276 Index
infinitesimals 162
Leibniz’s use 173, 174
Newton’s use 170
present day use 182–3
infinities 151–3
use by Galileo 154, 158–9
infinity, as concept in geometry 194, 197
instantaneous velocity 152, 154, 170
integration
relationship to differentiation 171–2
see alsocalculus
internal viewpoint 10–12
Internet 4
sources on OB mathematics 19
intrinsic equation 187–8
intuitionism 220, 221, 231–2, 238
see alsoBrouwer, L. E. J.
inverse-square law 176
Iraq, historical background 14–16
see alsoBabylonian mathematics
irrational numbers
Dedekind cut 215 –16, 231
Greek knowledge of 35
proof of 54
irrational ratios 46
Islamic mathematics 101–3
algebra, origins 110–14
al-Samaw’al 117–20
golden age 108–10
proportion 139
role of religion 123–5
‘second generation’ algebra 115–17
sources of information 103–5
spherical geometry 200
translations 136
Islamic work on parallels 196
Islamic world
general history 109
transfers of knowledge with Chinese 95–8
isosceles triangles, Thales’ statement 44
Jacquard loom 244, 246
James, I. M. 223
Japanese counting board 86
Jesuits, arrival in China 98
Jewish mathematicians, expulsion from Nazi Germany 238
Jia Xian 92
Jiuzhang suanshu see Nine Chapters on the Mathematical Art
job market 261–2
Jones, Vaughan 249
Joseph, George Gheverghese12, 101, 167
Eurocentrism 12–13
Islam 101–2
Keralan School 167
Julia set 248
Jyesthadeva 167, 168
Kant 193
Kepler
area law, Newton’s version 177– 8 , 186–7
Astronomia Nova151, 152– 3influences 147
Nova stereometria doliorum157–8
Keralan mathematics 167–9
Khayyam, Omar 103, 116–17, 144
algebra 103–4
parallel postulate 190, 196
Kit ̄ab al Fus ̄ul f ̄ı al-His ̄ab al-Hind ̄ı
(al-Uql ̄ıdis ̄ı) 106–7
Kit ̄ab f ̄ım ̄a yaht ̄aju ilayh ̄ı al-sani’min a’m ̄al al-handasah
(ab ̄u-l-Waf ̄a al Buzj ̄an ̄ı) 107
Klein, 192
Kline, Morris 217
knots 225 –6
Knorr, Wilbur 3, 36
circle squaring 137
cube duplication 58–9
knotted torus 224
Koran (Qur’an) 124
Kovalevskaya, Sofia 231, 252
Kuhn, Thomas 8–9
Kummer 254La Disme, Stevin 146, 149
Lambert, Johann Heinrich 200–1
Lambert’s quadrilateral 201
Landau
definition ofπ 238
expulsion from Nazi Germany 238
Lao-Zi 81
Law of Contradiction 162
Law of the Excluded Middle, Brouwer’s
attack 219, 220
leap years 50
Legendre 165
Lehrbuch der Topologie(Seifert & Threlfall) 224, 225
Leibniz 161–3
1684 publication 172–6, 185 –6
criticisms of work 179–80
infinite series 167, 168
priority dispute 165–6
Leibniz rule, first publication 173, 179
Leonardo of Pisa,Liber abbaci 141
L’Hôpital 163–4
Li Zhi 90
‘round town’ 91 , 92
Liber abbaci(Leonardo of Pisa) 141
limits 215
linear equations, solution by Egyptians 21
Listing J. B. 223
Liu Hui 82, 83
commentaries 83–4
use of negative numbers 88
Lobachevsky, Nikolai, I. 189, 191, 192, 193
construction of geometry 202
Géométrie Imaginaire 204
isolation 203
Lobachevsky–Bolyai geometry 205
logarithmic curve, finding of tangent to
(Leibniz) 175 –6
Lorenz, Edward 246, 247
Lovelace, Ada 231, 244