The Handy Math Answer Book

Dependent axiomatic sys-

tem, 116

Dependent variables, 135,

136

Derbyshire, John, 454

Derivatives, 222–28

Derivatives of simple func-

tions, 223

Derivatives of trigonometric

functions, 226–28

Descartes, René, 25–26, 30,

136, 137 (ill.), 193

Descriptive statistics, 258

Dewey Decimal System, 399

Dewey, Melville Louis Kos-

suth, 399

Diameter, 184, 184 (ill.)

Dice, 255, 255 (ill.), 433

Dichotomy paradox, 120–21

Diderot, Denis, 29

Difference engine, 354

The Difference Engine(Gib-

son and Sterling), 455

Difference of squares, 152

Differential calculus, 209,

212. See alsoCalculus; Dif-
     ferential equations; Inte-
     gral calculus; Mathemati-
     cal analysis; Vectors
     definition of, 222
     derivatives, 222–28
     derivatives of simple
     functions, 223
     derivatives of trigonomet-
     ric functions, 226–28
     higher derivatives, 224–25
     inverse of a derivative,
     222–23
     Mean-Value Theorem,
     226, 227 (ill.)
     partial derivative, 225
     rules for derivatives,
     225–26
     second derivative, 225
     simple derivatives, 223–24
     Differential equations. See
     alsoCalculus; Differential
     calculus; Integral calculus;
     Mathematical analysis; Vec-
     tors
     conditions, 233–34
     degree, 232

Euler’s method, 234–35

example of, 233

explicit, 232

first-order, 232–33, 234

first-order homogeneous,

234

implicit, 232

linear, 233

non-homogeneous linear,

234

nonlinear, 235–36

order, 232

ordinary, 232

solutions of, 233

systems of, 235, 236 (ill.)

Differential geometry, 241

Digit, 43

Digital computer, 360

Dihedral angle, 175, 176

(ill.)

Dilation, 191–92

Dimensional analysis, 326

Dimensional space, 239, 239

(ill.)

Dimensions, 169–70, 281

Dinosaurs, 457, 458 (ill.)

Diocletian, 61

Dionysius Exiguus, 61

Diophantine analysis, 140

Diophantine equation, 140

Diophantus, 16, 131, 140

Dip, 297, 299 (ill.)

Direct proofs, 118

Discontinuous, 221

Discount, 409

Discover(magazine), 451

Discovery.com(Web site),

459

Discrete variables, 259

Discriminant, 156

Disproof, 118

Dissection puzzles, 422–24

Distance, 172, 416–17

Distributive property,

142–43

Divergent sequences, 214–15

Dividend, 95

Dividend yield, 391

Dividends, 390–91

Divine proportion, 453

Division, 10, 14, 95–96

Division symbols, 95–96

Divisor, 95

DMS notation, 200–201

Dodgson, Charles, 162, 163

(ill.), 426

Dogs, 408, 408 (table)

Domain, 128

Doppler shift method,

293–94

Double bubble, 367, 367 (ill.)

Double integrals, 231–32

Dow index, 391

Dow Jones Industrial Aver-

age, 391

Doyle, Sir Arthur Conan,

455–56

Dudeney, Henry Ernest, 423,

424

Duodecimal system, 6

Dyson, Freeman, 383

E

E=mc^2 , 281

e: The Story of a Number

(Maor), 453

Earned run average, 435

Earth, 288, 291, 415, 416

Earthquakes, 300–302

Ecology, 318

Econometrics, 391

Economic indicators, 392

Economics, 391. See also

Business and economics

Edward II (king of England),

44, 46

eFunda(Web site), 460–61

Egyptian cubit, 43

Egyptian foot, 45

Egyptian fractions, 101

Egyptian Rhind papyrus, 39

Egyptians, 11

calendars, 59–60

division, 14

fractions, 13, 15 (ill.), 101

geometry, 166

hieroglyphs, 12

knowledge of mathemat-

ics from, 14–15

multiplication, 13, 14

need for mathematics, 14 489

INDEX

Handy Math BM 8/19/07 5:18 PM Page 489