periodic function 390
peripatetics 27
peripheral angle 77, 77
permillage 388
permutation 82, 127, 186,
209, 390–391, 490
permutation group 68
perpendicular 369, 391, 468
perpendicular bisector 46,
174–175, 338, 391, 507
perspective 149–150,
391–392, 419
peta- (10
15
) 465
Phaedo (Plato) 396
phyllotaxis 193
Physics (Aristotle) 532
physics, Aristotelian 27
pi (π) 55, 392–394
approximations of 20,
28–29, 291, 537
irrational 283, 300, 477
not constructible 97
transcendental 11, 301,
313–314, 393, 477
Piazzi, Giuseppe 219
pico- (10
-12
) 465
pie chart (graph) 479, 479
pigeonhole principle 394–395
Pitiscus, Bartholomaeus 511
pivoting. See Gaussian
elimination
place-value system 6, 51, 155,
192, 251, 359, 487
planar curve 114
planar graph 233
Planck, Max 158
plane 80, 315, 395
plane geometry 170
Plane loci (Apollonius) 189
Plato 166, 238, 395–396,
397, 498, 532
Platonic solids 159, 232, 238,
291–292, 395, 396,
396–398, 404, 424
Platonicus (Eratosthenes) 166
Playfair, John 171, 227, 355,
376, 377
Playfair’s axiom 46, 171, 227,
355, 376, 377
plot 398
Plouffe, Simon 183
plus 398
plus/minus symbol 398
plus sign 398, 486
Pneumatica (Heron) 248–249
Poincaré, Jules Henri 255,
314, 398–399, 500, 530
Poincaré disk 255
Poincaré’s conjecture 399
point 399
point of contact (tangency
point) 399
point of inflection. See
inflection point
point-slope form, of equation
of line 164
Poisson, Siméon-Denis 44, 71,
399–400, 414–415
Poisson distribution 44,
399–400
polar-coordinate graph 235
polar coordinates 22, 39, 63,
400, 400–401, 504
of cardioid 62
of complex numbers 86,
86
of logarithmic spiral 474
of rose 451
polar form 176
Polignac, Alphonse de 107
Pólya, George 401–402
polychoron 403
polygon 119, 149, 402–403,
403
area of 23, 24
circumcircle of 78
convexity of 88
exterior angles of 182
and tessellation 496–497
polygon division problem 64
polyhedral angle 469
polyhedron 88, 128–129,
176–177, 185, 236,
403–404
polynomial 404–405
polynomial equations 163,
215
polynomial time 405
polyomino 405–406, 406
polytope 403
Poncelet, Jean Victor 419
population and sample
406–407
population mean 483
population model 182,
407–408
position vector 395, 408
positive 408
positively oriented 369, 448
positively skewed 465, 480,
480
positive slope 467
postage-stamp problem 446
postulate (axiom) 31, 170,
409
potential 239
power series 121, 324, 399,
409, 495, 530
P problems vs. NP problems
357–358
Practica geometriae
(Fibonacci) 511
precision 66–67, 409,
529–530
“Preliminary and Elementary
Essay on Algebra as the
Science of Pure Time”
(Hamilton) 245
premise 409
primary data 116
prime 409–410, 461
prime factorization 187
prime numbers 186, 389
and Bertrand’s conjecture
71, 167
vs. composite numbers 87
and factorization 186–187
and fundamental theorem
of arithmetic 83,
186–187
infinitude of 171–172
Mersenne’s work on 338
prime-number theorem 71,
219, 410, 410–411, 447, 535
proofs of 167, 243, 518
principal axes 411
Principia (Newton) 293,
351–353, 352
Principia Mathematica
(Russell and Whitehead)
453, 530
Principia philosophiae
(Descartes) 125
The Principle of Relativity
(Whitehead) 530
The Principles of Empirical
Logic (Venn) 524
Principles of Mathematics
(Russell) 453
Principles of the Art of
Weighing (Stevin) 485
Prior and Posterior Analytics
(Aristotle) 27
prism 403, 411–412
prismatoid 412
prismoid 412
prisoner’s dilemma 218, 412,
412–413
probability 122, 143, 189,
243, 262–263, 413–418
and harmonic functions
246
Kolmogorov’s work on
296
Monte Carlo method
342–343
Monty Hall problem 343
and mutually exclusive
events 344
odds and 363
Pascal and 382
and permutations 391
Poisson and 399–400
Quételet and 432–433
and random walks 437
and set theory 178
and two-card puzzle 515
probability density function
143
probability models 416
probability tree 415–416, 416
procedure. See algorithm
Proclus 171, 239, 497
product of matrix 330
product rule 133, 273, 309,
418, 433–434
product set. See Cartesian
product
progression. See harmonic
sequence
projected vector 418–419
projection 337, 391–392,
418–419
projective geometry 123–124,
270, 339, 372, 382, 409,
418, 419
prolate spheroid 362
proof 420
proof by contradiction. See
indirect proof
proofs, defective
that 0 = 1 29
that 1 = 2 4, 248, 337
that 1 is the largest integer
284
that all horses are the same
color 266–267
that the moon is made of
cheese 90
proper factor 186
proper fraction 205
properly divergent 144
proper vector. See eigenvector
proportion 149, 230–232, 370
proportional 420–421, 439
proposition 421
Protagoras 374
p-series test 104
pseudoprime numbers 410
pseudosphere 300
Ptolemy 239, 253, 392, 421,
421–422, 510
Ptolemy’s theorem 52, 422,
422
public-key cryptography 111
pure mathematics 159, 168,
422–423
pure surd 490
pyramid 403, 423
pyramidal frustum 207
Pythagoras 9, 57, 172, 230,
238, 387, 396, 423,
423–424, 425
Pythagoras’s theorem 159,
165–166, 208, 226, 238,
256, 314, 424, 424–426,
425, 506
in Babylonian mathematics
34–35
in Chinese mathematics 73
converse of 506, 506–507
and distance formula 141
and law of cosines 303
and polar coordinates 400
and Pythagorean triples
426
tessellation and 474, 475,
497
and vectors 520
The Pythagorean Proposition
(Loomis) 425
Pythagorean triples 99, 137,
162–163, 190, 226, 360,
422, 426–427
564 Index