552
A
AAA (angle-angle-angle) rule
1, 463
AAS (angle-angle-side) rule 1
abacus 2, 2–3, 56, 74, 260
Abel, Niels Henrik 3, 10, 84,
215, 241, 405, 431–432
and solutions to polynomial
equations 471
Abelian groups 3, 5, 83, 241
Abel Prize 3
abscissa 62
absolute convergence 3–4,
248, 337
test for 3–4, 104
absolute error 167
absolute frequency 206
absolute maximum/minimum
330, 331
absolute value (modulus) 4–5,
131, 133, 142, 310, 328–329
of complex number 25, 86
abstract algebra 5, 10, 314,
354–355
abstract group 68
abundant number 389
Académie Française 8
acceleration 523
Accurate Rendering (Ahmes)
447
Achilles and the tortoise
(paradox) 532–533
acnode. See isolated point
Acosta, José de 260
actuarial science 5, 312
acute angle 5–6, 14
acute triangle 506
addend 6
addition 5, 6, 205
addition formulae
(trigonometry) 6, 41–42
addition law 344, 367
addition-multiplication magic
square 327, 328
addition rule, in probability
theory 415–416, 416
additive function 6
additive identity element (zero)
6, 257
additive inverse, and rings
448
Adleman, Leonard 111
affine geometry 6–7, 339
affine transformation 7
Agnesi, Maria Gaëtana 7–8,
58
Ahmes (Ahmose) 155, 447
Ahmes papyrus. See Rhind
papyrus
Alembert, Jean Le Rond d’ 8,
8–9, 209
and Fourier series 202
Alembert’s theorem, d’. See
fundamental theorem of
algebra
0
(aleph null) 60–61
Alexander, James Waddell
295–296
Alexander polynomial
295–296
algebra 9–11
and geometry 124
L’Algebra (Bombelli) 47–48
Algebra (Simpson) 463
algebraic curve 114
algebraic function 11
algebraic notation 51
algebraic number 11, 60, 97
and analytic number theory
360
algebraic structure 11
algebra of logic, Boole’s 48
Algebra with Arithmetic and
Mensuration (Colebrook)
42
algorithm 11, 294
Al-jam’ w’al-tafriq ib hisab al-
hind (al-Khw¯arizmı¯) 293
Almagest (Ptolemy) 421
alphamagic square 328, 328
alternate interior/exterior
angles 504
alternating harmonic series
248, 409
alternating knot 295
alternating series 11–12
alternating-series test 12,
104–105
altitude 12–13, 105
of triangle
concurrency of 12,
12–13, 165
and Euler line
174–175, 507
amicable numbers 13, 18,
423
Analemma (Ptolemy) 422
analog vs. digital 135–136
Analyse des infiniment petits
(L’Hôpital) 40, 310
analysis 13, 423
Analysis per quantitatum
series (Newton) 353
analysis situs. See topology
Analysis situs (Poincaré) 398
“The Analyst” (Berkeley) 58
analytic engine, Babbage’s 32
analytic geometry 13, 347
analytic number theory 13,
139–140, 360, 411
analytics 27
anchor ring. See torus
ancillary theorem 498–499
angle 13–15, 14, 276, 441
45º (octant) 363
of elevation/depression 14
of inclination 261
angle bisector 46, 260
angle brackets 50, 519
angle trisection. See trisecting
an angle
Annales de Mathématiques
(journal) 25
Annals of Eugenics (journal)
387
Annals of Mathematics 531
annulus 15, 89, 94, 177
anomalous cancellation 56
antiderivative 94–95, 211,
360
antidifferentation 15, 133,
272
antinomy. See Russell’s
paradox
I
NDEX
Boldface page numbers indicate main entries. Page numbers in italics indicate illustrations or diagrams.