antipodal points (antipodes)
15, 471, 473
antisymmetry 365
apex (apices) 15, 91, 423
Apollonius of Perga 15–16,
76, 78, 93, 105, 115,
136–137, 189, 239, 252,
253, 476
and duplicating the cube
149
and trisecting an angle 513
Apollonius’s circle 16
Apollonius’s theorem 16
apothem (short radius) 16,
403
Appel, Kenneth 200–201, 420
applied mathematics 17
appropriately nice functions
315
approximation 17
Arabic mathematics 17–18
Arbogast, Louis 249
arc 18, 76
Archimedean solids 398
Archimedean spiral 239, 400,
474
Archimedes 18, 18–21, 19,
20, 91, 93, 105, 115, 173,
180, 213, 238–239, 270,
272, 476
and Archimedean solids
398
on Fields medal 194
and his spiral 474
and semiregular polyhedra
404
and sum of first nnumbers
489
and trisecting an angle 513
Archimedes’ water screw 20,
21
Archytas 21–22, 172
arc length 22, 470
area 22–25, 23, 24
of annulus 15
of basic shapes 23, 23–24,
156, 248, 293
of circle 76, 222, 392
of curved figures 172
of ellipsoid 161–162
as ill-defined concept
22–23, 24, 526
of polygon 403
of quadrilateral,
Bretschneider’s formula
for 52–53, 430
of quadrilateral inscribed in
circle, Brahmagupta’s
formula for 51–52
of rectangle 443
of square 474
of trapezoid 504
of triangle 486
area hyperbolic functions 281
Argand, Jean Robert 25, 86
Argand diagram 25, 86, 359
argument 25–26, 86, 199,
524–525
Aristotle 26–27, 238, 270,
309, 532
and formal logic 25–26,
199
Aristotle’s wheel paradox 375
arithmetic 27
Arithmetica (Diophantus)
137–138, 189, 190, 239,
253, 525
Arithmetica infinitorum
(Wallis) 528
Arithmetica universalis
(Newton) 353
Arithmetices principia, nova
methodo exposita (Peano)
385
arithmetic–geometric-mean
inequality 219, 333
arithmetic mean 333
The Arithmetic of Logarithms
(Briggs) 53–54
arithmetic sequence 28,
139–140
arithmetic series 28
arrangement. See permutation
array 28
arrow paradox, Zeno’s 533
Ars conjectandi (Jacob
Bernoulli) 39–40, 414
Ars magna (Cardano) 10, 47,
59–60, 112, 190–191, 494
Artin, Emil 52
A
¯ryabhata (Indian
mathematician) 17, 28–29,
264, 392
A
¯ryabhatiya (A
¯ryabhata)
28–29
ASA (angle-side-angle) rule 1
“As I Was Going to St. Ives”
156
associative property 29, 83
of addition 5
in Boolean algebra 49
and groups 241
of matrices 223
and order of operation
366
and rings 448
of vector addition 520,
522
astroid 115
Astronomiae physicae et
geometricae elementa (D.
Gregory) 240
Astronomia nova (Kepler)
292
asymmetrical 490
asymptote 29–30, 234, 440
asymptotic series 39
atto- (10
-18
) 465
attractor 150
augend 6
automaton 30, 30–31, 37,
350–351
automorphic functions 398
average. See mean (average)
axiom (postulate) 31, 170,
314
axiom of choice 31, 530, 534
B
Babbage, Charles 32, 32–33,
322
Babbage’s difference engine 33
Babylonian mathematics 9,
33–35, 249, 425, 426, 428
Bacon, Francis 452
Bakhshali manuscript 264
balance point. See center of
gravity
La balancitta (Galileo) 213
Banach, Stefan 24, 35
Banach-Tarski paradox
24–25, 35, 374, 526
band ornament. See frieze
pattern
barber paradox 374–375,
453–454
Barbier, Joseph 95
bar chart 479, 479
“The Bargaining Problem”
(Nash) 347
Barrow, Isaac 35–36, 36, 54
Der barycentrische Calcül
(Möbius) 339
base of exponent 180
base of number system 36–38,
37
base of polygon/polyhedron
38, 506
base-10 logarithms 53
Bayes, Rev. Thomas 38–39
Bayes’s theorem 39, 302
bearing 39
Behennde unnd hüpsche
Rechnung auf fallen
Kauffmannschaften
(Widman) 6, 487
bel 118
Bell, Alexander Graham 118
bell-shaped distribution 356,
480, 480
Berkeley, George 58
Bernays, Paul 250
Bernoulli family 39–40, 50,
284, 529
Bernoulli, Daniel 40, 107, 202
Bernoulli, Jacob 39–40, 58,
414
Bernoulli, Jacob (II) 40
Bernoulli, Jacques 65–66, 489
Bernoulli, Johann 40, 58, 107,
114, 272, 310, 474, 494
Bernoulli, Johann (II) 40
Bernoulli, Johann (III) 40
Bernoulli, Nicolaus (I) 40
Bernoulli, Nicolaus (II) 40
Bernoulli numbers 40, 435,
489
Bernoulli’s inequality 267–268
Berry’s paradox 374–375
Bertrand, Louis François 40,
71
Bertrand’s conjecture 167
Bertrand’s paradox 40,
40–41, 75, 374, 417
“Beweis, dass jede Menge
wohlgeordnet werden kann”
(Zermelo) 533–534
Bha¯skara II (Bhaskaracharya)
10, 17, 41–42, 264, 392
and negative numbers 348
bias 42
biconditional (“if, and only if”
statement) 42, 91, 514
bifurcation point 151
Bijaganita (Bha¯skara) 41–42
bijection 209
bimodal distribution 480, 480
binary line search. See
bisection method
binary numbers 30, 42–43,
88, 150
binary operation 43, 257, 279
cancellation as 56–59
closure as 79
commutative property as
83
Binet’s formula 193
binomial 43
binomial coefficient 45,
64–65, 80, 418
binomial distribution 43–44,
44, 143, 180
binomial expansion 44–45
binomial theorem 18, 44–45,
80–81, 219, 309, 364
Biometrics (journal) 387
biquadratic equation. See
quartic equation
birectangular triangle 474
bisection method
(dichotomous line search,
binary line search) 45–46,
277, 451
bisector 46
bit 461
Blatzer, Richard 47
body mass index (BMI). See
Quételet index
Bohlen numbers 195
Bolyai, János 46–47, 171,
219, 255, 318, 355, 455
Bolzano, Bernard Placidus 47,
276
Bolzano’s theorem. See
intermediate-value theorem
Index 553