X and the City: Modeling Aspects of Urban Life

by John Adam

Overview

What mathematical modeling uncovers about life in the city

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.

Product Details

ISBN-13:	9780691154640
Publisher:	Princeton University Press
Publication date:	05/27/2012
Pages:	336
Product dimensions:	6.40(w) x 9.20(h) x 1.10(d)

About the Author

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).

Table of Contents

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

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

What People are Saying About This

From the Publisher

"In X and the City, John Adam proves himself to be a genial and endlessly curious companion as he takes us on a stroll through that fascinating place where reality meets the mathematical imagination. How many squirrels live in Central Park? Should you walk or run in the rain? Anyone who's ever pondered puzzles like these will find this book to be a treat."—Steven Strogatz, Cornell University

"Why did the chicken cross the road? Because the Jaywalker Equation said it had enough time between cars. How does the Ambler Gambler Graph tell if you can blast through a yellow traffic light before it turns red? And why are taxicabs slower than Euclid? These and many other mathematical conundrums are answered in John Adam's admirable new collection."—Neil A. Downie, author of The Ultimate Book of Saturday Science and Vacuum Bazookas, Electric Rainbow Jelly, and 27 Other Saturday Science Projects (both Princeton)

"This is a nice introduction to modeling that draws from questions arising naturally to people who are curious about how cities work. It will certainly interest readers of pop math books and will be useful to teachers of calculus and differential equations who are looking for good examples for their classes."—Anna Pierrehumbert, Community Charter School of Cambridge, Massachusetts

Editorial Reviews

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!

Mathematical Reviews Clippings - Sandra L. Arlinghaus

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

From the Publisher

"[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