Index 275
geometry
concept of infinity 194, 197
construction of 201–3
descriptive 198 , 236
development of axiom systems 206–7
projective 199 , 204
status of 10, 189
see alsonon-Euclidean geometry
Germain, Sophie 254
German mathematics, Second World
War 238–9
Girard, Albert, angle-sum of spherical
triangles 200
Gleick, James 246–7
globalization of technology 261
Gödel, Kurt 222
move to Princeton 239
Gödel’s Theorem 235
golden age
Islamic mathematics 108–10
Newton’s belief in 177
Song dynasty 90–3
golden ratio (section) 49, 53
Goldstein, Catherine 254
Göttingen mathematics 221–3
Gpcategory 250
gradients 169
gravitation, Newton’s ideas 176–7
Gray, Jeremy 2, 193
greatest common divisor 54
Great Wall of China 82
Greek mathematics 40
Archimedes 60–2
astronomy 66–9
Heron (Hero) 63–6
Hypatia 71–3
irrational numbers 46–7
lack of ‘hard’ facts 3
literature 35–6
Newton’s use of 176–7
Plato 33–5
proof by contradiction 219
Ptolemy 66–9
ratios 49–51
second revolution 44–5
sources, problems with 39–42
spherical geometry 200
theory & practice, interaction 57–60
Greek miracle (revolution), origin 42–4
dating of 45
Gregory’s series 167
group, fundamental (Poincaré) 226
HAAseehypothesis of the right
(acute, obtuse) angle
‘half-line angle’ 242
Halley, Edmond 176
Han dynasty 81–2
Hardy, G. H. 228, 229, 235
Hardy–Ramanujan asymptotic formula 229
harmonic series, Oresme, Nicholas 140
harvest yield record, Ur III period 28–9
Hasse-Scholz thesis 46–7
heavenly bodies, circular motion
restriction 66, 67
helium atom 252– 3
Helmholtz 191
extract from 1876 paper 209–10
publicization of hyperbolic geometry 205, 207
hermeneutics 7
Herodotus 42
Heron (Hero) 40, 63–6
Metrics73–4
slot machine 64
Heron’s theorem 64–5, 73– 4
hexagon, perimeter of 63
hexahedronseecube
Hilbert, David 214, 216, 217, 221–3, 232, 240
axiom systems 206–7
on Fermat’s Last Theorem 254
Hipparchus 40
planetary motion 67
Hippasos of Metapontum 46
Hippocrates of Chios 40, 60
quadrature of lunes 56
Hisab al-jabr wa al-muqa ̄bala
(al-Khw ̄arizm ̄ı) 103, 110
historicism 6–7
historiography 4
Hogben, Lancelot,Mathematics for the Million 235
Holbein,The Ambassadors 142
homomorphism 223, 224 , 250
horseshoe map (Smale) 249– 50
Høyrup, Jens 3, 7
Babylonians 19
Islamic miracle 110, 124
‘subscientific’ mathematics 65
Huygens 172
hydraulic project thesis, Egypt and Iraq 16
Hypatia 71–3
hyperbolic geometry 205
hyperbolic trigonometry 209
hypothesis of the right (acute, obtuse) angle (HRA, HAA,
HOA) 190– 1
construction of a geometry 202–3
Lambert’s work 200–1Iamblichus 46, 47
ibn al-Haytham 104
parallel postulate 190, 196
I Ching(Yijing,Book of Changes)78
icosahedron 46
idealism in wartime 240
ideals, Noether’s work 230–1
incommensurability 8, 9
impact on Greek mathematics 45–7
Indian numbers, possible derivation from
counting rods 87–8
infinite series
in Keralan mathematics 167–9
Oresme, Nicholas 139–40, 155–6
infinite sets 219