T
Tabulae (Regiomontanus) 444
tacnode (osculation) 148
tacpoint 493
Tait, Peter 295
tangency point. See point of
contact
tangent (geometric) 492, 493
tangent (trigonometric) 132,
492, 510
tangent plane 492
tangent theorems 76–77, 77
Tarski, Alfred 24, 35
Tartaglia, Niccolò 10, 60,
112, 190–191, 493, 493–494
task diagram 109
tautochrone property of
pendulums 114–115, 299
tautology 494, 515
Taylor, Brook 240, 274, 324,
325, 494, 495
Taylor, Richard 190, 531
Taylor series 152, 182,
240–241, 268, 271, 315,
324–325, 337, 409, 494–496
and approximation 16
convergence of 45
Chebyshev’s work on
71
and Euler’s formula 175
and general binomial
theorem 45
and history of calculus 57
and permutations 391
of sine function 536
Tchebyshev. See Chebyshev
technique. See algorithm
tensor 447, 496
The Tenth (Stevin) 485
tera- (10
12
) 465
tessellation (covering, tiling)
403, 430, 475, 496–497,
497, 507
tesseract 256
“The Testing of Statistical
Hypotheses in Relation to
Probabilities A Priori”
(Neyman) 354
tetragon. See quadrilateral
tetrahedral dice 462
tetrahedral numbers 195, 497
tetrahedron 165, 396, 397,
403, 423, 497
tetromino 406
Teutsche algebra (Rahn) 146
Thabit ibn Qurra 18
Thales 238, 423, 497–498,
510
Theaetetus (Plato) 498
The Grammar of Science
(Pearson) 387
Theodorus 82, 283, 475–476,
498
Theon of Alexandria 252–253
Theon of Smyrna 99
theorem (proposition)
498–499
theorem of Thales 77
Theorems Stated by
Ramanujan (Watson) 436
Theoria motus corporum
coelestium (Gauss) 219
Théorie analytique de la
chaleur (Fourier) 201
Théorie analytique des
probabilités (Laplace) 301,
415
Theorie der Parallellinien
(Lambert) 300
“Théorie des opérations
linéaires” (Banach) 35
The Theory of Games and
Economic Behavior (von
Neumann and Morgenstern)
216, 350–351
The Theory of Numbers
(Hardy and Wright) 246
“Theory of Systems of Rays”
(Hamilton) 245
three-body problem 299
three-dimensional coordinates
63, 363
three-dimensional vectors 520
three-fold rotational symmetry
490
three-utilities problem 233,
499, 499
tiling. See tessellation
Timaeus (Plato) 396, 397
time, as fourth dimension
136, 256
time-series graph 479, 479
topological space 500
topology 121, 307, 339,
499–500
Torricelli, Evangelista 114
torus 94, 399, 470, 500–501,
501
Euler’s formula for 236
Euler theorem and 177
and Jordan curve theorem
76, 288
and three-utilities problem
499
totally ordered set 365–366
tournament (round-robin
tournament, complete
digraph) 501, 501–502
towers of Hanoi (Brahma)
443, 502–503
tractrix (equitangential curve,
tractory) 503
Traité analytique des sections
coniques (L’Hôpital) 310
Traité d’algèbre (Rolle) 449
Traité de dynamique
(d’Alembert) 8
Traité de la résolution des
équations numériques de
tous les degrés (Lagrange)
299
Traité de l’équilibre et du
mouvement des fluides
(d’Alembert) 8
Traité de mécanique céleste
(Laplace) 301
Traité des proprietés des
figures (Poncelet) 419
Traité des substitutions et des
equations algebraique
(Jordan) 288
trajectory 503
transcendental curve 114
transcendental numbers 11,
59, 297, 301, 317–318, 477
transfinite numbers 368
transformation 503–504
transitive law 367
transitive reasoning 26
translation 206, 225,
283–284
transmitter 501–502
transpose of matrix 330
transposition 390
transversal 336, 375, 377,
504, 504
trapezoid (trapezium) 23, 24,
430, 504
trapezoidal rule for integration
360–361
traveling-salesman problem
55, 505
traverse 504, 504
Treatise of Fluxions
(Maclaurin) 324
A Treatise on Algebra
(Maclaurin) 324
Treatise on Algebra (Wallis)
529
Treatise on Demonstration of
Problems of Algebra (Omar
Khayyám) 363
Treatise on Human
Proportions (Dürer) 231
The Treatise on the Chord and
Sine (al-Kashi) 291
Treatise on the Equilibrium of
Liquids (Pascal) 382
Treatise on Universal Algebra
(Whitehead) 530
tree (graph theory) 233
triangle (trigon) 114, 505–508
area of 23, 23, 249
diameter of 130
Euler line in 174–175
exterior angles of 182–183
triangle inequality 267, 425,
506, 508
triangular numbers 194,
194–195, 349, 405, 497
trichotomy law 31, 365, 367
trigon. See triangle
Trigonometria (Pitiscus) 511
trigonometric functions 254,
369
trigonometry 16, 28, 239,
444–445, 508–512, 516–517
Trigonometry (Simpson) 463
Trigonometry and Double
Algebra (De Morgan) 122
trinomial 512
Le triparty en la science des
nombres (Chuquet) 526
triple (3-tuple) 358
triple integral 148
triple torus 501
triple vector product 376,
448, 512
trirectangular triangle 474
trisecting an angle 97, 239,
291, 372, 512, 512–513, 525
Tristram Shandy paradox
269, 513
trivial 183, 514
trivial ring 449
trivial solution 513–514
tromino 406
truncation 452
truth table 25, 514, 514–515,
515
for biconditionals 42
for conjunction 94
for contrapositives
101–102
for disjunction 141
for hypothetical 90, 90
for negation 348
Tsu Chung Chi. See Zu
Chongzhi
Turing, Alan 244
turning point 515
twin primes 410, 515
twisted curve 114
two-card puzzle 91, 515
two-chord theorem 78, 78
two-dimensional vectors 520
two-pancake theorem 245,
277
two-point form 164
two-secant theorem 457, 457
type, in set theory 454
U
“Über die Addition transfiniter
Cardinalzahlen” (Zermelo)
533–534
“Über die Hypothesen welche
der Geometrie zu Grunde
liegen” (Riemann) 227
“Über die Stabilität des
Gleichgewichts” (Dirichlet)
140
Über die Zahl (Lindemann)
314
“Über einen die Erzeugung
und Verwandlung des Lichtes
betreffenden heuristischen
Gesichtspunkt” (Einstein)
158
Ulam, Stanislaw 15
unary operation 364, 516
unbounded interval 278
uncertainty, and error
167–168
undefined fraction 205–206
unexpected quiz (hanging)
paradox 374–375, 375
Index 567