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| Nahin P.J. — When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible |
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| Ïðåäìåòíûé óêàçàòåëü |
action see "Least action"
Algorithm, computational efficiency of 295 309—310 see
Almgren, Frederick 262 274
Anti-solar line 179—180 187 189 see
Apollonius of Perga 37
Appel, Kenneth 90
Archimedes 15 37 47
Area, of a figure 15 39 218—219 252 352—358
Aristotle 46 105
Bacon, Roger 192
Basketball 158—165
Bellman, Richard 312—314 316—317
Beltrami's identity 240 248—249 261 see
Beltrami, Eugenio 240
Berkeley, George 140 166
Bernoulli, Daniel 211
Bernoulli, Jacob 172 219 244—245
Bernoulli, Johann 139 172 174 197—198 210—212 214—215 217 219—221 228 233 240—245 249
Bertrand, Joseph 61
Besicovitch, Abram 60
Bird, Larry 160
Bolzano, Bernard 115
Boscovich, Ruggero 344
Bouvelles, Charles 217
Boys, C.V. 270 273—274
Boys, Marion 273—274
Brachistochrone 210—217 219—226 229—231 233—234 238—241 246
Calculus, differential 117—119 123 140—147
Calculus integral
Carroll, Lewis (Sylvie and Bruno Concluded) 230
Catenary 241—251
Catenoid 262 266—269
Cavalieri, B.F. 279
Chain rule 22 117 126 169 185 218 227 236 350
Chebyshev, Pafnuty 61—62
Clifford, William Kingdon 301
Computers, use of 24—36 79 84—85 88—94
Concave figure 54 60
Concave
Convex, figure 53—54 345—346 353—354
Convex, function 63 336—337 339—341
Convex hull
Cooper, Paul 229—230
Cuts, method of see "Integer programming"
Cycloid 217—224 228—229 234 see
da Vinci, Leonardo 134
Dantzig, George 294—295 298 308—310
De L'Hospital, G-F-A 171—172 174 211 215
Delta Airline problem 284—285
Derivative of composite function 124—126 198—199
Derivative definition
Derivative of product 144—145 173
Derivative
Derivative, partial 236 358—359
Descartes, Rene 99—101 103—108 117 119—120 131 139 187—188 190 192
Dido, Queen of Carthage 45—46
Diet problems 297—304 308
Differential, arc length 221 238 243 247 252 260
Differential equation
Directed graph 290—293
Dirichlet, Peter 59
Dispersion of refracted light 138—139
Dorfman, Robert 308
Double bubble conjecture 269—271
Douglas, Jesse 263
Duality 6 13 55—56 68
Dynamic programming 291 295 305 312—329
Ehlers, G. 13
Ellipsoid algorithm 310
Elliptic integral 202 351
Energy, conservation of 167 204 214 221 347
Energy kinetic
Energy, potential 204 214 247 347
Equilibrium, stable 176—177 242 243
Erdos, Paul 62
Escape velocity 21 23—24
Euclid 7—8 60 72 101 134 331
Euler — Lagrange equation 145 231—242 248—250 252—257 260—262 359—360 see
Euler, Leonhard 70 233 259 262 264 351
Exponential time 309 311 see computational
Extrema, definition 3 7 112 142 155
Extrema global
Extrema, maximum/minimum 26—33 62—69 72—79 113 136 142—144 147 149—152 158 177 185
Factory problem 284
Fagnano, G.C.T. 65
Fagnano, G.F. 65
Feasible solution set 29—30 32—33 301—304 306 311 324
Fejer, Lipot 66
Fermat's point 279
Fermat, Pierre 90 99—100 104 106—115 117—120 123—124 127—128 130—134 140 211 279
fibonacci 71
Fields medal 309
Fizeau, Hippolyte 106
Folded envelope problem 79—85
Folium of Descartes 119—120
Fontana, Niccolo see "Tartaglia"
Forysth, Andrew 274
Foucault, Jean 106
Four-color conjecture 90
Fourier, Joseph 296
Functional 210 222 233
Functional equation 313—314 316 318—319 324—328 see
Fundamental lemma, of calculus of variations 238
Galileo, Galilei 200—202 204 208—211 214 217 221 223 240—241 351
Gamma function 70
Gauss, C.F. 272 292
Geodesic 38
Ghost hubs 285—286
Goldschmidt, G.W.B. 266 271—272
Goldstein, Rebecca (Strange Attractors) 191 274
Golf 157—158
Gomory, Ralph 307
Gravitational field, motion in 21—24 95 152—171 200—210 347—351
Gregory, David 232
Gunnery problem 165—171
Haken, Wolfgang 90
Hales, Thomas 51 90
Halley, Edmond 166—168 171 198 220
Hanging chain problem 240—247 262
Hanging picture problem 73—77 91—94 147—148
Hariot, Thomas 103 106
Hawking, Stephen 197
Helprin, Mark (Winte's Tale) 246—247
Heron's formula 15 39 43
Heron, of Alexandria 15 102 127 132—134
Hoelder, Otto 341
Hoffmann, J.E. 280
Honeycomb conjecture 51 90
Hooke, Robert 250
Hudde, Johann 115
Huygens, Christiaan 7 104 220—221 241
Index of refraction 137—139 182 188
Induction, proof by 13 315—316 333 339—341
Inequality, AM-GM 13—20 49 75 77 331—333 338
Inequality AM-QM
Inequality, constraint 29 276 278 296—306 310—311 313
Inequality Jensen's
| Inflection point 145
Integer programming 304—307 324 326
Integration, by parts 145 236—237 254
Interior algorithm 311
Isoperimetric problem 6 37—38 45—47 53—59 219 231 251—257 354;
Isoperimetric quotient 47—51 62
Jefferson, Thomas 250
Jensen, J.L.W.V. 53
Jungius, Joachim 241
Kakeya, S. 60
Kantorovich, Leonid 308—309
Karmarkar, Narendra 311—312
Kepler sphere packing conjecture 90
Kepler, Johannes 102 108—109
Khachiyan, Leonid 310
Kierkegaard, Soren 320
Klee, Victor 310—311
Koenig, J.S. 134 344
Koopmans, Tjalling 308
l'Hospital's rule 172—174
Lagrange multiplier 63 248 253 257 274
Lagrange, Joseph 117 134 233 262—263
Laplace, P.S. 117
Least action, principle of 134
Least time, principle of 107—108 127—128 174 210—211 221 231
Legendre, A.M. 351
Leibniz's rule see "Derivative of
Leibniz, Gottfried 90 99 109 115 117 126 132 134 140 145 172 200 210 215 219 241 348
Length, of a curve 230 238 252 259
Leonardo of Pisa see "Fibonacci"
Lhuilier, Simon 54
Light as particles 104
Light as waves
Linear programming 29 295—304 308—312
Maclaurin, Colin 331
Mailable package paradox 149—152
Mascheroni, Lorenzo 250
MATLAB 79 365
Maupertuis, P.L.M. 133—134
Mean, arithmetic 13 331 334;
Mean, geometric 13 331
Mean quadratic
Melville, Herman (Moby-Dick) 228
Minty, George 310—311
Muddy wheel problem 94—97
Mueller, Johann see "Regiomontanus"
Nash, John 309
Newton — Raphson method 120—123 223 264
Newton's equation, for the Nth order rainbow 194
Newton's function 120—123
Newton, Isaac 21 90 99 109 115 117—120 122—123 140 143 166 171—172 193 197—198 200 210 215 219—220 231—232 250 351
Nobel Prize in economics 308—309
Nonlinear programming 326
Objective function 296 300—303 305—306 313
Optimal location problem 283—286
Optimal policy 314 319 321—329
Optimality, principle of 313—314 316—318
Pappus Of Alexandria 47 113 343
parabola 110—111 118—119 154 241 245—247 336—337
Parametric equations 217—219 222 224 252 259 352—353
Pipe-and-corner problem 85—89
Plateau problem 262 269
Plateau's rules 269—270 272 274 279
Plateau, Joseph 262 269 272
Polybius 38—39 45
Polynomial time see "Algorithm computational
Polytope see "Simplex"
Prime numbers 60—62 90
probability 8—9 183—184 251 328
Proclus 39 45
Ptolemy 102
Pulley problem 174—178 247
Rado, Tibor 263
Rainbow, infrared 198
Rainbow Nth
Rainbow, secondary 180 187—192
Rainbow tertiary
Raphson, Joseph 120 123
Recurrence, additive 318
Recurrence multiplicative
Reflection, law of 101—102 127 132—133 181 see
Refraction, law of 100—105 107—108 127 see
Regiomontanus 71 73—74
Riccati, J.R. 243 249
Roemer, Olaus 106
Saturn problem 77—79
Schmidt, Erhard 70
Schwarz, H.A. 70 263
Second law of motion 21 176 277
Shepard, Alan 2
simplex 301
Simplex algorithm 294 298—304 308—313 326
Simplicius 47
SIMPSON, THOMAS 123
Snel, Willebrord 102—104 127
Snell's law 102—108 127—132 138—139 179 182 184—185 187 190 193—195 201 210—213 231 see "Refraction"
Snowflake curve 40—45
Soap films 262—274 279
Solar line 196—197 see
Spanning circle 67—68
Steiner span 285
Steiner's number 199
Steiner's point see "Fermat's point"
Steiner, Jacob 54—59 146—147 279
Stigler, George 297—298
Strange attractors see "Goldstein Rebecca"
Surface, area of 15—19 259—271 352—358
Surface, energy of 262 269
Sylvester, J.J. 68
Tanenbaum, Robert K. (No Lesser Plea) 297
Tangent line 54 97 102 110—111 118 120—123 242 266
Tartaglia 71—72
Tautochrone 220 223—226 see
Taylor, Jean 262 269 274
Theodoric of Freiberg 192
Theon of Alexandria 47
Torricelli's point see "Fermat's point"
Torricelli, Evangelisto 279
Toth, L.F. 344
Traveling salesman problem 293—294
Vector 11—12 31 357
Verne, Jules 24
Viviani, Vincenzo 279
Voltaire 134
Von Freiberg, Dietrich see "Theodoric of Freiberg"
von Koch, Helge 40
Vos Savant, Marilyn 196
Water crossing problems 24—33 135—137
Weierstrass, Karl 251—252
Wells, H.G. 273
Wine barrel problem 108—109 148—149
Woods, Tiger 230
Zenodorus 47 49 51 54
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