274 Index
dodecahedron 46
Douady’s rabbit 248 –9
double entry bookkeeping, invention 142
double false position method 83–4
doubling of cube 6, 58 –9
doubling of square, Plato’sMeno 34–5,
50, 51–2
Duhem, Pierre 135
dynasties, Chinese 80–2
Dzielska, Maria, on Hypatia 71–3e, transcendence of 221
eccentric model, sun’s movements 69, 75 –6
ecliptic 67
Edinburgh school 11
Egypt, historical background 16–17
Egyptian mathematics 42
solution of linear equations 21
Eilenberg 250–1
Einstein, Albert
General Theory of Relativity 204
move to Princeton 239
Special Theory of Relativity 207
Eisenhower, Dwight D. 260
electrodynamics, quantum 253
elementary equivalence of knots 226 –7
Elements(Euclid) 36–9
comparison withNine Chapters on
the Mathematical Art 83
proportion theory 47–8
Éléments de mathématiques, (‘Bourbaki’) 241–2
elliptic curves 255, 256
encryption 236
epicycle model, sun’s (or planet’s) movements 69
epistemological break 42
equal parallelograms, Euclid 37 –8
equal ratios, Euclid 49
equant 152
equation of time 69
equations
in Babylonian mathematics 18–19, 20–1, 25
from Qin Jiushao’s work 94
Eratosthenes 195
doubling of cube 58–9
Escher, Moritz,Circle Limit III 192
ethnomathematics 14
Euclid 40, 45
China, introduction of methods to 98
‘common measure’ (greatest common divisor), method
for finding 54
Elements4, 5, 36–9, 48
comparison withNine Chapters on
the Mathematical Art 83
Islamic interpretations 113, 114, 115, 127
parallel postulate 194–6
attempts at proof 190–1, 196
proportion 139
proposition I.16 207– 8
theory of ratios 3, 35, 45, 48, 49
use of proof by contradiction 219
Euclidean geometry, continued validity 9–10Eudoxus of Cnidus 3, 40, 48, 49
theory of proportions 47
Euler 223
Euler’s constant 229
Eupalinus, tunnel of 70
Eurocentrism 12–13, 17
attitudes to Islamic mathematics 102
example, explanation by 111
excess and deficit rule 83–4
existence proof 137
exponential curve, tangent to (Leibniz) 175 –6
external viewpoint 10–12
extreme and mean ratio 53
see alsogolden ratio‘false position’ solution of linear equations 21, 143
Fangcheng (Array) Rule 89
Fara period 15, 27–8
F ̄ars 108
Fauvel, John 2
Feigenbaum quadratic map 248
Fermat’s Last Theorem 220, 254–5
proof 235–6
first principles 36
Fixed Point Theorem, Brouwer 219– 20
fluents 171, 172
fluxions 170, 171
formalists 222
Forman, Paul 220–1
Foucault, Michel 43
Fowler, David 3, 35–6
on Eudoxus 48
his reconstructions 49
Meno 33
on Hasse–Scholz thesis 47
fractions
Archimedes, use of 62
in Babylonian mathematics 23–4
free fall, Galileo’s work 154
Frege, Gottlob 216
Frey Gerhard 255
functors 250–1
fundamental group, Poincaré 226Galileo 133–4, 152, 153–4
infinities 158–9
influences 147
motion of projectiles 150
Gauss 165, 191, 254
caution 203
General Theory of Relativity (Einstein) 204
geocentric model of heavens 67
geodesic 209
geometric constructions, ab ̄u-l-Waf ̄a al Buzj ̄an ̄ı 107
geometric language, use in Greek mathematics 5,
45, 46–7
geometric proof, quadratic equations 112
geometric solutions, Plato’sMeno34–5
Géométrie(Descartes) 149–51
Géométrie Imaginaire(Lobachevsky) 204