sky. Here we find upper and lower sun pillars, shafts of light above the setting sun caused by the ice crystals in the atmosphere. The author then asks and answers how we can represent the shape of a bird’s egg, both algebraically and with calculus. Later, the author looks to the sky to discuss eclipses and a simple model for a star. For an ending, Adam models walking itself; while the model is crude, it shows how a little thought mixed with algebra and some simplifying assumptions allows us to study what is in front of us everyday.

Overall, this is a well written guide not only to seeing our world with simplified and useful models and mathematics, but to asking good questions of what we see and then answering those questions on our own.

I found the book delightful, engaging, and interesting. It’s written for anyone with a calculus background, and that’s all one needs. If you’re looking for a fun book with a touch of complexity, this is a good one.

David S. Mazel received his Ph. D. from Georgia Tech in electrical engineering and is a practicing engineer in Washington, DC. His research interests are in the dynamics of billiards, signal processing, and cellular automata.