external direct product. See
Cartesian product
extraction 183–184
extrapolation 184, 278, 405
extreme and mean ratio. See
golden ratio
extreme-value theorem 49,
119, 184, 330, 442
extremum 184
F
face 185, 403
face angle 185
face-centered cubic lattice 472
face of graph 185
faceted polyhedron 404
factor 185–186
factorial 80, 174, 186–187,
444, 486
factorization 118–119, 187
factor theorem 187
factor tree 210
Fagnano, Giovanni 387
fair division (cake cutting)
187–188
fallacy of the converse 26
fallacy of the inverse 26
false position, method of 9,
156
Faltings, Gerd 190
Fano plane 419, 419
Farey, John 188
Farey sequence (series)
188–189
al-Farisi 18
F-distribution 484
feedback 150
femto- (10
-15
) 465
Ferguson, D. F. 461
Fermat, Pierre de 138,
139–140, 189, 272, 410, 531
and amicable numbers 13
and coordinate geometry
63, 226, 234–235
and figurate numbers 66,
287
and history of calculus 57
little theorem of 342
and probability theory
413, 414, 417
Fermat’s last theorem 137,
138, 139–140, 189–190,
227, 531
Fermat’s little theorem 342
Ferrari, Ludovico 10, 60,
190–191, 431–432, 470, 494
Ferro, Scipione del (Ferreo, dal
Ferro) 10, 59–60, 112, 191,
493–494
Feuerbach, Karl Wilhelm 354
Fibonacci 10, 155, 156,
191–192, 409, 511
and Hindu-Arabic
numerals 251
and minus sign 487
and zero 534
Fibonacci numbers 192–193,
193, 197, 384, 443, 458
and golden ratio 231
and polyominoes 406
field 5, 85, 442
Fields, John Charles 194
Fields medals 193–194, 531
fifteen puzzle. See slide 15
puzzle
figurate numbers 66, 99, 194,
194–195, 287, 381, 389, 423
Fincke, Thomas 511
finger multiplication 195–196
finite 196, 270
finite differences 33, 75,
196–197
finite induction. See induction
finite projective geometry 419
finite sets 106
Fiore, Antonio Maria 493–494
first-derivative test 331–332
Fisher, Sir Ronald Aylmer
197–198, 387, 415
five-fold rotational symmetry
490
five stone problem 43
fixed point 198
floor/ceiling brackets 51
floor function (greatest-integer
function) 198
fluid mechanics 8, 144, 248,
299
flux 144
fluxion 57–58, 198, 309, 352
focal chord 198
focal radius 198
focus (foci) 155, 199
of an ellipse 161
of hyperbola 253, 253–254
of parabola 373
of paraboloid 374
foot (unit of length) 309
force field 101
Ford, Lester R. 188
formal logic (symbolic logic)
25, 89–90, 94, 101, 199,
238, 304–305
Aristotle and 26
expressions in 182
founded by Boole 48
Gödel and 228–229
set theory and 460
formula 199–200
Formulario mathematico
(Peano) 385
foundations of mathematics
47, 200
four-color theorem 55,
200–201, 420, 472
and Möbius band 340
and torus 501
four elements (earth, air, fire,
water) 397
Fourier, Jean-Baptiste Joseph
139, 201, 202, 208
Fourier series 139–140, 177,
201–203, 202, 307, 522, 530
fourth dimension 136
fractal 136, 203–204, 204,
456, 463
fractal shapes
and Banach-Tarski paradox
24
and chaos 71
fraction 146, 204–206, 341,
358, 439, 444
in binary notation 43
reciprocal of 442
fractional dimensions 136
fractional exponent 181, 368
fractional part brackets 51
fractional part function 98,
198
Fraenkel, Adolf 534
Français, Jacques, and
complex numbers 25
Franklin, Benjamin 325
freedom equations. See
parametric equations
Frege, Gottlob 199
frequency 206
frequency distribution 479
frequency polygon 479, 479
frequency table 479, 479
frequency theory of
probability, Venn’s 524
friendly numbers. See amicable
numbers
frieze pattern 206, 206–207
frustum 207
F-test 484
full linear group 222–223
full turn 14, 362, 390
function 139, 173, 207–209,
208, 445
functional analysis 35
function of a function. See
composition
function of a function rule. See
chain rule
fundamental principle of
counting. See multiplication
principle
fundamental property of least
time 189
fundamental theorem of
algebra 85, 112, 186–187,
209–210, 359, 405, 451
and polynomial equations
471
proofs of 10, 25, 218
and zeta function 536
fundamental theorem of
arithmetic 83, 118–119,
186–187, 210–211, 283,
409, 439, 476
proved by Gauss 218
and zeta function 535
fundamental theorem of
calculus 133, 153, 211–212,
240, 272, 494
formulated by Leibniz 308
in history of calculus
57–58
fundamental theorem of
isometries 212, 284
fuzzy logic 212, 305
fuzzy-set theory 212
G
Galilei, Galileo 65, 93, 114,
125, 213–215, 214, 270,
485, 523
Gallai, Tibor 80
galley method 159
Galois, Évariste 10, 215, 242,
288, 432, 471
Galton, Sir Francis 215–216,
415
Galton graph. See scatter
diagram
gambler’s ruin 216, 437
game theory 216–218,
346–348, 350–351, 415
gamma function 174, 187
Gardner, Martin 218
Garfield, James 425
Garnier, René 288
Gauss, Carl Friedrich 119,
140, 218–219, 226, 268
and fundamental theorem
of algebra 209
and geometry 47, 97,
355–356
and group theory 242
and knot theory 295
and number theory 10, 25,
28, 87, 195, 287, 359,
489
and prime numbers 243,
410–411, 518
and probability 356, 414
and topology 500
Gaussian elimination
(pivoting) 119, 219–222,
282, 288, 438, 491
Gelfond, Aleksandr 11
general form of an equation
222
general linear group 222–223,
314
general maximum/minimum
331
general theory of relativity
158
General trattato di numeri et
misure (Tartaglia) 493
generating circle 500
generator 91, 115
geodesic 219, 223
geodesic dome 223
Geography (Ptolemy) 422
Geometriae pars universalis (J.
Gregory) 240
Geometriae rotundi (Fincke)
511
Geometrica organica
(Maclaurin) 324
geometric distribution 44
geometric mean 333
558 Index