Famous puzzles of great mathematicians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2009
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVIII, 325 S. |
| ISBN: | 9780821848142 |
Internformat
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| 100 | 1 | |a Petković, Miodrag |d 1948- |e Verfasser |0 (DE-588)135724244 |4 aut | |
| 245 | 1 | 0 | |a Famous puzzles of great mathematicians |c Miodrag S. Petković |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2009 | |
| 300 | |a XVIII, 325 S. | ||
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Datensatz im Suchindex
| _version_ | 1804145363995590656 |
|---|---|
| adam_text | Titel: Famous puzzles of great mathematicians
Autor: Petković, Miodrag
Jahr: 2009
CONTENTS
Preface xiii
Art and Photo Credits xvii
1. RECREATIONAL MATHEMATICS 1
2. ARITHMETICS 9
Diophantus age (Diophantus) 10
Number of arrows (Mahävira) 11
How many rabbits? (Fibonacci, p. 11) 12
Fibonacci s sequence 13
Chessboard paradox 14
Square numbers problem (Fibonacci) 15
Money in a pile (Fibonacci) 16
Magic configuration (Hui) 17
Triangle with integral sides (Backet) 17
Weights problem (Fibonacci, Tartaglia, Backet) 20
MacMahon s general approach 23
Division of 17 horses (Tartaglia, p. 23) 24
Wine and water ( Tartaglia) 25
Coins in hands (Recordé) 25
Sides of two cubes ( Viète, p. 25) 26
Animals on a field (Newton) 27
Pólya s solution 28
Dome s variant 28
Other variants 29
?
i Contents
Gathering an army (Alcuin of York) 29
Answers to Problems 30
3. NUMBER THEORY 37
Cattle problem (Archimedes, p. 38) 41
Dividing the square (Diophantus) 44
Wine problem (Diophantus) 45
Amicable numbers (ibn Qorra) 45
Qorra s formula 47
Euler s rule 47
How many soldiers? (Bhäskara) 48
Horses and bulls - a Diophantine equation (Euler) 50
The sailors, the coconuts, and the monkey (P. Dirac) 52
Dirac s solution 56
General solution 56
Unknown address (Ramanujan) 57
Stamp combinations (Frobenius, Sylvester, p. 60) 61
Generalized problem 62
Answers to Problems 64
4. GEOMETRY 67
Arbelos problem (Archimedes) 68
Archimedean circles 69
Perpendicular distance 70
Two touching circles 73
Minimal distance (Heron) 73
A fly and a drop of honey 75
Peninsula problem 76
The same distance of traversed paths (Brahmagupta) 77
Broken bamboo (Brahmagupta) 78
Height of a suspended string (Mahävira) 78
The diameter of the material sphere (ibn Qorra) 80
Dissection of three squares (Abu l-Wafa) 81
Dudeney s six-cut dissection 82
Contents vü
Dissection of four triangles (Abu I- Wafa) 83
Billiard problem (Alhazen) 83
Distance of the optimal viewpoint (Regiomontanus) 86
Rugby football problem 88
Saturn problem 89
The minimal sum of distances in a triangle
(Steiner, Fermât, Torricelli, Cavalieri) 91
Volumes of cylinders and spheres (Kepler, p. 93) 94
Dido s problem (Steiner, p. 95) 96
Division of space by planes (Steiner) 98
Division of plane 99
Number of bounded regions 101
Road system in a square (Steiner) 101
Kissing circles (Soddy, Descartes, Kowa) 104
Kazayuki s problem 108
Five kissing spheres 109
?-dimensional kissing spheres 110
The shortest bisecting arc of area (Polya) 110
Answers to Problems 112
5. TILING AND PACKING 119
Mosaics (Kepler) 121
Escher s mosaics 124
Nonperiodic tiling (Penrose, Conway) 126
Penrose s kite-dart tiling 126
Conway s pinwheel tiling 128
Maximum area by pentaminoes (Knuth) 129
Pentamino tilings 131
Squaring the square 132
Kissing spheres (D. Gregory, Newton) 134
The densest sphere packing (Kepler, Gauss) 137
Kepler s conjecture 137
Circle packing 138
Hales solution 141
a Contents
Cube-packing puzzles ( Conway) 142
Answers to Problems 144
6. PHYSICS 151
The gold crown of King Hiero {Archimedes) 152
The length of traveled trip (Oresme) 153
Meeting of ships (Lucas, p. 155) 156
A girl and a bird (Von Neumann, p. 157) 158
Von Neumann s easy series 158
More difficult problems 160
The lion and the man (Littlewood, Besicovitch, R. Rado) 161
Answers to Problems 166
7. COMBINATORICS 171
Combination with flavors (Mahävira) 172
Married couples cross the river (Backet) 173
Four married couples cross the river 175
Josephus problem (Backet and others) 176
Dudeney s version 177
Japanese version 177
Graham-Knuth-Patasnik s version 178
Rings puzzle (Cardano, p. 180) 181
Gray-code numbers 182
The problem of the misaddressed letters (N. (II) Bernoulli, Euler) 184
Eulerian squares (Euler) 186
Latin squares 187
Graeco-Latin squares 187
Euler s officers problem 188
Euler s conjecture 188
Parker s square of order 10 189
Kirkman s schoolgirls problem
(Kýrkman, Steiner, Sylvester, Cayley) 189
Steiner triple system 190
General problem 192
Sylvester s problem 192
Contents ¡?
Counting problem (Cayley) 193
Races with ties 194
The Tower of Hanoi (Lucas) 196
Benares temple 198
Interchanging the checkers (I) (Lucas) 199
Interchanging the checkers (II) (Lucas) 200
Shunting problem (Lucas) 200
Problem of married couples (probleme des ménages) (Lucas) 201
The tree planting problem (Sylvester) 202
Dudeney s military puzzle 203
Dudeney s four planting problem 204
Different distances (Erdös, p. 205) 206
Answers to Problems 206
8. PROBABILITY 209
The problem of the points (Fermât, Pascal, p. 211) 212
Pascal-Fermat s general problem 213
Gambling game with dice (Huygens) 215
Gambler s ruin problem (Pascal, Fermât, Huygens) 217
General problem 218
The Petersburg paradox (N. (HI) Bernoulli, D. Bernoulli, Cramer) 220
Bernoulli s moral expectation 221
Cramer s variant 222
The probability problem with the misaddressed letters
(N. (II) Bernoulli, Euler) 222
Matchbox problem (Banach) 224
Combinatorial sum 225
Answers to Problems 225
9. GRAPHS 229
The problem of Königsberg^ bridges (Euler) 230
Diagram-tracing puzzle 231
Euler s theorem 231
Euler s path 231
Contents
Crossing over 15 bridges 232
Tait s net 233
Hamilton s game on a dodecahedron (Hamilton, p. 233) 234
Icosian puzzle 234
Hamiltonian cycles and the Tower of Hanoi 236
Hamiltonian cycles on the Platonic solids 237
Dirac s theorem 238
Ore s theorem 238
King Arthur s knights 239
A man, a wolf, a goat and a cabbage (Alcuin of York) 240
A stout family crosses the river (Alcuin of York) 242
Explorers and cannibals 243
Seven towns and one-way roads (Erdös) 244
Poinsot s diagram-tracing puzzle (Poinsot) 245
Complete graph K-j and dominoes 246
Milk puzzle (Poisson) 247
Graph solution 248
Listing s diagram-tracing puzzle (Listing) 249
Answers to Problems 250
10. CHESS 257
Knight s re-entrant route
(de Moivre, de Montmort, Vandermonde, Euler) 258
De Moivre s re-entrant route 259
Euler s re-entrant route 260
Vandermonde s approach 260
Schwenk s theorem 262
Semi-magic re-entrant route 262
Non-attacking rooks (Euler) 265
The eight queens problem (Gauss, p. 268) 269
?-queens problem 271
Number of solutions 272
The longest uncrossed knight s tour (Knuth) 273
Guarini s knight-switching problem 274
A variant of the knight-switching problem 276
Contents xí
Answers to Problems 276
11. MISCELLANY 283
Problems from Alcuin of York 283
Problems from Abu 1-Wafa 283
Amusing problems from Fibonacci 284
Problems from Bachet 285
Huygens probability problems 285
Problems from Newton 286
Problems from Euler 286
APPENDIX A: Method of continued fractions for solving
Pell s equation 289
APPENDIX B: Geometrical inversion 293
APPENDIX C: Some basic facts from graph theory 294
APPENDIX D: Linear difference equations with constant
coefficients 296
Biographies — a chronological order 299
Bibliography 311
Name index 319
|
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| spelling | Petković, Miodrag 1948- Verfasser (DE-588)135724244 aut Famous puzzles of great mathematicians Miodrag S. Petković Providence, RI American Mathematical Society 2009 XVIII, 325 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Unterhaltungsmathematik (DE-588)4124357-2 gnd rswk-swf Unterhaltungsmathematik (DE-588)4124357-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1599-0 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022285478&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Famous puzzles of great mathematicians |
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