geometric progression. See
geometric sequence
geometric sequence 223–224,
489
geometric series 103, 163,
409, 441, 488
geometric transformation
224–225, 258, 316, 503
La géométrie (Descartes) 63,
124–125, 226
“Geometrische
Untersuchungen”
(Lobachevsky) 318
geometry 124, 125, 225–228,
238–239
Geometry (Simpson) 463
Germain, Marie-Sophie 190,
226–228
giga- (10
9
) 465
Girard, Albert 209, 398
glide reflection 206, 225, 228
global maximum/minimum
330
gnomon 228
gnomonic projection 485
Gödel, Kurt 31, 101, 199,
200, 228–229, 453, 458
Gödel’s incompleteness
theorems 101, 199, 229,
250, 458
Goldbach, Christian 229,
230, 410
Goldbach’s conjecture
229–230, 250, 359, 410
golden ratio 193, 230–231,
388–389
golden rectangle 231–232, 232
golden triangle 232
Goodwin, E. J. 394
googol/googolplex 232, 389
Gosset, William Sealy 232,
387, 415, 483
grad 233
grade. See slope
gradian 14
gradient 139, 233, 466–468,
467
Graeco-Latin square 302–303
Grandi, Guido 451
graph (network) 94, 233, 233,
501
graphical solution 163, 234,
491
graph of function 114, 207,
234–235, 275, 368
graph theory 82, 174,
235–236, 245, 505
Graunt, John 312, 415
gravitation, theory of
399–400
great circle 223, 314
greatest common divisor
(greatest common factor)
82, 169–170, 236–237, 290,
305, 446
greatest-integer function. See
floor function
Greek alphabet 237, 237
Greek mathematics 9,
237–239
Green, George 239–240
Gregory, David 240
Gregory, James 57, 240, 241,
476–477, 494, 496
Gregory series 11–12, 241,
325, 393, 461
Grelling’s paradox 374–375
The Grounde of Artes
(Recorde) 443
group 59, 241–242, 252, 279,
398, 490
group theory 5, 10, 215, 242,
288, 299, 350, 432
Grundbegriffe der
Wahrscheinlichkeitsrechnung
(Kolmogorov) 296
Grundlagen der Geometrie
(Hilbert) 171, 250
Grundlagen der Mathematik
(Hilbert and Bernays) 250
gry 310
Gunter, Edmund 369, 466
H
haberdasher’s puzzle 165
Hadamard, Jacques 243, 411,
518
Haidao suanjing (Liu Hui) 73
hairy ball theorem 472, 521
Haken, Wolfgang 200–201,
420
half-chord 511
half-cone 91–93, 473
half-line. See ray
half-open interval 278
half-plane 94, 235, 243–244,
267, 473
half-space 243–244
Hall, Monty 343
Hall, Philip 244
Halley, Edmund 5, 312, 353,
445
Halley’s comet 445
Hall’s matching (marriage)
theorem 244
halting problem 88, 244
Hamilton, Sir William Rowan
10, 87, 236, 244–245, 359,
432, 520
Hamiltonian circuit 236, 505
Hamiltonian path 236, 502
ham-sandwich theorem 245
hand (unit of length) 309
handshake lemma 121, 236,
245
handshakes across a table
problem 65
Hardy, Godfrey Harold 246,
381, 435–436
harmonic function 246
harmonic mean 21, 333
harmonic sequence
(progression) 246–247
harmonic series 4, 104–105,
174, 247–248, 368, 409
Haros, C. 188
hatcheck problem 391
al-Haytham 18
Heawood, Percy 200–201
height
of cone 91
of cylinder 115
of pentagram 388
of prism 412
of tetrahedron 497
of triangle 506
Heisenberg, Werner 68
helix 114, 248
hemisphere 471
Hermite, Charles 11, 154,
301, 314
Herodotus 498
Heron 248–249
Heron’s formula 52–53, 78,
248, 249, 336, 486, 506, 508
Heron’s method 34–35, 183,
248, 249, 285, 353, 476
hertz (Hz) 206
Hertz, Heinrich 158
Heumann, Casper 312
hexadecimal notation 135
hexagonal lattice 472
hexahedron. See cube
hierarchy 454
Hieronymus 497–498
higher arithmetic. See number
theory
higher derivative 249
highest common factor. See
greatest common divisor
Hilbert, David 137, 170, 171,
199, 229, 249–250, 355, 533
Hilbert’s axioms 171
Hilbert’s infinite hotel paradox
250–251, 269
Hilbert space 250
Hindu-Arabic numerals
191–192, 251, 263, 370, 451
Hipparchus 510
Hippasus 172, 283
Hippocrates 251–252,
322–323, 476, 513
Hippocrates lune 251
Hisab al-jabr w’al muqa¯bala
(al-Khwa¯rizmı¯) 10, 17, 251,
293, 517
histogram 143, 479, 479
Historia natural y moral de las
Indias (Acosta) 260
HOMFLYPT polynomial 296
homogeneous 252
homomorphism 252
homotopy 398–399
honeycomb 292, 372
Horner, William George 72
How to Solve It (Pólya) 401
hundkurve 503
Hutchings, Michael 469
Huygens, Christiaan
114–115, 180, 414, 503
Hydrodynamica (Daniel
Bernoulli) 40
hydrodynamics 140
hydrostatics 18–19, 20
Hypatia 239, 252–253
hyperbola 30, 92–93, 93, 137,
155, 189, 239, 253,
253–254, 513
hyperbolic cosine 65–66,
254–255
hyperbolic cylinder 411
hyperbolic functions 254,
254–255, 369
hyperbolic geometry 219,
227, 255, 318, 355–356, 455
hyperbolic paraboloid 374,
411
hyperbolic sine 254
hyperbolic spiral 474
hyperboloid 255–256, 256
hyperboloid of one/two sheets
411
hypercomplex numbers 432
hypercube 112, 256
hypersphere 136, 471
hypocycloid 115
hypotenuse 77, 256, 509
Hypothesis physica nova
(Leibniz) 309
hypothesis testing 143
I
i(square root of –1) 85, 173,
358–359, 529
i(unit vector) 520
Ibrahim ibn Sinan 18
icosahedron 232, 396, 397
“Idealtheorie in
Ringbereichen” (Noether)
355
identity 163, 257, 304
identity element 257, 258,
279, 295, 366
additive 534
multiplicative 344
identity matrix (unit matrix)
128, 257, 257–258, 281
identity property 222, 241
image (range) 207, 258, 481
imaginary numbers 87. See
also complex numbers (C)
implicit differentiation
258–259
implicit function 259
improper factor 186
improper fraction 205
improper integral (unrestricted
integral, infinite integral)
104, 144, 259–260
In artem analyticam isagoge
(Viète) 525
Incan mathematics 260
incenter 260
inch 309
incircle 260–261, 354
inclination 261, 261
Index 559