inclined plane 261
inclusion-exclusion principle
48–49, 261, 391, 460
incomposite numbers 409
increasing/decreasing 89,
261–262
increment 262
indefinite integral 95, 272,
275
independent. See pairwise
disjoint
independent axiom 171, 262
independent events 91, 178,
262–263, 417
independent variable 519
indeterminate. See unknown
indeterminate equation 263
index (indices) 263. See also
exponent
index of summation 488
Indian mathematics 263–265
indirect proof (proof by
contradiction, reductio ad
absurdum) 139, 171, 265,
336, 420
induction 122, 126, 176–177,
261, 265–267, 270, 420
inductive definition. See
recursive definition
inductive reasoning 120–121
Indus inch 263
inequality 267–268
inference 268, 415
inferential statistics. See
statistics: inferential
infinite 196
infinite integral. See improper
integral
infinite order 406
infinite product 144,
268–269, 312, 459
infinite series 102, 324, 351,
368, 439
infinitesimal 47, 57–58, 67,
269, 271, 533
infinity (∞) 269–270, 529
inflection (inflexion) point 89,
89, 270, 492
information theory 271
injective function 209
inner product. See dot product
inradius 260
inscribe/circumscribe 78
inscribed-angle theorems 77,
77–78
inscribed circle 387
instantaneous value 271
instantaneous velocity 523
integer (directed number,
signed number) 271, 358
integer triangle 507–508
integral 66, 180, 380, 447,
523
integral calculus 22, 24, 56,
133, 271–273, 272, 308–309
and Archimedes’ method of
exhaustion 18
vs. differential calculus
211–212
and volume calculation
470, 527
integral domain 449
“Intégrale, longeur, aire”
(Lebesgue) 307
Intégrales de Lebesgue (Vallée-
Poussin) 518
integral test, for convergent
series 104
integrand 148–149, 273, 274,
360
integration 15, 133, 272
by parts 95, 273–274,
443, 486
by substitution (change of
variable, substitution rule
for integration) 274–275,
287
intercept 275
intercept form 164, 275
interest 275–276
interior angle 276, 504, 504
intermediate-value theorem
(Bolzano’s theorem) 100,
184, 276–277, 367, 442
bisection method and 46
Bolzano’s proof of 47
and Dedekind cut 119
and ham-sandwich theorem
245
in history of calculus 58
and logarithmic function
320
interpolation 184, 405. See
also Lagrange’s formula
intersection 144, 460
interval 278
Introduction à l’analyse des
lignes courbes algébriques
(Cramer) 107–108
“Introduction to Mathematical
Philosophy” (Russell) 453
An Introduction to
Mathematics (Whitehead)
530
“Introduction to the Doctrine
of Fluxions” (Bayes) 38–39
invariant 278–279
inverse element 279–280
inverse function (inverse
mapping, reverse function)
280–281
inverse hyperbolic functions
281
inverse mapping. See inverse
function
inverse matrix 222, 280,
281–282
inverse property 5, 49, 223,
241
inverse square law 282
inverse trigonometric functions
280–281, 282–283
inversion in a circle 225
An Investigation of the Laws
of Thought (Boole) 48
irrational numbers 59, 238,
283, 358, 423
and definition of real
number 441–442
Kronecker’s doubts about
297
Theodorus’s work on 498
irreducible polynomial 186
Isagoge ad locos planos et
solidos (Fermat) 189, 226
isogonal transformation. See
conformal mapping
isolated point (acnode) 283
isometry (congruence
transformation) 140,
283–284
isomorphism 284
isoperimetric inequality 268
isoperimetric problems 130,
284–285, 469, 472,
474–475, 484–485, 529
isosceles trapezoid (trapezium)
285, 504
isosceles triangle 238, 285,
285, 506
“Ist die Trägheit eines Körpes
von seinem Energieinhalt
abhängig?” (Einstein) 158
Istituzioni analitiche (Agnesi)
7
iterated integral 148
iteration 150–151, 285–286
Iverson, Kenneth 198
J
j(engineers’ i) 85
j(unit vector) 520
Jacobi, Carl Gustav Jacob
287–288
Jacobian determinants 287
Jacquard, Joseph-Marie 33
jerk 523
Jiuzhang suanshu
(anonymous) 73, 226
Jones, Vaughn 295–296
Jones, William 393
Jones polynomial 296
Jordan, Marie Ennemond
Camille 288, 307
Jordan, Wilhelm 288
Jordan canonical form 288
Jordan curve theorem 76, 288
Josephus problem 288–289
Jourdain’s paradox 289
Journal de Mathématiques
Pures et Appliqués
(Liouville’s journal) 317
Journal for Pure and Applied
Mathematics (Crelle’s
journal) 3
J-shaped distribution 480,
480
jug-filling problem 137, 170,
289–290
Julia, Gaston Maurice
203–204
Julia set 203–204
Jungius, Joachim 65
K
k(unit vector in three-
dimensional space) 520
al-Kashi, Jamshid Mas’ud 18,
291, 392
Kasner, Edward 232
Kempe, Alfred Bray 200
Kendall, M. G. 438
Kendall’s coefficient 438
Kendall’s method 438
Kepler, Johannes 93, 291–293,
292, 396, 397, 472, 528
Kepler’s laws, Newton and
353
The Key to Arithmetic (al-
Kashi) 291
Khandakhadyaka
(Brahmagupta) 51
Khayyám, Omar. See Omar
Khayyám
al-Khwa¯rizmı¯, Muhammad
ibn Mu¯sa¯ 9, 10–11, 17, 251,
293–294, 517, 534
kilo- (10
3
) 465
kinematics 27, 213
kite 430, 430
Klarner, David 406
Klarner’s constant 406
Klein, Felix Christian 294,
314, 355, 473–474
Klein bottle 200–201,
294–295, 339–340
Klein-four group (viergruppe)
295
knot theory 295, 295–296
Koch, Nils Fabian Helge von
203
Koch curve 203
Kolmogorov, Andrey
Nikolaevich 296
Kramp, Christian 187
Kremer, Gerhard (Mercator)
337
Kronecker, Leopold 296–297
Kruskal’s count 297–298
Kulik, Yakov 463
L
Laczovich, Miklov 165
laddered exponents 65
Lafforgue, Laurent 194
Lagrange, Joseph-Louis 99,
201, 249, 278, 299–300,
379, 399, 414
and group theory 242
and history of calculus 58
and mean-value theorem
334
and square numbers 195
and Taylor series 494
560 Index