# X and the City: Modeling Aspects of Urban Life

## Synopsis

X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid?

Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader.

Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.

## Excerpt

After the publication of A Mathematical Nature Walk, my editor, Vickie Kearn, suggested I think about writing A Mathematical City Walk. My first reaction was somewhat negative, as I am a “country boy” at heart, and have always been more interested in modeling natural patterns in the world around us than man-made ones. Nevertheless, the idea grew on me, especially since I realized that many of my favorite nature topics, such as rainbows and ice crystal halos, can have (under the right circumstances) very different manifestations in the city. Why would this be ? Without wishing to give the game away too early into the book, it has to do with the differences between nearly parallel “rays” of light from the sun, and divergent rays of light from nearby light sources at night, of which more anon. But I didn’t want to describe this and the rest of the material in terms of a city walk; instead I chose to couch things with an “in the city” motif, and this allowed me to touch on a rather wide variety of topics that would have otherwise been excluded. (There are seven chapters having to do with traffic in one way or another!)

As a student, I lived in a large city—London—and enjoyed it well enough, though we should try to identify what is meant by the word “city.” Several related dictionary definitions can be found, but they vary depending on the country in which one lives. For the purposes of this book, a city is a large, permanent settlement of people, with the infrastructure that is necessary to . . .

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