The Collected Mathematical
Papers of Arthur Cayley 68
Collection (Pappus) 13, 253
collinear 79–80, 233
Colson, John 7–8
combination (selection,
unordered arrangement)
80–82
combinatorial coefficient 45,
384
combinatorics 82, 243
commensurable 82, 172, 238
common denominator 82–83
common difference 28
common divisor 83
common factor 83
common fraction 205
common multiple 83, 305
common notions 170
common ratio 223
commutative group 83
commutative property 83
of addition 5
in Boolean algebra 49
of dot products 148
and groups 241
of multiplication 10, 344
and quaternions 432
and rings 448–449
and subtraction 487
of vector addition 520,
522
commutative ring 449
comparison test 4, 103
compass and straightedge 95
complement (set operation)
460
complementary angles 14
complete digraph. See
tournament
complete directed graph 501
complete graph 233
complete induction. See
induction
completeness law 367
completeness property, of real
numbers 47
completing the square 84, 84,
428
complex conjugate of complex
number 526
complex Euclidean space 170
complex fraction 206
complex numbers (C) 85–87,
219, 358–359, 408, 522
completing the square and
84
and Euler’s formula 176
history of 25, 47–48, 245,
398
and intersecting circles 76
multiplication of 86
order properties and 367
polar coordinates of 86
and Pythagorean triples
426
reciprocal of 442
in trigonometry 121–122
and zeta function 535–536
components of a vector 519
composite 87, 186, 409
composite number 87, 463
composition (of functions)
69–70, 87–88, 274, 280
composition (of matrices) 330
compound interest 153–154,
275–276
compound statement 514–515
Comptes Rendu (journal) 66
computer 88. See also
calculator, mechanical
and Boolean algebra 49
and critical path 109
history of 32–33, 167,
321, 351
concave 88
concave polygon 402
concave up/concave down 89,
89, 429
concentric 89
“A Concise Outline of the
Foundations of Geometry”
(Lobachevsky) 318
conclusion (of syllogism) 27
concurrent 89, 261, 335, 338,
399, 507
conditional (“if . . . then”
statement) 89–90, 514
conditional convergence 4,
104
conditional equation 163
conditionally convergent series
4
conditional probability 39,
90–91, 263
condition—necessary and
sufficient 91
cone 91
conformal mapping (equi-
angular transformation,
isogonal transformation) 91,
337, 485
congruence 92
congruence transformation.
See isometry
congruent angles 14
congruent figures 92, 463
congruent triangles 1–2
conical frustum 207
conical helix 248
The Conics (Apollonius of
Perga) 15–16, 93, 253
conic sections 18, 76, 92–93,
93, 123–124, 149, 238, 419
conjecture 31, 499
conjugate of complex number
86–87
conjugate of sum/difference
131
conjugate of surd 490
conjunction (“and” statement)
93–94, 514
conjunction circuit 94
connected 94
connected graph 233
consistent 94
constant 94
constant of integration 94–95,
272, 273
constant width 75, 95, 130
constructible 95–97, 97, 149,
218, 238, 403, 475, 476,
513
constructivism 297
contact number 472
contingency table 98, 98
continued fraction 98–100,
487
calculation of πusing 54
and definition of real
number 441
golden ratio as 231
and Pythagorean triples
427
continuity, defined by Cauchy
66
“Continuity and Irrational
Numbers” (Dedekind) 119
continuous function 88, 100,
184, 276, 386
continuously compounded
interest 276
continuous random variable
143
continuum hypothesis 59, 62,
100–101, 250, 533
contour integral (curvilinear
integral, line integral) 101,
239
contour line 101
contradiction 94, 101, 170,
171, 228, 229, 473
contrapositive 101–102, 265
contrapositive reasoning 26
convergence 66, 324
convergent sequence 102,
312, 458
convergent series 3, 12,
102–105, 182, 240, 260,
409, 459, 530
d’Alembert’s ratio test 8,
223
converse 105, 506
convex 88
convex polygon 402
Conway, John Horton 296
cooperate vs. defect, in
prisoner’s dilemma 412
coordinate geometry 63, 368
coordinates 105, 399
coordination number 472
Copernican theory 214
coprime. See relatively prime
corner 403
corollary 498–499
correlation, and chi-squared
test 74–75
correlation coefficient 79,
106, 107, 306–307, 386,
456–457
corresponding angles 504
cosecant function 510
cosine function 139, 509, 510
cosine rule. See law of cosines
“the cossic art” 10, 517
cotangent function 510
countable 11, 106, 348, 441
countable number. See natural
number; whole number
counterexample 107, 120,
229
counterharmonic mean 333
counting number. See natural
number
Cours d’analyse (Cauchy) 66
Cours d’analyse (Vallée-
Poussin) 518
A Course of Pure Mathematics
(Hardy) 246
cousin primes 515
covariance 106, 107, 306
covering. See tessellation
Cramer, Gabriel 107–108
Cramer’s rule 107, 108–109,
223, 282
Crelle, August Leopold 3
Crelle’s Journal 3
critical path 109, 109
critical point 331
cross product (vector product)
63, 110, 520
cryptography 111, 410, 525
cube (hexahedron) 111–112,
115, 396, 397
cube numbers 195
cube root 112, 451
cubic equation 34, 84,
112–114
discriminant of 141
history of 59–60,
190–191, 493–494
cubic lattice 472
cubit 309
cumulative distribution
function 143
cuneiform tablets 33, 34
curl 144
curve 114, 314
curves, Cramer’s classification
of 108
curvilinear integral. See
contour integral
cusp 492, 493
cycle (graph theory) 233
cyclic group 295
cyclic polygon 114
cyclic quadrilateral 78, 264,
430
cycloid 114–115, 310
cylinder 115, 411
cylindrical coordinates 115,
504
cylindrical helix 248
D
data 116, 478
Data (Euclid) 169
Index 555