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National Council of Teachers of Mathematics Historical Topics for the Mathematics Classroom Thirty-First Yearbook
National Council of Teachers of Mathematics  Historical Topics for the Mathematics Classroom Thirty-First Yearbook







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: Historical Topics for the Mathematics Classroom Thirty-First Yearbook

: National Council of Teachers of Mathematics

: en

: /

:

ed2k: ed2k stats

: 1969

: 524

: 03.04.2008

: | | ID
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$\phi$ (phi)      see Golden section
$\phi$ (phi), $\tau$ (tau)      205
$\pi$ (pi)      [44] 148153 squaring
$\pi$ as a ratio      148 150 151 152
$\pi$, approximations for      103 109 110 149152 169 174 226 377 403 453454
$\pi$, Archimedian approximation for      150 174 403
$\pi$, Babylonian approximation for      149
$\pi$, biblical approximation for      149
$\pi$, Brounckers expression for      151152 269
$\pi$, Chinese value of      109 150
$\pi$, classical method of computing      108 150151 174 226 403
$\pi$, computation of      108110
$\pi$, computation of, by computer      152153 174
$\pi$, continued fraction form of      269270
$\pi$, Egyptian approximation for      149
$\pi$, Hindu approximations for      150151
$\pi$, irrationality of      152
$\pi$, Lamberts expression for      270
$\pi$, Leibniz series for      152153 393 421
$\pi$, Ludolphian number      109 151
$\pi$, Machins formula for      109 152
$\pi$, probability methods of computing      153
$\pi$, Ptolemys value of      103 109
$\pi$, symbols for      153
$\pi$, transcendence of      84 152 204
$\pi$, Vietes expression for      151
$\pi$, Wallis expression for      152 414
$\tau$ (tau)      see Golden section
Abacists      119
abacus      [28] 28 46 94 117120 130 242
Abacus as counting table      91 117120
Abacus, Chinese (suan phan)      9192 119
Abacus, contest with      9293
Abacus, etymology of      91 117
Abacus, Japanese (soroban)      9192 119
Abacus, Roman      9192 118
Abel, Niels Henrik      115 246 251 253 254 255 256 266 278 311 433 434
Abstract algebra      234 284287
Abstract spaces      188189
Abu Kamil      307308
Abundant numbers      [12] 5961
Abul-Wefa      103 177 195 351 352 355 373 375
Acta Eruditorum      229 393 397
Actuarial mathematics      247
Adams Bashford method      115
Additive principle      6 23 27 37 38 41 42
Adelard of Bath      48 119
Agnesi, Maria Gaetana      211
Agnesi, witch of      [56] 210211
Ahmes papyrus      see Rhind papyrus
Ahmes, Ah-mose or Ahmose      123
Aiken, Howard H.      112 162
Al-jabr (al-Khowarizmi)      233 242 260 306
Alcuin of York      121
Alembert, Jean Le Rond d      214 318 433 438 449 460
Aleph null      85
Alexander, James Waddell      187
Alexandria      73
Algebra      see also Equations
Algebra (Wallis)      213 292
Algebra in medieval Europe      309
Algebra of logic      257
Algebra, abstract      234 284287
Algebra, Arabic      [80] 7677 241242 260261 305308 332
Algebra, associative division      297
Algebra, Babylonian      235236 237 240 276 312 377378
Algebra, boolean      [74] 257258 284287
Algebra, Egyptian      237 332
Algebra, etymology of      233
Algebra, European      [81] 242245 309311
Algebra, fundamental theorem of      [84] 186 278 311 316318
Algebra, geometric      172 236 237240 242 276 298301 308 338
Algebra, Greek      [78] 236 237240 261262 298300 332
Algebra, Hindu      [79] 241242 261262 301305
Algebra, laws of      248251 256257 279280 285286 296297
Algebra, linear      283
Algebra, matrix      257259 281283
Algebra, modern      234 284287
Algebra, names for unknown      242
Algebra, noncommutative      256257 259 279280 29697
Algebra, quaternionic      280
Algebra, renaissance of      242245 277278 309310
Algebra, rhetorical      234 235236 237 242 260 303 305 387
Algebra, stages in      234
Algebra, symbolic      234 243244 387
Algebra, symbolism in      181 241 243244 245 291 310
Algebra, syncopated      234 240241 243 260262 277 303
Algebraic numbers      [26] 8384
Algebraic symbolism      260263
Algorism      see Algorithm
Algorismus vulgaris (Sacrobosco)      48
Algorists      119
Algorithm (or algorism), etymology of      48 234
Algorithm, Euclidean      [17] 69 267 378
Algorithm, square root      45
Almagest (Ptolemy)      [91] 50 90 96 101 242 337 338 342 344 359361 370
Almagest (Ptolemy), contents of      361
Almagest (Ptolemy), etymology of      359
Alternating Series Test      421 433
American Mathematical Monthly      471
Amicable (friendly) numbers      [11] 5859
Ampere, Andre      160
An Index of Mathematical Tables (Comrie)      107108
An Investigation of the Laws of Thought (Boole)      258 284
Analemma      339342
Analemma (Ptolemy)      342
Analyse des infiniment petits (LHospital)      397 435
Analyst      397 399
Analytic geometry      146 179 180182 190 247
Anaxagorus      202
angle      [92] 362
Angle, definitions of      362
Angle, degrees in      365366
Angle, measure of      363364 364368
Angle, mil      367368
Angle, radians      366367
Angle, right      [93] 363364
Angle, symbol for      362 364
Angle, trisection of      [52] 173 193 199201
Angular measure      [94] 364368
annuities      [88] 325326
Anthologia Palatina      240
Anthoniszoon, Adriaen      109
Antiphon      202
Apices      118
Apollodorus      215
Apollonius of Perga      174 175 178 180 182 222 223 239 387
Apollonius, circle of      175
Apollonius, Conic Sections      175 178 222 239
Application of areas      222
Arabic (modern) numeration system      29 49
Archibald, R.C.      107
Archimedes      [98] 4 73 82 8990 108 132 150 174 182 199 202 380382 385 386 403405 430431 432
Archimedes, anticipation of the calculus      [98] 403405 409
Archimedes, area of parabolic segment      403405
Archimedes, determination of pi      403
Archimedes, lemma of      379
Archimedes, Metaphysics      51
Archimedes, Method      381382 385
Archimedes, method of      [109] 380382 385 403404 430431
Archimedes, On the Sphere and Cylinder      174
Archimedes, postulate of      174
Archimedes, spiral of      202204
Archimedes, The Measurement of the Circle      93 100 132 150
Archimedes, The Sand-Reckoner      8990
Archytas of Tarentum      198 222 276
Area of circle      126 149150 169 202 377 386 403 407 430 440
Argand, Jean Robert      15 246 292 293
Aristophanes      202
Aristotle      11 51 64 70 73 212 362
Arithmetic (theory of numbers)      32 36
Arithmetic mean      377
Arithmetic triangle      see Pascals triangle
Arithmetic, Calandris      134
Arithmetic, etymology of      233
Arithmetic, Treviso      94 97 134
Arithmetica (Diophantus)      57 79 240 261 332
Arithmetica Infinitorum (Wallis)      387388 414
Arithmetica integra (Stifel)      140
Arithmetica Universalis (Newton)      319320 322
Arithmetische und geometrische Progress-Tabulen (Buergi)      106 143
Arithmetization of analysis      401402
Ars Conjectandi (Bernoulli)      159 266
Ars magna (Cardano)      212 244 277 278 310
Art of Numbring By Speaking-Rods (Leybourn)      141
Artis analyticae praxis (Harriot)      319
Aryabhata      69 150 301 370
Asoka      47
ASSC      112 162163
Astrolabe      340
Astronomy      175 177 333 339342 470
Astronomy, Arabic      350
Astronomy, astronomical instruments      194
Astronomy, Babylonian      37 360 364365
Astronomy, concepts of      38
Astronomy, Greek      12 359361 365
Astronomy, Hindu      140 346350
Ausdehnungslehre (Grassmann),      279 280
Automata theory      473
Automatic Sequence Controlled Calculator (ASCC)      112 162163
Axiomatic method      462467 476
Axiomatic method as a research tool      465 472
Axiomatic structure      9
Axiomatics      23 173 189190 191
Axiomatics, interpretation of      189
Axiomatics, role of, in teaching      471
Axioms      9 1516
Axioms, Euclids      9 16
Axioms, independence of      462
Babbage, analytic engine      112 162
Babbage, Charles      112113 161 423
Babbage, difference engine      112 161162
Babbage, H.P.      112 162
Babylonian algebra      377378
Babylonian astronomy      3738
Babylonian numeration system      [1] 4 6 28 3638 47 49 89 130132 135 360 364365 370
Bakhshali manuscript      50 136 332
Baldwin, Frank S.      112
Ball, W.W. Rouse      160 214
Bank      120
Barlow, Peter, New Mathematical Tables      101 108
Barrow, differential triangle      416417
Barrow, Isaac      [104] 153 390391 392 415417 418 419
Barrow, Lectiones Opticae et Geometricae      391 416
Battani, al-      103
Bede, De temporum ratione      89
Bede, the Venerable      8889 122
Bell, Eric Temple      127 170
Beltrami, Eugenio      185
ben Ezra, Abraham      136
Benedetti, Giovanni B.      195
Berkeley, George      399 445
Bernoulli, Daniel      438 449
Bernoulli, Jakob or Jacques      181 229 266 397 440 441 458
Bernoulli, Jakob, Ars conjectandi      159 266
Bernoulli, Johann or Jean      145 227 228 312 358 397 398 399 435439 440 441 446
Bertrand, Joseph L.F.      63
Bessel, F.W.      246
Beyer, Johann Hartmann      138
Bhaskara      30 68 218 241 304 455 456457
Bidder, George Parker      160
Binary numeration system      69 89 93 130
Binary quadratic form      323
Binet, Jacques P.M.      78
Binomial coefficients      156157 (see also Pascals triangle)
Binomial theorem      [67] 114 264266 294 310 392 421 433
Birkhoff George D.      471
Biruni, al-      336 353 355 373 375
Blater, J.      78 105
Boethius      95 119 219
Boethius, Institutis arithmetica      95
Bolyai, Farkas      209
Bolyai, Janos      10 184 185 209 462 464
Bolzano, Bernhard      401
Bombelli, LAlgebra      327328
Bombelli, Rafael      243 263 267 291 292 310 327328 330
Boole, Finite Differences      428
Boole, George      115 257 284 428 429
Boole, Laws of Thought      258 284
Boole, Mathematical Analysis of Logic      284
Boolean algebra      [74] 257258 284287
Brachistochrone      228 440
Brahe, Tycho      407
Brahmagupta      68 69 151 176 241 243 261 262 301 349 455456
Brahmagupta, Brahmasphuta Siddhanta      349
Brahmagupta, Uttara Khandakhadyaka      349
Brahmasphuta Siddhanta (Brahmagupta)      349
Brianchon, Charles J.      179 230
Brides Chair      218
Briggs, Henry      98 106 145 247
Brossin, George      see Mere George chevalier
Brouncker or Brounker, William      151 269
Brouwer, L.E.J.      111 187 468
Brouwers number      111
Buergi, Arithmetische und geometrische Progress-Tabulen      106 143
Buergi, Jobst or Joost      15 106 138 143 329 331
Buffon, Georges Louis Leclerc, comte de      153
Buffons needle problem      153
Bugilai tribes      1921
Burali-Forti, Cesare      85 467
Burroughs, William S.      113
Buteo, Jean      263 329 330
Buxton, Jedediah      160
Cajori, Florian      214
Calandri, Filippo      134
Calculating machines      111114 (see also Computers digital)
Calculating machines, Leibniz      112 161
Calculating machines, Pascals      112 161
Calculating prodigies      [48] 159160
Calculating rods      281
Calculation      see also Computation
Calculation, etymology of      87
Calculator, desk      9293
Calculus      173 182 275
Calculus in Japan      [118] 452454
Calculus of finite differences      115
Calculus of variations      [112] 439440
Calculus, conception in antiquity      376378
Calculus, differential      418
Calculus, etymology of      376
Calculus, integral      170 174 405406 419
Calculus, medieval contributions to      383386
Calculus, notations in      394395
Calculus, priority controversy in      397398 443
Calculus, search for rigor in      399402
Calculus, tensor      183 280
Calendar, Mayan      89
Campanus, Johannes      177
Canon foecundus (Reinhold)      103
Cantor, Georg      36 72 84 8586 313 402 465 468
Cardan, Jerome      see Cardano
Cardano, Girolamo, or Jerome Cardan      157 158 195 212 243 244 245 263 277 291 309 310 317 319 329 330 358
Cardans formula      277
Cardinal numbers      21
Carnot, Lazare      179
Carroll, Lewis      see Dodgson Charles
Casting out nines      [38] 140
Cataldi, Pietro      269 329 331
Catenary      392
Cauchy Riemann equations      438
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