In Pursuit of the Unknown (66 page)

topology
100

vectors
186

wave equations
144–5

Diophantus
78

discontinuous functions
143
,
154
,
155

discrete cosine transform
159

disease clusters
128

divergence (Maxwell's equations)
187

division by zero
45
,
51
,
322n

DNA

encoded information
281–2
,
319

Fourier transforms
157

topology and
105–6

dodecahedra
91

Doppler effect
236–7
,
241

dotcom companies
307
,
311

drug testing
122
,
127

drums
144–6

E

E
=
mc
²
219
,
227–9
,
327n–328n

e (constant)
30
,
84

Earth

interior of
147

Moon effects on
291

shape of
8–9

size of
11
,
12
,
56

views of
167–8

earthquakes
30
,
144–7
,
157
,
221

economics, classical
310

ecosystems

and chaos
286–7
,
291–2

modelling, finance analogy
312–14

edges, in topology
58
,
98
,
99

Edison, Thomas
183

efficiency, in error detection
270
,
279

eggs

assembling
214

unboiling
211–12

Egyptian mathematics
8
,
11

eigenfunctions
251–2
,
255–9

Einstein, Albert
219–20

and atomic weapons
229–30

Brownian motion
208

E
=
mc
²
219
,
227–9
,
327n–328n

field equations
231
,
235
,
240–1

photoelectric effect
249

special relativity
224–5

electromagnetic field
185–6
,
221

electromagnetic induction
186

electromagnetic spectrum
189
,
192–3

electromagnetism

impact on everyday life
181

magnetohydrodynamics and
318

electrostatics
85
,
151
,
242

Elements
(Euclid)
4
,
14–15

ellipses
41
,
57–8
,
59
,
61
,
63

Hohmann transfer ellipses
65
,
69

energy

conservation of
48
,
68
,
200–2
,
205
,
225

dark energy
237

defined
48–9

kinetic energy
48–9
,
68
,
202
,
203
,
205
,
229

potential energy
48–9
,
68

renewable resources
209–10

energy landscapes
68–72

engineers' use of logarithms
29
,
30

Enron Corporation
308

entropy
203–4
,
206
,
209
,
211
,
213–14

as ‘missing information'
281

enzymes
106

equals sign
vii

equations

alternatives to
319–20

describing lines on planes
13–14

E
=
mc
²
as archetype
219
,
227–9
,
327n–328n

‘most beautiful'
84

Pythagoras's Theorem
5

quadratic
78–9

symmetry of
211

types of
vi–vii
,
318

wider influence of
317–18

see also
differential equations

Eratosthenes Batavus
12

Eratosthenes (of Cyrene)
11

error-detection and -correction codes
267–8
,
270
,
276
,
278
,
280

errors

channel capacity and
275

normal distribution
115
,
116
,
119

‘ether'
221–3
,
247

Euclid of Alexandria

on conic sections
57

fifth axiom
14–15

proof of Pythagoras's Theorem
4

on regular solids
4
,
91

eugenics movement
124

Euler, Leonhard
69
,
78
,
84
,
160

fluid dynamics
168–9
,
170

formula for polyhedra
89
,
92–4
,
97

Euler characteristic
95
,
97
,
101

Everett, Hugh, Jr.
258–60

evolution of sensory perception
33–4

evolutionary computing
319

exchange traded funds (ETFs)
311–12

‘expectation' and probability
111

exponential functions
30

complex numbers
83–4

heat equation
152
,
154

extreme events
302–4
,
306–7

F

faces, regular solids
58

Faraday, Michael
vii
,
181–6

fat tails
302–3
,
306
,
309

Fechner, Gustav
33

Fermat, Pierre de
39
,
44
,
111

Feynman, Richard
257
,
261

Feynman diagrams
105

fields, in electromagnetism
85–6
,
96
,
182
,
185–7

‘financial ecosystems'
313–14

financial instruments
297
,
299
,
306
,
308

see also
derivatives
;
futures and options

financial transactions tax
313

fingerprints
162

Fisher, Ronald Aylmer
122
,
128

five-body dynamics
71

fluid dynamics

before Euler
169

magnetohydrodynamics
318

fluids

application of Newton's laws of motion
170

mathematics of magnetism and
185

fluxions
42
,
46
,
50

Food and Drugs Administration (US)
174

forces

in laws of motion
47
,
55

lines of force
85
,
185
,
187

related to curvature
18
,
20

see also
gravity

Fourier, Joseph
151

Fourier analysis
155

Fourier transform
149

blips
160

data compression
159

error distributions and
119

Schrödinger's equation
251

uses
149
,
156

free will
116

friction
47
,
170
,
201–2
,
212–13

Fukushima Dai-ichi power plant
31

functions

complex functions
85–6

exponential functions
30
,
83–4
,
152
,
154

futures and options
299
,
305
,
308
,
330n

fuzzy boundary theory
69

G

galactic rotation curves
237–8
,
241

Galileo Galilei
39–42
,
47–8
,
224
,
230

Galois fields (Évariste Galois)
280

Galton, Francis
119–21

games of chance
109–11

gas laws
200–1
,
205–6

Gauss, Carl Friedrich

electromagnetism
183

imaginary numbers
81–2

least squares method
118

magnetism
96

and non-Euclidean space
16–17
,
18–19

notation
78

‘Gaussian curvature'
18

general relativity
220
,
231
,
240

tests of
233–5
,
242
,
243

geocentric universe
8
,
56

geometry

coordinate geometry
13

curved surface geometry
12
,
15–19
,
231–2

multidimensional
276
,
278–9

non-Euclidean
15–16

relation to algebra
9

topology
91–100
,
105

global warming
175–7