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Cambridge University Press 978-0-521-75613-6 - Knots and Borromean Rings, Rep-Tiles, and Eight Queens: Martin Gardner's Unexpected Hanging Martin Gardner Index More information

Index

“Bet a Nickel” Nick, 156 Cat’s Cradle, 219 3D printer, 239 cat’s-cradle, 214 catenary, 29 Abbott, Edwin Abbott, 143 Cavalieri, Bonaventura, 194 antimatter, 116 Challenger shuttle, 243 Aragon, Louis, 217 Charosh, Mannis, 133 Archimedes, 185, 194 checkerboard, 196 Archimedes’ cylinders, 193 4 × 4, 250 Astria, 145 checkers, 92, 97, 101, 137 computer programs, 103 backtracking, 204 Checkers, 101 Barth, Karl, 66 Cheney, Fitch, 71, 156, 181 baseball pitcher, automatic, 145 chess, 92, 101 Bell Telephone Laboratories, 24, 97 computer, 92 Bennett, G. T., 48 computer programs, 103 Bergholt, Ernest, 129 maximum-attack problem, 81, 88 Bernoulli, Jakob, 111 minimum attack problem, 80, 88 Besicovitch, A. S., 233, 237 chessboard, 200 Bierce, Ambrose, 91 Chesterton,G.K.,118 blackjack, 52, 57 Chevalier de Mer´ e,´ Antoine, 52 Bligh, William, 214 Chinook, 103 Boole, Alicia, 145 closed curve, 223 Boole, George, 151 closed curve of constant width, 223 Boole, Lucy, 151 closed-space curve, 209 Borromean rings, 16, 18, 26 compound interest, 28 illustration, 17 congruent, 170 Botvinnik, Mikhail, 92, 100 continued fraction, 31 Brock, Thomas D., 24 convex ﬁgure, 233 Brotherhood of American Magicians, cryptarithms, 181 154 cube Buffon Noodle Theorem, 242 cross-section, 144, 151 Curry, Paul, 51 card tricks, 159, 162 curves of constant width binary system, 159, 162 unsymmetrical, 228

271

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-75613-6 - Knots and Borromean Rings, Rep-Tiles, and Eight Queens: Martin Gardner's Unexpected Hanging Martin Gardner Index More information

272 Index

cylindrical rollers, 223 evolute, 107 exponential function, 29 de Moivre, Abraham, 31 extrasensory perception (ESP), 51 Deep Blue, 103 deltoid curve, 233, 236 Fabre, Jean Henri, 30, 110 Demaine, Erik, 48 factorial, 31 Democritus, 194 faro shufﬂe, 161 Descartes, Rene,´ 111 Feynman, Richard, 243 Dewdney,A.K.,152 Flatland, 63, 143 dice, 51 fourth dimension, 145 dealer, 59 fractals, 257 digital root, 168 Frederickson, Greg N., 46 Dillingham, G. W., 121 dissecitons, geometrical Gabriella Computer Kit, 102 Greek cross, 43 galaxy, spiral, 112 dissection, 181 Gale, Gabriel, 118 dissection, geometrical, 38 gambling, 51 dodecagon to a Greek cross, 40 cheating, 58 hexagon to a square, 40 Nevada, 58 Latin cross to square, 41 garter trick, 210 Maltese cross, 40 Go (game), 97, 101 octagon to a square, 42 Golomb, Solomon W., 198, 247 strip method, 42 Gomory, Ralph, 197 divisibility, 168 Great Jasper, The, 154 test for 10, 169 Greek cross, 198, 205, 233 test for 11, 169 test for 12, 169 Hackenberg, Chi Chi, 103 test for 2, 168 Hansel, Mark, 51 test for 3, 168 Heim, Karl, 66 test for 4, 168 Heubeck, George, 164 test for 5, 168 hexagonal holes, drill for, 239 test for 6, 169 hexapawn, 93, 98, 101, 102 test for 7, 169 HER (Hexapawn Educable Robot), test for 8, 169 94 test for 9, 169 Hexapawn, 98 dodecahedron, 232 Hexapawn Educable Robot (HER), 94 dominoes, 196 Hexapawn Instructable Matchboxes Dudeney, Henry Ernest, 38, 132, 185, (HIM), 97 198, 202 hexominoes, 253 Durer,¨ Albrecht, 248 Hight, Stuart, 97 Hinton, Charles Howard, 145 e (constant), 28 Hinton, Howard Everest, 151 Eigen, Victor, 159 Hinton, James, 145 eight-queen problem, 202 Hinton, Joan, 151 Einstein, Albert, 64 Hinton, William, 151 Euler, Leonhard, 31 homeomorphic, 78

Index 273

Huffman, David A., 16 machine learning, 103 hypercube, 62 Mandelbrot, Benoit, 239 hyperspace, 64 Mario, Ed, 161 Matchbox Educable Naughts And i (imaginary number), 34 Crosses Engine (MENACE), 92 icosahedron, 232 mathemagic, 154 infin-tiles, 257 McCarthy, John, 203 involute, 106 Merian, Matthaus, 121 Michie, Donald, 92 Jacob’s Ladder, 215 microbe, 24 James, William, 67 Milky Way, 112 Josephus problem, 164 minicheckers, 97 minichess, 98, 103 Kakeya, Soichi,ˆ 232 Minkowski, Hermann, 231 Kakeya conjecture mixed-up hats, 32 Euclidean, 238 Mobius¨ strip, 18 Kakeya needle, 232 molecule Kakeya sets, 237 knot structure, 25 Kant, Immanuel, 66 More, Henry, 66 Kasparov, Garry, 103 multiplicity, 253 knot, 16, 22 multiplier series, 171 amphicheiral, 22 Chefalo, 24 Nabokov, VLadimir, 106 figure-of-eight, 20 Neale, Bob, 73 granny, 22 Newell, Peter, 119 of five crossings, 21 Nim, 97 of four crossings, 21 Nim Box Logic Engine (NIMBLE), 97 of seven crossings, 21 of six crossings, 21 O’Beirne, T. H., 250 order of, 18 octahedron, 232 prime, 22 Octapawn, 99 square, 22 Osage Diamonds. See cat’s cradle trefoil, 22 Out of this World (magic trick), 51 with zero crossings, 16 knot polynomial, 20 paradox, 1–15 unexpected egg, 3, 6, 10 Lamb, Charles, 214 unexpected hanging, 1, 8, 11, 12, 15 Laplace, Pierre Simon, 84 unexpected spade, 4 Lasker, Edward, 92 Pascal, Blaise, 52, 170 Latin cross, 63, 129 Peirce, Benjamin, 32 Leibniz, Gottlieb von, 127 pentominoes, 198 lightning calculator, 172 Perigal, Henri, 47 Lindgren, Harry, 39, 44 permutation, 32 Littlewood, J. E., 184 Perron Tree, 233 loxodrome, 110 Petrosian, Tigran, 101 Loyd, Sam, 255 Plato’s grotto, 62, 63

274 Index

Platonic dualism, 66 horizontal, 117 polygon rotational, 117 irregular, 246 twofold, 117 irregular star, 228 vertical, 117 stellated, 250 symmetry operation, 117 polyominoes, 197 psychokinesis, 148 Tait, Peter Guthrie, 24 tangled space curve, 23 Ravelli, 164 Taylor, Geoffrey, 151 relativity theory, 72 tessellation, 42 rep-tiles, 247 tetrahedron, 232 Reuleaux triangle, 224, 225, 240 The Lady or the Tiger?, 75 Reuleaux, Franz, 224 Theobald, Gavin, 46 rhumb line, 110 Thinland, 150 rooks Thomson, J. J., 23 nonattacking, 205 Thomson, William, 23 rotor, 232 Thoreau, Henry David, 118 roulette, 53 Thorp, Edward, 103 cancellation system, 55 Thorp, Edward O., 57 d’Alembert system, 54 tiling, 246 martingale system, 54 tippy top, 158 parlay system, 55 topologically equivalent, 17 Ruiz, Sebastian Martin, 36 transcendental number, 30 trisection, 108, 114 Scarne, John, 51, 162 tumble rings, 154, 161, 166 Schaeffer, Jonathan, 103 Schwartz, Sam, 163 unexpected hanging Slade, Arthur, 62 origin, 9 Slade, Henry, 67 slot machines, 52 Verbeek, Gustav, 119 solitaire (peg), 127 Voynich, E. L., 151 spiral, 106 logarithmic, 109 of Archimedes, 107 Wankel engine, 225 spiral illusion, 113 Wankel, Felix, 225 Stein, Sherman, 242 Wefa, Abul, 38 stereoisomers, 115 Whistler, Rex, 119 Stockton, Frank, 75 White, Morton, 121 Stoddart, J. Fraser, 25 Wiener, Norbert, 91 Stover, Mel, 159 Wilsun, Lucius S., 78 string play, 209 Winchell, Paul, 123 superqueens, 205 Wood, Robert W., 122 superstrings, 72 symmetry Zollner,¨ J. K.-F.,67 fourfold, 117 ␲ (constant), 30