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X and the City

Book Description

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.

Table of Contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. Acknowledgments
  9. Chapter 1 Introduction: Cancer, Princess Dido, and the city
  10. Chapter 2 Getting to the City
  11. Chapter 3 Living in the City
  12. Chapter 4 Eating in the City
  13. Chapter 5 Gardening in the City
  14. Chapter 6 Summer in the City
  15. Chapter 7 Not Driving in the City!
  16. Chapter 8 Driving in the City
  17. Chapter 9 Probability in the City
  18. Chapter 10 Traffic in the City
  19. Chapter 11 Car Following in the City–I
  20. Chapter 12 Car Following in the City–II
  21. Chapter 13 Congestion in the City
  22. Chapter 14 Roads in the City
  23. Chapter 15 Sex and the City
  24. Chapter 16 Growth and the City
  25. Chapter 17 The Axiomatic City
  26. Chapter 18 Scaling in the City
  27. Chapter 19 Air Pollution in the City
  28. Chapter 20 Light in the City
  29. Chapter 21 Nighttime in the City–I
  30. Chapter 22 Nighttime in the City–II
  31. Chapter 23 Lighthouses in the City?
  32. Chapter 24 Disaster in the City?
  33. Chapter 25 Getting Away from the City
  34. Appendix 1 Theorems for Princess Dido
  35. Appendix 2 Dido and the sinc Function
  36. Appendix 3 Taxicab Geometry
  37. Appendix 4 The Poisson Distribution
  38. Appendix 5 The Method of Lagrange Multipliers
  39. Appendix 6 A Spiral Braking Path
  40. Appendix 7 The Average Distance Between two Random Points in a Circle
  41. Appendix 8 Informal “Derivation” of the Logistic Differential Equation
  42. Appendix 9 A Miniscule Introduction to Fractals
  43. Appendix 10 Random Walks and the Diffusion Equation
  44. Appendix 11 Rainbow/Halo Details
  45. Appendix 12 The Earth as Vacuum Cleaner?
  46. Annotated references and notes
  47. Index