Klee V., Wagon S. — Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Mathematical Expositions Series #11) :: Электронная библиотека попечительского совета мехмата МГУ

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Klee V., Wagon S. — Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Mathematical Expositions Series #11)

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Название: Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Mathematical Expositions Series #11)

Авторы: Klee V., Wagon S.

Аннотация:

Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 352

Добавлена в каталог: 09.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Ishihata, K.      225
Isohedral      39—40 111
James, R.      111
Jamison, R.E.      108
Johnson, P.D.      123
Johnson, S.      95
Jones, J.      230
Jordan curve      4 58—65 69—70 137—138 272
Jordan curve theorem      58—59
Jordan polygon      9—11 114
Jordan region      12—15 112
Kakeya set      92—93
Kakutani, S.      124
Kanada, Y.      253
Kannan, R.      247 256
Karush, J.      130
Kasimatis, E.A.      115—116
Katok, A.      71
Keane, M.      71
Kelly, J.B.      84
Kelly, L.M.      105 139
Kelly, P.J.      85
Kemnitz, A.      133
Kershner, R.B.      111
Kieisel, G.      196
Kilian, J.      222
Kind, B.      93
Kirszbraun, M.      88
Klamkin, M.S.      92
Klee, V.      71 88 126
Kleinschmidt, P.      93
Kneser, M.      86—87 89 275
Koenig, D.      72
Korec, I.      203
Kranakis, E.      103
Kreinovic, V.      75
Kronecker, L.      72
Kronheimer, E.H.      138 142
Kronheimer, P.B.      138 142
Kuiper, N.H.      75
Kummer's criterion      169
Kummer, E.      132 169 199—200
Kuperberg, w.      111 117
Kupitz, Y.      109
Labeling      146—147 150 298
Laczkovich, M.      xii—xiii 50 287
Lagrange's four squares theorem      127 197 289
Lagrange, J.      132
Lame, G.      169
Lander, L.J.      171
Larman, D.G.      78 80 121—122 135
Lassak, M.      78 94
Lattice      36—37
Lawrence, J.      118
Lazutkin, V.E.      74
Lebesgue tiling theorem      122
Lebesgue, H.      91
Leech, J.      132 205
Legendre, A.M.      169
Lehman, R.S.      218
Lehmer, D.H.      169 200
Lehmer, E.      169 200
Lenstra, A.K.      221 247
Lenstra, H.      221
Level set      141—142 144
Levi, E.W.      78
Levy, P.      140
Lieb, E.      87
lighting      see "Illumination"
Lindemann, F.      50 214 255 293
Line      see "Ordinary line" "Connecting "Pseudoline" "Line
Line at infinity      103—104
Liouville's number      239 245—246 312
Liouville, J.      258
Listable      230—231
Littlewood, J.E.      184 218
Lloyd, E.K.      120
Logarithmic integral, li(x)      182—185 218—219
Lovasz, L.      95 247 256
Loxton, J.H.      258
Lubiw, A.      287
Lucas, E.      209
Mahler, K.      258—259
Manasse, M.      221
Marchetti, M.      71
Masur, H.      71
Mather, J.N.      74
Matijasevic, Y.      195—196 230 232
McGeoch, L.      256
McMullen, P.      117
Mead, D.G.      116
Measure      86
Melchior, E.      105
Melrose, R.      74
Mendes-France, M.      259
Mersenne primes      178—179 209—210 224
Mertens, F.      219
Meyerson, M.D.      137 142
Michelacci, G.      80
Midpoint-free      27
Miller, G.      189 221—222 224
Minty, G.J.      89
Moebius function, $\mu(n)$       184 219
Monagan, M.B.      201
Monier, L.      189
Monohedral      36 39 41 43—44 117
Monotone subsequence      27—28 95—101
Monsky, P.      xii 115
Mordell, L.J.      132 204
Morphine      258
Moser, L.      3 121
Moser, W.      3 95 105 121
Motzkin, T.S.      98 105 107 282
Murty, U.S.R.      146
Nagell, E.      132
Nakayama, N.      208
Near-pencil      33—34 284
Nickel, L.      209
Nivat, M.      115
Niven, I.      252 258
Nocco, G.      214
Noll, c.      209
Noncomputable set      226
Nondeterministic polynomial time ( $\mathbb{NP}$ )      222—224 232
Nonseparating continuum      66 69
Normal numbers      251
Normed linear space      83 85
O'Neill, P.E.      98
O'Rourke, J.      77
octahedron      140
Odlyzko, A.      219
Ogilvy, G.S.      137
Ordinary circle      34 106 282
Ordinary line      29 33—35 109
Ordinary plane      107 109
Overmars, M.      98
p-hexagon      39 44 118 286
Pach, J.      3 87 89—90 95 106 276
PAGANINI, N.      181
painting      45—49 120—127 289—291
Pal, J.      91—92
parabola      106
Parallel body      276
Parallel pencil      103—104
Parallelogram      36 57 132 294
Parallelotope (= parallepiped)      140 276 296
Parkin, T.R.      171
Pencil      see "Near-pencil" "Parallel
Penrose rhombs      113—114
Penrose, L.      71

Penrose, R.      113
Pentagon      38 44 111—112 114 286
Perfect box      173 203
Perfect numbers      167 178—181 209—213
Perimeter      19 22 87 276 279
Periodic      see "Periodic billiard path" "Periodic
Periodic billiard path      7—8 71—75 271
Periodic tiling      36—37 40 111—112
Perles, M.      109 124 127
Perrin, R.      99
Perron, O.      118
Petty, C.M.      81
Phase space      73
Picnic      141—142
Pigeonhole Principle      26
Pintz, J.      219
Pocchiola, M.      103
Point at infinity      103—104
Pollack, R.      99
Pollard, J.      221
Polygon      see "Names of special types"
Polynomial-time algorithm      186 189 221—224
Pomerance, C.      213 221
Pratt, V.      222
Prime number theorem      183 218
Prime numbers      182 186—189 196 209—212 216—223 231 262
PRODUCT      147 148 299
Projective plane      103—104
Prototile      36—40 44
Pseudoline      101
Purdy, C.      124
Purdy, G.      3 107—108 124
Putnam Competition      205
Putnam, H.      230
Pythagorean triples      168 171—174 201
Quadrilateral      65 132 137 139 286
quantum mechanics      242
Quarles, F.S.      123
Rabin, M.      189 221—223
Radon's theorem      277—278
Radon, J.      277
Raiskii, D.E.      120 122 126
Ramsey's theorem      26 142 280
Ramsey, F.P.      26
Random polynomial time ( $\mathbb{RP}$ )      222
Rappaport, D.      98
Rathbun, R.L.      204—205
Rational polygon      6 71—73 79 271—272
Rational set      54—57 132—136 294
Rationally approximable set      54—57 132—136 294
Rauch, J.      71
Real-time computable      244—246 259
Reflection      3—8 10—11 71—76 79 269—272
Regular n-gon      23—24 65 75 109
Regular prime      170 199—200
Rehder, W.      87
Reinhardt, K.      93 111
Renegar, J.      116
Rennie, B.C.      92
Retraction      68—70 297—299
Reuleaux triangle      21—22 24
Rhind papyrus      176
Ribenboim, P.      170—171
Rice, M.      111
Richman, F.      115
Riemann $\zeta$ -function      182 215—218 249 261—264
Riemann hypothesis      168 182—184 188 215—219 256
Riemann, B.      182 216
Riesel, H.      221
right triangle      7
Rigid cover      23—24 91—92
Ringworm problem      92
Robertson, J.      75
Robertson, S.A.      84
Robinson, J.      230 232
Robinson, R.M.      232
Rogers, C.A.      78 80 121—122 130 135
Rogers, J.      80
Rolle's theorem      140
Root, S.C.      214
Rosenbaum, J.      84
Rosetta stone      176
Rothe, H.      80
Rothschild, B.L.      136
RSA cryptography scheme      223
Rumely, R.S.      221
Saint Augustine      180
Salamin, E.      252
Sawyer, E.T.      105
Schaefke, R.      80
Schattschneider, D.      111
Schinzel, A.      212
Schneider, T.      255—256
Schoenberg, I.J.      88 93 132
Schoenhage, A.      260
Scholten, B.      98
Schramm, O.      78
Schubert, H.      204
Scott, P.R.      108
Seidel, J.J.      135
Senechal, M.      117
Separating continuum      138
Sharir, M.      103
Sheng, T.K.      132—133
Shephard, G.C.      3 111—112 114 117
Shermer, T.      77
Shtogrin, M.I.      111
Siegel, C.L.      256
Sierpinski — Mazurkiewicz Paradox      131
Simmons, G.J.      124
Simon, B.      87
Simple closed curve      see "Jordan curve"
Simplicial subdivision      146
Sine, R.      75
Skewes, S.      218
Skolem, T.      232
Slowinski, D.      209
Smillie, J.      72
Smooth      5—6 8 11—14 74—76 79 137 271
Snakelike continuum      148
Sompolski, R.W.      170 200
Spaltenstein      81
Spemer, E.      146
Sperner's Lemma      146
Sphere      81 86 116 119 136 289 294
Spieker, T.      123
Spirakis, P.G.      87
Sprague, R.      91
Square      xii 22 36—37 43 58—65 72 79 133 137—138 142
Starshaped      3 93
Steiger, F.      135
Stein, R.      112
Stein, S.K.      115—116 118
Steuerwald, R.      212 214
Stewart, B.M.      207
Stoneham, R.G.      251
Stopping time      225—229
Straus, E.G.      116 136 176
String construction      76 79 113 272
Stromquist, W.      137
Sudakov, Y.N.      87
Sudan, G.      72
Suess, W.      80
Suiyanarayana, D.      212
Swinnerton-Dyer, H.P.F.      73
Sydler, J.P.      129
Sylvester, J.J.      105 214 306
symmetric      14—15 36 40 42—43
Szabd, S.      118
Szekeies, G.      95

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