scatter diagram (scatter plot,
Galton graph) 106, 456–457
Schickard, Wilhelm 382
Schnirelmann, L. 230
schubfachprinzip. See
pigeonhole principle
Schwarz, Hermann 469
scientific notation 125, 168,
457
screw propeller 174
secant 457, 493, 510
secant theorem 1, 457, 457
second (measure of angle) 14
secondary data 116
second-derivative test 332
segment bisector 46
Segner, J. A. 64
selection. See combination
self-reference 244, 457–458
semi-magic square 327, 458
semimajor axis 161
semiminor axis 161
semiregular polyhedron 404
semiregular tessellation 496
sequence (progression)
458–459
sequence (totally ordered set,
chain) 365–366
series 459–460, 488
set complement 460
set direct product. See
Cartesian product
set intersection 460
set operations 524
set theory 144, 422–423,
460–461
and axiom of choice 31
as Boolean algebra 49
and De Morgan’s laws 123
difference in 131
and probability 178
and Russell’s paradox
453–454
von Neumann and 350
Zermelo’s attempt to
axiomatize 534
set-theory paradoxes 530
set union 460
seven bridges of Königsberg
problem 235, 235, 500
sexagesimal numbers 33–34
shadows 149
Shamir, Adi 111
Shanks, William 392, 461
Shannon, Claude Elwood
271, 461–462
short radius. See apothem
Shushu jiuzhang (Ch’in) 72
Siamese method 327
Sicherman, Col. George 462
Sicherman dice 462, 462
Sidereus nuncius (Galileo) 213
Sierpinski, Vaclav 203
Sierpinski’s triangle 203–204,
204
sieve of Eratosthenes 410,
462–463
sigma notation 459, 488
sigma squared 481
signed number. See integer
significant figures 168, 409
similar figures 456, 463
similar triangles 1–2
simple fraction 205
simple interest 275
simple root 451
simplification, by cancellation
56
Simpson, Thomas 463–464
Simpson’s rule 361, 464
simultaneous linear equations
219–220, 234, 282, 315,
464, 486, 491
and determinant of matrix
126–128
solved by Cramer’s rule
108–109, 128
sine function 291, 509,
510–511, 511
history of 28–29, 51,
444–445
sine rule. See law of sines
single cusp 492, 493
singularity 464
singular point 464
sink 501–502
Sirotta, Milton 232
SI units 464–465
68-95-99.7 rule 356
Siyuan Yujian (Chu Shih-
Chieh) 383
skew curve 114
skew lines 465
skewness 465
Skolem, Thoralf 534
slide 15 puzzle (Boss puzzle,
fifteen puzzle) 391,
465–466, 466
slide rule 369–370, 466
slope (grade, gradient) 132,
466–468, 467
slope-intercept form 164
smooth vs. non-smooth
surface 357
Snell, Willebrord van Roijen
468–469
Snell’s law of refraction 365,
468, 468–469
soap bubbles 469, 472
Socrates 374
solar system, mathematical
stability of 296
solid angle 15, 469
solid geometry 170
solid of revolution 57, 372,
382, 469–470, 500
solution by radicals 3, 215,
470–471
Soma cube 218
“Some Properties of
Bernoulli’s Numbers”
(Ramanujan) 435
source 501–502
space-filling curve 385
Spearman, Charles 438
Spearman’s coefficient
438–439
Spearman’s method 438
special theory of relativity 158
specific gravity 18
speed vs. velocity 519
Sphaerica (Menelaus) 336
sphere 76, 136, 166, 471–472
connectedness of 94
diameter of 130
four-color map on
200–201
great circle as “straight”
314
volume of, vs. cylinder 20,
91, 115
sphere packing 292, 472
spherical coordinates
472–473, 504
spherical excess 474
spherical geometry 225–226,
227, 270, 323, 355–356,
472, 473–474
spherical helix 248
spherical segment 472
spherical triangle 472, 474
spheroid 161
spiral of Archimedes 372,
474, 476
spirals in nature 193
splitting game 279, 279
square 430, 474–475
square brackets 50–51
square matrix 329
square model 416, 416–417
square numbers 194, 194–195
square pyramid 423
square root 157, 249, 451,
475–476, 486
squaring the circle (circle
squaring, quadrature of the
circle) 97, 238–239,
251–252, 313–314, 393,
476–477
squeeze rule (sandwich result)
16, 321, 477, 477–478, 526
SSS (side-side-side) rule 1–2,
463
Stäckel, Paul 515
stadium paradox 533
stair climbing problem 65
standard deviation 44, 386,
481–482
vs. mean and z-score 537
standard form. See scientific
notation
Statistical Methods for
Research Workers (Fisher)
197, 415
statistics 414, 437, 478
descriptive 116, 478–482
inferential 143, 268, 354,
478, 482–484
Bayes and 38–39
and central-limit
theorem 69–70
Steiner, Jakob 284, 484
Steiner point 484–485
Steiner surface 484
stellated polyhedron 404
stem-and-leaf plot 479, 479
steradian 15, 465, 469
stereographic projection 485
Stevin, Simon 485–486
Stifel, Michael 180, 348–349
Stirling’s formula 122, 486
straight angle 14, 362
straightedge and compass 95
stratified sampling 407
strictly increasing/decreasing
261–262
Student’s t-distribution 484
Student’s t-test 415, 484
subfactorial 486
substitution 486–487, 491
substitution rule for integra-
tion. See integration: by
substitution
subtraction 146, 205, 487
subtrahend 487
successive doubling 156
Sulbasutram 425
summation (Σ) 173, 487–488
summation, index of 148
summation problem 65
sums of powers 51, 488,
488–490
supplementary angles 14
surd 490
surjective function 208
“Sur la décomposition des
ensembles de points en
partiens respectivement
congruent” (Banach, Tarski)
35
Sur l’homme et le
developpement de ses
facultés, essai d’une physique
sociale (Quételet) 432–433
“Sur l’intégration des
functions discontinues”
(Lebesgue) 307
Su-yuan yu-chien (Chu Shih-
Chieh) 73–74, 75
syllogism 27
symbolic logic. See formal
logic
Symbolic Logic (Venn) 524
symmetric difference 131
symmetry 206–207, 490
Synagoge (Pappus) 239,
371–372
Synopsis of Elementary
Results in Pure Mathematics
(Carr) 435
Synopsis palmariorum
matheseos (Jones) 393
Syntaxis mathematic (Ptolemy)
421–422
systematic sampling 407
system of equations 121, 491
“Systems of Right Lines in a
Plane” (Hamilton) 245
566 Index