uniform distribution 480, 480
uniform motion 522
union (set operation) 144,
460
unique factorization theorem.
See fundamental theorem of
arithmetic
unique solution 516
unitary ratio 439
unit circle 427, 516–517
unit denominator rule 204
unit fraction. See Egyptian
fractions
unit matrix. See identity
matrix
unit sphere 469
universal calculus 199
universal language 199
universal mathematics 199
universal quantifier (“for all”)
430–431
unknown (indeterminate,
variable) 517
unordered arrangement. See
combination
unordered partition 381
unrestricted integral. See
improper integral
“Untersuchungen über ein
Problem der Hydrodynamik”
(Dirichlet) 140
V
valence. See degree of a vertex
Vallée-Poussin, Charles-Jean
de la 411, 518
Varahamihira 264
variable 517, 518–519
variance 106, 306, 481, 484
Variorum de rebus
mathematicis responsorum
(Viète) 525
Veblen, Oswald 288
vector 14, 142, 147, 164,
310, 519–520
and collinearity 80
decomposition of 119
vector addition 376, 520
vector equation
of line 520–521
of plane 521
vector field 101, 521
vector multiplication 329, 520
vector operations 520
vector product. See cross
product
vector space 5, 71, 201, 243,
315, 520, 521–522
vector subtraction 520
vector triple product of three
vectors 512
velocity 132, 408, 519,
522–523
Venn, John 523–524
Venn diagram 123, 524,
524–525
Verhulst, Pierre-François 408
vertex 91, 233, 403, 505
vertical angles 364
vibrating strings 8, 299
viergruppe. See Klein-four
group
Viète, François (Franciscus
Vieta) 10, 113–114,
348–349, 511, 525
Viète’s formula (Vieta’s
formula) 231, 393, 511,
525–526
vinculum 81, 526
Vinogradoff, Ivan 230
Vlacq, Adriaan 54, 320
Voevodsky, Vladimir 194
volume 526–527, 527
of cone 91, 173, 293, 527
of cube 111
of cylinder 115, 156
of frustum 207, 527
as ill-defined concept 526
of parallelepiped 376
of Platonic solids 397
of prism 412
of pyramid 173, 293, 423
of solids of equal height
67–68
of sphere 293
of sphere vs. cylinder 20,
91, 115
of tetrahedron 497
von Neumann, John 216,
218, 415, 436
Vorlesungen über
Zahlentheorie (Dirichlet)
140
vortex theory, Descartes’s 125
vulgar fraction 205
W
Waerden, Bartel Leendert van
der 355
al-Wafa, Abu 510
Wallace, William 165
wallet paradox 375
Wallis, John 63, 180, 269,
370, 528, 528–529
and complex numbers 25
Wallis’s product 269, 393,
486, 528, 529, 536
wallpaper pattern 207
Wantzel, Pierre Laurent 149,
513
Waring, Edward 229
warping of space 447
Watson, George Neville 436
weak transitivity 365
Weaver, Warren 461
Weierstrass, Karl Theodor
Wilhelm 5, 58, 284, 297,
312, 529–530
Weierstrass’s product
inequality 268
well-ordered set 530, 533
Wessel, Casper 25, 86
The Whetstone of Witte
(Recorde) 443
Whitehead, Alfred North 199,
229, 452–454, 530
Whitworth, W. Allen 486
whole number 443, 530–531.
See also natural number
Widman, Johannes 6, 131,
398, 487
Wiles, Andrew John 190,
531
Wilson’s theorem 299
word (braids) 52
Wright, E. M. 246
Y
Yang Hui 325
year, length of 333, 363
Yi, Tien-Lien 71
yocto- (10
-24
) 465
Yorke, James 71
yotta- (10
24
) 465
Youngs, J. W. T. 200
Z
Zadeh, Lofti 212
Zahlbericht (Hilbert) 250
Zeno 57, 238, 270, 532
Zeno’s paradoxes 269,
532–533
zepto- (10
-21
) 465
Zermelo, Ernst Friedrich
Ferdinand 31, 350, 461,
530, 533–534
zero (naught) 5, 6, 41, 51,
332, 534–535
in Boolean algebra 49
as exponent 534
factorial of 534
on number line 359
as number vs.placeholder
51, 293
and rings 448
zero fraction 205
zero matrix 147, 534
zero of function. See root
zero-sum game 217, 534
zero-th term, of series 223
zeta function 105, 174, 243,
246, 250, 393, 447–448,
489, 535–536
and proofs of prime-
number theorem 518
Zeteticorum libri quinque
(Viète) 525
zetta- (10
21
) 465
Zhu Shijie. See Chu Shih-
Chieh
zone 472
z-score (z-value) 357, 483,
537
Zu Chongzhi (Tsu Chung Chi)
74, 392, 537
“Zur Elektrodynamik
bewegter Körper” (Einstein)
158
Zur Theorie der Abelschen
Functionen (Weierstrass)
529
568 Index