INDEX

acceleration “noise,” 85–87

accidents, car, 12, 77

avoiding, 80–85

advection-diffusion, 183

air pollution, 179, 191

its effect on visibility, 191

air travel, 7–10, 13

analogies, 2–3

asteroids, 248

capture cross section for, 303

close encounters with, 303–7

collisions with, 249

Astronomy Picture of the Day (APOD), 248

bamboo, growth of, 42

bedbugs, 142

beltways, 133

M25 in UK, 125, 133

Brownian motion, 181

buses, bunching of, 64

cancer. See tumors

Central Park: jogging in, 49–51

squirrels in, 47

sunbathing in, 48–49

circumhorizontal arc, 301

cities: Bessel, 163–64

equilibrium models of, 159

scaling in, 171

Cobb-Douglas production function, 30

comet, Shoemaker-Levy, 247

concert halls, 19–21

dental offices, number of, 16

dewbows, 230

diamond dust, 229, 301

Dido, princess, 4–5

and the sinc function, 263–68

theorems for, 261–62

differential equations: Bernoulli, 172

delay-, 108

diffusion, 182–83, 188, 293–95

nonlinear, 137, 140

diffusion equation, 293

and diffusion coefficient, 294. See also differential equations

dimension: Hausdorff-Besicovitch, 288

topological, 288

distributions: exponential, 91

negative exponential, 91, 96

Poisson (see Poisson distribution)

doomsday, 136, 139, 176

earthquakes, in Virginia, 25

ellipses, 219–20

expectation value, 95

eruption of, 180

flashlight beams, 242–43

fractal, 3

box-, 289

Cantor dust, 290

and fractal dimension, 3, 169–70, 288–90

Koch snowflake, 289

Menger sponge, 290

Sierpinski triangle, 289

fruit, 36–37

gaps, at school crossings, 92–94

gasoline, consumption of, 74–76

geometrical optics, 193

Goldilocks principle, 11, 17, 39, 251

grass seed, 42–43

halos: ice crystal, 204, 224

in lighthouse beams, 239–240

harmonic mean, 74

headway, 88, 94

heat island, urban, 58, 61

houses of worship, 16–17

hyperbolic orbit, 304

isoperimetric inequality, 261

isoperimetric theorem, 261

jogging, 49–51

Lagrange multipliers, 31, 277

leaves, 45

light: and diffraction, 192–93

and light bulbs, 222

and light pillars, 222–23

and polarization, 198–200

reflection and refraction of, 192

and scattering of (see scattering)

wavelengths of, 192–93

London, population of, 144

M25 motorway, 105, 133

malls, 25–27

Malthusian growth, 137

Mandelbrot set, 287

Manhattan distance, 270

Manhattan metric, 26

maps, 10–11

mathematical models: continuum, 136, 284

deterministic vs. probabilistic, 89

incorporating reaction time, 117–20

kinematic vs. dynamic, 89–90, 99

metaphors, 2–3

meteor crater (Winslow, Arizona), 249–50, 252–53

Minnaert, Marcel, 216, 225

and “apples,” 224

and “cigars,” 224–25

moonbows, 230

mortgages, 32–33

museums, 17–19

normal distribution, 184

Old Dominion University, 253

orchids, maturation of, 43–44

overtaking (passing), 88

pedestrians, 72

petrol. See gasoline consumption

Poisson distribution, 28, 91, 273

derivation of, 274–75

population: of certain cities, 151–52

and population densities, 152

population growth: exponential, 136

Gompertz-like, 173

logistic, 140

Malthusian, 137

post office, 27–28

probability: density function of, 94

geometric, 29, 281–82

and probability distribution, 275

puddles: rain sparks in, 216

wave patterns on, 256–57

rain: and circles, 217

precipitation rate, 52

and reflections, 218–19

running or walking in, 51–56

and sparks, 216

speed of, 259

rainbows, 193, 203–4, 223–34

details of formation, 297–302

in lighthouse beams, 234–39

in searchlight beams, 240–42

tertiary and quaternary, 297

random walk, 291–93

rats, 142

reaction time, 80–83, 108, 113–14, 116, 117–20

refractive index, 204–5, 212–14, 299

Reynolds number, 23–24, 60, 181–82

ring roads. See beltways

risk: of dying while driving, 12

of dying while flying, 12

restaurants, number of, 16

roadbows, 203–7

scaling, 38, 167, 169–71

allometric, 168

geometrically similar, 168

isometric, 168

scattering, 192

Mie, 200

Rayleigh, 194, 198, 200–202

searchlights, 234

shadows, 58, 210

skyscrapers, 21–23, 309

slugs, 44–45

smog, 59, 179, 191

smokestacks, 185–87

speed, terminal, 180

Stirling’s approximation, 274

Stokes’ law, 180

stopping distance, 80–85

Strouhal number, 24

sunbathing, 48–49

taxicab geometry, 65

taxicab metric, 26, 270

taxis, 11–12

tomatoes, consumption of, 39–40

traffic: equation of continuity for, 99

flow of, 97

reaction time in, 117

shock waves in, 90, 101

and traffic jams, 97, 100–101, 126–27

at traffic signals, 100–103

in tunnels, 103–5

traffic signals: delays at, 101–3

legal maneuvers for, 76–80

transportation, public, 63–71

average speed of, 65–68

trips, average length of, 68–71

tumors, 1, 3

turkey, cooking, 37–39

visibility, as affected by air pollution, 191

watermelons. See fruit

weather, in cities, 56–58

wind: effects of on tall buildings, 21–24, 52, 58–59

effects of on pollution, 182–84, 186–88

windows, 211–16

worms, 44

Zipf’s law, 168