Bombelli, Rafael 47–48, 50,
113
Boole, George 10, 48, 48–49,
199, 309, 460
Boolean algebra 49, 460,
461–462
border square 328, 328
Borel, Félix Edouard Émile
216, 307
Borromean rings 49, 49
Borsuk, Karol 15
Borsuk-Ulam theorem 15, 471
Bosse, Abraham 124
Boss puzzle. See slide 15 puzzle
bound 49–50
bounded above/below,
definition of 50
Bourbaki, Nicolas 50, 168
braces 50, 460
brachistochrone problem 39,
114, 310
brackets 50–51, 366
Brahe, Tycho 292
Brahmagupta 9, 51, 114, 264,
348, 534
Brahmagupta’s formula
51–52, 53, 249, 264, 430
Brahmasphutasiddhanta
(Brahmagupta) 51, 264
braid 52, 52
braid group 52
breadth 309
Bretschneider’s formula 52–53
Briggs, Henry 53–54, 320,
346
Briggsian logarithms 53
Brinkley, John 245
British Association for the
Advancement of Science 68
Bromhead, Sir Edward
239–240
Brouillon project d’une
atteinte aux evenemens des
recontres du cone avec un
plan (Desargues) 123–124
Brouncker, Lord William 54,
529
Brouwer, Luitzen Egbertus Jan
198
Brouwer fixed-point theorem
198
Brownian motion 158
brute force 54–55, 461
Buffon, Georges 55
Buffon-Laplace problem. See
Buffon needle problem
Buffon needle problem 55, 55,
302, 393
Bürgi, Jobst 320
Buridan, Jean 368
butterfly effect 151
C
cake cutting. See fair division
Calandrini, Giovanni
Ludovico 107
calculator, mechanical 382,
383
calculus 7, 8–9, 56, 100, 320
history of 57–58, 67, 126,
325, 368
and optimization 365
and Snell’s law of
refraction 468–469
calculus of variations,
Weierstrass’s 284, 529
calendar, Chinese 537
cancellation 56–59
cancellation law, for fractions
204–205
Canon doctrinae triangulorum
(Rhaeticus) 511
Canon mathematicus seu ad
triangula (Viète) 525
Cantor, Georg 11, 59, 203,
208, 270, 297, 533
on cardinality 60–62,
129–130, 271, 460–461
and continuum hypothesis
100
on infinity 47
and number theory 63,
359, 367–368, 441, 442
Cantor set 203
Cardano, Girolamo (Jerome
Cardan) 10, 47, 59–60, 112,
190–191, 431, 494
and imaginary numbers
87
and negative numbers
348–349
and probability theory
413, 414, 417
Cardano’s formula 112–113,
431, 470, 494
cardinality 60–62, 100, 106,
129–130, 209, 270, 359
and number theory 123,
359, 368, 442
cardioid 62, 115
Carr, G. C. 435
“carrying digits” 2, 6
Cartesian coordinates
(orthogonal coordinates)
62–63, 105, 114, 124, 226,
275, 504
of cardioid 62
vs. cylindrical coordinates
115
and direction cosines 138
vs. polar coordinates 400
quadrants in 428
of torus 500
Cartesian product (cross
product, external direct
product, product set, set
direct product) 63
Cartesian space. See Euclidean
space
Cassini, Giovanni Domenico
370
Castillon, Johann 62
casting out nines 63–64
Catalan, Eugène Charles 64
Catalan conjecture 64
Catalan numbers 64–65
catenary 65–66, 255
Cauchy, Augustin-Louis 47,
66, 66–67, 103, 287, 529
and definition of limit 269,
312, 459
and mean-value theorem
335
and number theory 442
Cauchy-Riemann equations
67
Cauchy-Schwarz inequality
268
Cauchy sequence 442
Cavalieri, Bonaventura
Francesco 57, 67, 74, 293,
527, 528
Cavalieri’s principle 57,
67–68, 115, 412, 527, 537
Cayley, Arthur 68, 200
Cayley-Hamilton theorem
68–69
Cayley numbers 359, 432
ceiling/floor brackets 51
ceiling function (least-integer
function) 198
center-limit theorem 69–70
center of gravity 18–19, 69,
372, 470
center of mass vs. center of
gravity 69
centile. See percentile
central angle 77, 77
central-angle/peripheral-angle
theorem 77, 77
central-limit theorem 143,
401, 482–483
and normal distribution
356
central projection 418
central tendency, measures of
480
centroid 335, 372, 470, 507
Ceva, Giovanni 70
Ceva’s theorem 70
Ceyuan Haijing (Li Ye) 318
chain 365–366
chain rule 70–71, 88, 133,
138, 258, 274, 281, 282,
378, 433–434
change of variable. See
integration: by substitution
chaos 71, 151, 203
chaos game 204
characteristica universalis 309
characteristic polynomial
68–69, 156
characteristic vector. See
eigenvector
Chebyshev (Tchebyshev),
Pafnuty Lvovich 71, 72,
167, 415
Chebyshev polynomials 71
Chebyshev’s theorem 71, 72,
304
Chen, Jing-Run 230
Chêng Ta-wei 325
chessboard puzzle 224
chicken (game) 218, 413, 413
Ch’in Chiu-shao 72, 73
Chinese mathematics 72–74
Chinese proof 425
Chinese remainder theorem
73
chi-squared test 74–75, 98,
386, 415
choice set 31
chord 75, 76, 457, 510, 511
Chords in a Circle (Menelaus)
336
chord theorems 78
chord values, Hipparchus’s
239
Chou pei suan ching
(anonymous) 73, 425
Chudnovsky, Gregory and
David 393
Chuquet, Nicola 526
Chu Shih-Chieh (Zhu Shijie)
73–74, 75, 383
circle 75–76, 92, 136,
141–142, 166, 188
area of 24, 24
diameter of 130
eccentricity of 155
Circles of Proportion and the
Horizontal Instrument
(Oughtred) 369
circle squaring. See squaring
the circle
circle theorems 75, 76–78,
114, 425, 430
circular inversion 225
circumcenter 78, 338, 507
circumcircle 76, 78, 165,
303–304, 321, 354
circumference
of circle 75–76
of earth 29
circumscribe/inscribe 78
“C
1
Isometric Imbeddings”
(Nash) 347
cissoid 136–137
clarity 66–67, 529–530
Clavis mathematicae
(Oughtred) 344, 370
clock math 92, 340–341
closed curve 114
closed half-plane 243–244
closed half-space 243–244
closed interval 184, 276, 278
closure property 79
of addition 5
and groups 241
of matrices 222
cluster sampling 407
coefficient 79, 404, 525
Cogitata physico-mathematica
(Mersenne) 338
Cohen, Paul 101
Colebrook, H. J. 42
Collatz’s conjecture 79
554 Index