Synopses & Reviews
"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
Review
"[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
Review
"For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice
Review
"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
Review
"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
Review
"[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
Review
"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
Synopsis
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.
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.
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
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