X and the City (ebook)

Argumento de X and the City (ebook)

"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

"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

"[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

"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

"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

"[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 Reviews0Preface 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