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Hayes D.F. (ed.), Shubin T. (ed.) — Mathematical Adventures for Students and Amateurs
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Название: Mathematical Adventures for Students and AmateursАвторы: Hayes D.F. (ed.), Shubin T. (ed.) Аннотация: How should you encode a message to an extraterrestrial? What do frogs and powers of 2 have in common? How many faces does the Stella Octangula have? Is a plane figure of constant diameter a circle, and what has this to do with NASA? 210 = 5 x 6 x 7 = 14 x 15, so just how many numbers can be the product of both two and of three consecutive integers? Is there any such thing as a truly correct map? What patterns are possible in juggling?
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 304Добавлена в каталог: 11.04.2008Операции: Положить на полку |
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Abel, Niels Henrik 246 257 Ahlfors' "five islands" theorem 255 Ahlfors, Lars V. 255—257 Aleksandrov, A.D. 214 Alexanderson, Gerald L. 34 Algebraic integer 58 Analytic continuation 78 Appel, Kenneth 17 Archimedes 219 221—225 227 228 230 231 Arecibo Message 5 Aristaeus 219 Armstrong, Neil 9 Asymptote 168 174 181 191 231 275 Babylonians 53 54 164 Banach's matchbox problem 145 Banach, Stefan 145 146 Bayesian probability distribution 139 153 Benford's law 47 Berra, Yogi 27 Bertrand's paradox 150 151 Beukers, Frits 61 Bijection 91 101 103 108 109 111 116 see Binary operation 168 Binet formulas 97 Binomial coefficient 106 107 110 Birch and Swinnerton — Dyer conjecture 61 78—80 Birthday problem 138 Bloch's constant 254 256 Bloch's principle 254 Bloch's theorem 254—56 Bloch, Andre 254 257 Boethius 52 Bonk and Eremenko theorem 256 Bonk, Mario 256 257 Boole, George 278 Brianchon's theorem 173 174 179—183 Bryant, Robert 7 Buffon Needle Problem 138 149 153 Cardioid 186 Carroll, Lewis 259 261 271 275 278 280 see Cartan — Hadamard theorem 202—203 208 211 212 Cartan — Hadamard — Gromov theorem 208 Cauchy — Riemann equations 246—248 Centroid 221 223 228—231 Challenger (Space shuttle) 7 10 11 16 Check digit 27 33 34 38 Chromatic polynomial 114 116 Coates and Wiles theorem 79 Coates, John H. 79 80 Cole, Frank Nelson 20 Collinear 165 166 168 173—176 178—182 Complex cosine 253 complex derivative 247 248 Complex exponential 248 250 Complex function 247 248 250 252 255 Complex logarithm 249 250 254 Complex number 78 246—248 250 251 Complex plane 246—248 251 252 Complex sine 253 Complex variable 78 233 251 Conformality 233 244—246 248—250 252—256 Conic section 157 165 166 181 Conjecture 74 Connolly, Robert 144 145 Contractibility 205—208 211 212 Convergence 56 78 136 138 247 248 Convex polygon 120 171 Convex polyhedron 120 121 Copernicus, Nicolaus 38 Coprime 58 Coram, Marc 152 153 Cubical complex 202 209—211 214 cuboid 51 61 62 Curvature 201 202 205 206 257 Curvature, Gaussian 201 202 206 209 Curvature, nonpositive 202—212 214 215 Curve of constant width 11 13 see Cusp 185—189 191 194 197 198 Cycloid 185 188 D'Alembert, Jean le Rond 247 Darwin, Charles 38 de Fermat, Pierre 74 de Morgan, Augustus 269 278 De Morgan, William 269 Defect 253 Degree of a polynomial equation 246 density 44 143 152 186 197 219 221—225 227—231 252 Desargues' theorem 173 175—177 183 Developable surface 250 Diaconis, Perci 139 153 Differential 244 245 248 256 Directed ratio 173 DNA 5 dodecahedron 120 122—124 128—132 Dodgson, Charles Lutwidge 259—262 265 267—280 see Doyle, Peter 116 Drake's equation 6 Drake, Frank 4 6 Dual statement 180 Duality 122 Egyptians, ancient 157 Eilenberg — MacLane theorem 212 Einstein, Albert 38 51 ellipse 165 166 181 186—189 191 241—243 250 256 Elliptic curve 60 61 63 65 66 69 71 73 75—77 79 80 253 Enigma code 17 Equidistribution 44—48 Eremenko, Alexandre 256 257 Error, correction 32 Error, detection 27 33 38 Euclid 121 184 219 259 272—275 279 Euclid's Elements 273 Euclidean distance 203 204 209 Euclidean geometry 183 184 Euclidean plane 204 208 247 Euclidean space 209 Euclidean triangle 204—206 210 Eudoxus 273 Euler's theorem 234 236 250 Euler, Leonhard 20 53 58 60 62 63 234 247 257 Evolute 186 187 191 Extended complex plane 252 Fake circle 11 14—16 see Feller, William 141 144 153 Fermat's last theorem 25 61 65 Feynman, Richard 9 10 16 Fields medal 255 Flat torus 206—209 214 Four Vertex Theorem 187 Four-color theorem 17 18 25 114 267 Freshman sum 84 Freudenthal, Hans 3 6 Function, analytic 247 248 252—255 Function, complex 247 248 250 252 255 Function, entire 247 248 251—255 Function, linear 158—160 Function, meromorphic 251—257 Function, multiple-valued 250 Function, rational 251 252 Fundamental theorem of algebra 247 248 250 251 Galilei, Galileo 38 Gallian, Kristin 32 Gardner, Martin 136 144 153 Gauss' theorema egregium 250 Gauss, Carl Friedrich 55 56 246 247 250 257 Generator 166 212—214 Geodesic path 203—206 208—210 Geodesic space 203 205—209 212—214 Gladstone, William Ewart 274 Graham, Ronald L. 44 Graph 114—116 Graph, coloring 114 115 Graph, incomparability 114 115 Greeks, ancient 19 51 52 Gromov's lemma 211 214 Gromov, Mikhail L. 214 Group 67 69 105 116 122 123 128 131 202 203 211—215 Group presentation 212—214 Group, abelian 67 69 105 116 Group, finitely-generated 69 Group, fundamental 202 203 211—215 Group, homology 214 215 Group, symmetric 105 Group, symmetry 122 123 128 131 212 Haken, Wolfgang 17 Hall, Marshall 105 116 Halley, Edmund 245 257 Harmonia Mundi 126 Harrison, George 33 Hasse, Helmut 78 Heath, Thomas L. 219 231 Hexahedron (cube) 120 122 123 125 128 Homeomorphism 201 202 206 215 Homothety (simple scaling) 243 Homotopy 201 202 205 207 208 211 212 214 Huxley, Thomas 30 Hyperbola 166 168 174 181 icosahedron 117 120 122 123 128 131—133 Independent identically distributed sequence (HD) 141 142 Induction, mathematical 110 133 163 Infinite product 78 Infinite series 247 Invariant 201 202 214 219 inversion 180 182 183 Isometry 202 207 208 Isomorphic groups 211—214 Kepler, Johannes 126 Klein bottle 214 Klimek, Paul 99 Knuth, Donald 31 39 44 L-function 78 Lagrange, Joseph 247 Lambert's map 239 240 242 243 256 Lambert, Johann 234 257 Laplace, Pierre Simon 136 141 Law of Large Numbers 136 Legendre, Adrien Marie 273 274 Lennon, John 27 32 36 Liddell, Alice Pleasance 259 261 279 LINCOS 3 4 6 Line at infinity 168 176 177 181 Linear, approximation 244 Linear, equation 18 157 158 275 276 Linear, extension 114 115 Linear, function 158—160 Linear, map 241 244 Linear, order 115 Linear, recurrence 97 98 Linear, transformation 241 243 244 256 Link of a vertex 210 211 214 Magnusson, Bengt 99 103 Maple™ 18 Markov chain 98 142 Mathemagician 83 Mathematica® 18—20 McAuliffe, Christa 7 9 McCartney, Paul 27 McNair, Ron 7 9 Menelaus' theorem 173—175 178 179 183 Mercator map (projection) 233 235 237—240 243—245 249 250 Mercator, Gerhardus 233 235 237 239 256 Mersenne Prime Search 20 Mersenne, Marin 19 20 Metric 207 Moebius inversion 111 Moebius strip 214 266 Monte Carlo simulation 149 Monty Hall problem 136 Mordell, Louis 65 69 71 National Aeronautics and Space Administration (NASA) 11 14—16 Needham, Tristan 250 257 Nevanlinna's theorem 253 255 Nevanlinna, Rolf 252 253 255—257 Newton's method 157 163 165 Newton, Sir Isaac 38 Non-Euclidean geometry 183 184 Number, complex 78 246—248 250 251 Number, congruent 73—75 77—79 Number, Eulerian 108 110 111 Number, harmonic 54—57 59 60 Number, irrational 41 42 44 46—48 97 Number, perfect 20 21 Number, prime 3—6 19—25 58 70 77 78 Number, rational 41 42 47 48 54 69 73—75 Number, triangular 52 54 55 59 60 Numbers, Fibonacci 83—85 89 90 92 97 98 Numbers, Gibonacci 92 96 97 Numbers, Lucas 89—92 96—98 O-ring 9 10 octahedron 120 122 123 126—128 132 One-to-one correspondence 87 88 94 101 107 111 112 see Order relation 114 Pappus' theorem 173—175 182 183 parabola 160 166—168 181 185 219—221 227—231 Paraboloid 219 221 222 225 229—231 Partial order 114 115 Partially ordered set 99 113 see Pascal's theorem 157 162 165 166 168 173 174 178 180—183 Pascal's triangle 106 110 111 Pascal, Blaise 166 Pasteur, Louis 38 Patashnik, Oren 44 116 Peirce, Benjamin 273 Permutation 99 101—116 Permutation, cyclic 103 111 Permutation, descent of 108—110 112 113 115 116 Picard's theorems 251—255 Picard, Emile 251 252 257 Picasso, Pablo 194 195 Pigeonhole Principle 41 42 44 47 48 Plimpton collection 54 Poincare disk 204 205 Point at infinity 65 66 168 176 251—253 Point, inflection 66 191 Point, integer 70 71 Point, rational 54 61—63 69 71 75—79 Poisson process 143 Pole 251 252 Polya, George 28 39 48 Polyhedron 16 117 120—124 132 133 Poncelet — Brianchon theorem 173 174 181—183 POSET 99 100 111 113—116 see Power of point theorem 178 Power series 78 247 248 251 Price, Bartholomew 259 268 269 271 273—277 279 Prime 19—21 25 Prime factorization 19—23 25 58 Projection 152 166—168 181 197—199 207 208 235—240 242—245 249—253 256 Projection, covering 207 208 Projection, cylindrical 235—240 243 245 249 Projection, plate carree 239 240 242 256 Projection, stereographic 245 249—253 256 Projective 2—space 66 Projective geometry 66 168 175 176 181 183 Projective plane 168 176 181 265 Projective transformation 166 176 183 Pythagoras 51—54 63 Pythagorean cuboid 61 62 Pythagorean Theorem 53 73 Pythagorean triple 54 61 62
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