days-of-the-week formula
116–118
decibel 118
decimal representation 36–38,
72–73, 260, 264, 370, 485
declination 261, 261
decomposition 118–119
De configurationibus
qualitatum et motuum
(Oresme) 368
decrement 262
Decker, Ezechiel de 54
Dedekind, Julius Wilhelm
Richard 58, 119, 120,
172–173, 270, 367, 442
Dedekind cut 119–120,
172–173, 262, 277, 367
and bounded real numbers
50
and definition of real
number 442
and extreme-value theorem
184
De determinantibus
functionalibus (Jacobi) 287
deductive logic 420
Aristotle and 26
deductive reasoning 120–121
defect vs. cooperate, in
prisoner’s dilemma 412
deferent, of cycloid 115
deficient number 389
definite integral 148–149, 275
deformation 121
Degen, Ferdinand 3, 5
degenerate hyperbola 373
degenerate quadrics 411
degree (measure of angle) 14
degree of a polynomial 121,
404
degree of a vertex (valence)
121, 233
degrees of freedom 121
Dehn, Max 165
Delian altar problem. See
duplicating the cube
deltoid 430, 430
De methodis serierum et
fluxionum (Newton) 352
De Moivre, Abraham 85, 107,
121–122, 471, 486, 494
and normal distribution
356, 414, 486
De Moivre’s formula (De
Moivre’s identity) 85, 122
De Moivre’s quintic 471
Démonstration d’une méthode
pour resoudre les égalitez de
tous les degrez (Rolle) 449
“Démonstration d’un
théorème sur les fractions
continues périodiques”
(Galois) 215
De Morgan, Augustus
122–123, 200, 265, 270, 349
De Morgan’s laws 123, 460,
525
denominator 204
dense subset 441
denumerable (enumerable,
numerable) 123
denumerable sets 59, 60–62,
100, 106
dependent events 262–263
dependent variable 519
derangement 390–391, 486
De ratiociniis in ludo aleae
(Huygens) 414
derivative 132, 132, 198, 262,
271–272, 418
and calculation of velocity
and acceleration 523
first and second, and
graphing 234
Desargues, Girard 123–124,
270, 391, 418, 419
Desargues’s theorem 124,
270, 391, 419
Descartes, René 10, 57,
124–125, 125, 180, 189,
431–432, 519
and amicable numbers 13
and analytic geometry 13
and coordinate geometry
62–63, 226, 235
and Euler-Descartes
formula 177
and imaginary numbers
87
Descartes’s rule of signs 124,
125–126
descriptive statistics. See
statistics: descriptive
determinant 126–128, 223,
281–282, 287, 309
determinant function 108
De triangulis omnimodis
(Regiomontanus) 444, 511
deviation 481
diagonal 128–129, 376, 402,
443
diagonal argument 59, 60,
100, 106, 123, 129,
129–130, 359, 441–442
diagonal Latin square 302
Dialogo (Galileo) 214
diameter 75, 76, 130, 471
diamond 376, 474
dice, tetrahedral 462
dichotomous line search. See
bisection method
dichotomy paradox, Zeno’s
533
Dido’s problem 130, 284
Dieudonné, Jean 288
“Die von der
molekularkinetischen
Theorie der Wärme gefurdete
Bewegung von in ruhenden
Flüssigkeiten suspendierten
Teilchen” (Einstein) 158
difference 130–131, 487
difference engine, Babbage’s
32–33, 33
difference formula 511–512,
512
difference machine. See
difference engine
difference of two cubes 131
difference of two squares 9,
131, 257
differential 131–132, 132,
310
Differential and Integral
Calculus (Babbage) 32
differential calculus 56,
132–134, 226, 308–309
vs. integral calculus
211–212
differential equations
134–135, 234, 252, 299,
309, 385, 399
and partial fractions 380
differential geometry 226
differentiation 133, 309
digit 135–136
digital vs. analog 135–136
digit extraction 183
dihedral 136
dihedral angle 136
dilation 225, 278, 317
dimension 136
dimension of a matrix. See
order of a matrix
Diocles 136–137
Diophantine equations 54, 99,
137, 239, 250, 289–290, 360
Diophantus 9, 137–138, 180,
189–191, 239, 252–253
directed number. See integer
directional derivative
138–139, 233
direction cosines 138
direction numbers 138
direction ratios 138
directly congruent solids 92
direct proof 139, 265, 420
direct reasoning 26
directrix 155
of cone 91
of cylinder 115
of parabola 373
Dirichlet, Peter Gustav Lejeune
139–140, 172, 208, 337, 394
Dirichlet’s principle. See
pigeonhole principle
disc method 470
discontinuous functions 100
Discorsi e dimostrazione
matematiche intorno a due
nuove scienze (Galileo) 213
discrete 140
discrete mathematics 167
discrete transformation 140
discriminant 84, 140–141,
429
discriminant of cubic 113
disjoint events. See mutually
exclusive events
disjunction (“or” statement)
141, 514
disjunction circuit 141
disjunctive reasoning 26
dispersion, measures of
480–482
displacement 141
Disquisitiones arithmeticae
(Gauss) 218–219
distance
of point from line 142
of point from plane 142
and velocity 522–523
distance formula 22, 75,
141–142, 310, 520
distribution 72, 142–143,
143, 197, 218
chi-squared 74–75
distributive property
143–144
in Boolean algebra 49
of dot products 148
and Elizabethan
multiplication 160
Pythagoreans and 9
and quaternions 432
and rings 448
div (divergence operator) 144
divergent 144
divergent sequence 102
divergent series 240, 459
divine proportion. See golden
ratio
divisibility rules 92, 144–146
division 146, 205
divisor of zero 147
Doctrine of Change (De
Moivre) 122
dodecahedron 396, 397
donut. See torus
dot product (inner product,
scalar product) 110, 136,
138, 147–148, 520
double angle formula 525
double cusp 492, 493
double integral 148, 239, 400,
473
double point 148
double root 140, 451
double torus 501
doubling the cube 149
drawer principle. See
pigeonhole principle
duality in projective geometry
124
Dudeney, Henry Ernest 165
dummy variable 148–149,
488
duplicating the cube 18, 21,
97, 136–137, 149, 166, 172,
239, 525
Dürer, Albrecht 149–150,
231, 232, 325, 391
dyadic 150
dyadic fraction 43
dynamical system 71, 88,
150–151, 203, 296
dynamics 299
556 Index