X and the City

John A. Adam is professor of mathematics at Old Dominion University. He is the author of A Mathematical Nature Walk and Mathematics in Nature, and coauthor of Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin (all Princeton).

• Preface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317

"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics Teacher