Mathematical recreations & essays:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Toronto [u.a.]
Univ. of Toronto Press
1974
|
| Ausgabe: | 12. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 1. - 3. Aufl. u.d.T.: Ball, Walter W.: Mathematical recreations and problems of past and present times |
| Beschreibung: | XVII, 428 S. graph. Darst. |
| ISBN: | 0802018440 0802061389 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical recreations & essays |c Walter W. Ball ; Harold S. Coxeter |
| 250 | |a 12. ed. | ||
| 264 | 1 | |a Toronto [u.a.] |b Univ. of Toronto Press |c 1974 | |
| 300 | |a XVII, 428 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a 1. - 3. Aufl. u.d.T.: Ball, Walter W.: Mathematical recreations and problems of past and present times | ||
| 650 | 4 | |a Chiffres (Cryptographie) | |
| 650 | 4 | |a Cryptographie | |
| 650 | 4 | |a Géométrie - Problèmes et exercices | |
| 650 | 4 | |a Jeux mathématiques | |
| 650 | 7 | |a Recreatieve wiskunde |2 gtt | |
| 650 | 4 | |a Ciphers | |
| 650 | 4 | |a Cryptography | |
| 650 | 4 | |a Geometry |x Famous problems | |
| 650 | 4 | |a Mathematical recreations | |
| 700 | 1 | |a Coxeter, Harold S. M. |d 1907-2003 |e Verfasser |0 (DE-588)118522507 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005703511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1805082763230969856 |
|---|---|
| adam_text |
CONTENTS
Preface to the Tenth Edition v
Preface to the Eleventh Edition vii
Preface to the Twelfth Edition ix
I ARITHMETICAL RECREATIONS 3
To find a number selected by someone 5
Prediction of the result of certain operations 8
Problems involving two numbers 11
Problems depending on the scale of notation 12
Other problems with numbers in the denary scale 14
Four fours problem 16
Problems with a series of numbered things 17
Arithmetical restorations 20
Calendar problems 26
Medieval problems in arithmetic 27
The Josephus problem. Decimation 32
Nim and similar games 36
Moore's game 38
Kayles 39
Wythoff s game 39
Addendum on solutions 40
II ARITHMETICAL RECREATIONS (continued) 41
Arithmetical fallacies 41
Paradoxical problems 44
Probability problems 45
Permutation problems 48
Bachet's weights problem 50
The decimal expression for l/« 53
Decimals and continued fractions 54
Xii CONTENTS
Rational right angled triangles 57
Triangular and pyramidal numbers 59
Divisibility 60
The prime number theorem 62
Mersenne numbers 64
Perfect numbers 66
Fermat numbers 67
Fermat's Last Theorem 69
Galois fields 73
III GEOMETRICAL RECREATIONS 76
Geometrical fallacies 76
Geometrical paradoxes 84
Continued fractions and lattice points 86
Geometrical dissections 87
Cyclotomy 94
Compass problems 96
The five disc problem 97
Lebesgue's minimal problem 99
Kakeya's minimal problem 99
Addendum on a solution 102
IV GEOMETRICAL RECREATIONS (continued) 103
Statical games of position 103
Three in a row. Extension to / in a row 103
Tessellation 105
Anallagmatic pavements 107
Polyominoes 109
Colour cube problem 113
Squaring the square 115
Dynamical games of position 116
Shunting problems 116
Ferry boat problems 118
Geodesic problems 120
Problems with counters or pawns 121
Paradromic rings 127
Addendum on solutions 129
CONTENTS Xiii
V POLYHEDRA 130
Symmetry and symmetries MO
The five Platonic solids 131
Kepler's mysticism 133
Pappus, on the distribution of vertices 134
Compounds 135
The Archimedean solids 136
Mrs. Stott's construction 139
Equilateral zonohedra 141
The Kepler Poinsot polyhedra 144
The 59 icosahedra 146
Solid tessellations 147
Ball piling or close packing 149
The sand by the sea shore 151
Regular sponges 152
Rotating rings of tetrahedra 154
The kaleidoscope 155
VI CHESS BOARD RECREATIONS 162
Relative value of pieces 163
The eight queens problem 166
Maximum pieces problem 172
Minimum pieces problem 172
Re entrant paths on a chess board 175
Knight's re entrant path 175
King's re entrant path 186
Rook's re entrant path 187
Bishop's re entrant path 187
Routes on a chess board 187
Guarini's problem 189
Latin squares 189
Eulerian squares 190
Euler's officers problem 192
Eulerian cubes 192
VII MAGIC SQUARES 193
Magic squares of an odd order 195
Xiv CONTENTS
Magic squares of a singly even order 196
Magic squares of a doubly even order 199
Bordered squares 200
Number of squares of a given order 201
Symmetrical and pandiagonal squares 202
Generalization of De la Loubere's rule 204
Arnoux's method 206
Margossian's method 207 ,
Magic squares of non consecutive numbers 210
Magic squares of primes 211
Doubly magic and trebly magic squares 212
Other magic problems 213
Magic domino squares 213
Cubic and octahedral dice 214
Interlocked hexagons 215
Magic cubes 216
VIII MAP COLOURING PROBLEMS 222
The four colour conjecture 222
The Petersen graph 225
Reduction to a standard map 227
Minimum number of districts for possible failure 230
Equivalent problem in the theory of numbers 231
Unbounded surfaces 232
Dual maps 234
Maps on various surfaces 234
Pits, peaks, and passes 238
Colouring the icosahedron 238
IX UNICURSAL PROBLEMS 243
Euler's problem 243
Number of ways of describing a unicursal figure 250
Mazes 254
Trees 260
The Hamiltonian game 262
Dragon designs 266
\
\ CONTENTS XV
X COMBINATORIAL DESIGN^ 271
A projective plane 271
Incidence matrices 272
An Hadamard matrix 273
An error correcting code 274
A block design 276
Steiner triple systems 278
Finite geometries 281
Kirkman's school girl problem 287
Latin squares 290
The cube and the simplex 295
Hadamard matrices 296
Picture transmission 297
Equiangular lines in 3 space 299
Lines in higher dimensional space 303
C matrices 308
Projective planes 310
XI MISCELLANEOUS PROBLEMS 312
The fifteen puzzle 312
The Tower of Hanoi 316
Chinese rings 318
Problems connected with a pack of cards 322
Shuffling a pack 323
Arrangements by rows and columns 325
Bachet's problem with pairs of cards 326
Gergonne's pile problem 328
The window reader 333
The mouse trap. Treize 336
XII THREE CLASSICAL GEOMETRICAL PROBLEMS 338
The duplication of the cube 339
Solutions by Hippocrates, Archytas, Plato, Menaechmus,
Apollonius, and Diocles 341
Solutions by Vieta, Descartes, Gregory of St. Vincent, and
Newton 343
xvi CONTENTS
The trisection of an angle 344
Solutions by Pappus, Descartes, Newton, Clairaut, and
Chasles 334
The quadrature of the circle 347
Origin of symbol n 349
Geometrical methods of approximation to the numerical
value of n 349
Results of Egyptians, Babylonians, Jews 350
Results of Archimedes and other Greek writers 351
Results of European writers, 1200 1630 352
Theorems of Wallis and Brouncker 355
Results of European writers, 1699 1873 356
Approximations by the theory of probability 359
XIII CALCULATING PRODIGIES 360
John Wallis, 1616 1703 361
Buxton, circ. 1707 1772 361
Fuller, 1710 1790; Ampere 364
Gauss, Whately 365
Colburn, 1804 1840 365
Bidder, 1806 1878 367
Mondeux, Mangiamele 372
Dase, 1824 1861 372
Safford,1836 1901 374
Zamebone, Diamandi, Ruckle 375
Inaudi, 1867 375
Types of memory of numbers 377
Bidder's analysis of methods used 378
Multiplication 379
Digital method for division and factors 381
Square roots. Higher roots 382
Compound interest 384
Logarithms 385
Alexander Craig Aitken 386
XIV CRYPTOGRAPHY AND CRYPTANALYSIS 388
Cryptographic systems 389
CONTENTS xvii
Transposition systems 391
Columnar transposition 392
Digraphs and trigraphs 394
Comparison of several messages 397
The grille 401
Substitution systems 402
Tables of frequency 404
Polyalphabetic systems 406
The Vigenere square 407
The Playfair cipher 410
Code 412
Determination of cryptographic system 414
A few final remarks 416
Addendum: References for further study 418
index 419 |
| any_adam_object | 1 |
| author | Ball, W. W. Rouse 1850-1925 Coxeter, Harold S. M. 1907-2003 |
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| dewey-hundreds | 700 - The arts |
| dewey-ones | 793 - Indoor games and amusements |
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| dewey-search | 793.7/4 |
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| dewey-tens | 790 - Recreational and performing arts |
| discipline | Sport Mathematik |
| edition | 12. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T07:37:50Z |
| institution | BVB |
| isbn | 0802018440 0802061389 |
| language | English |
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| physical | XVII, 428 S. graph. Darst. |
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| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Univ. of Toronto Press |
| record_format | marc |
| spelling | Ball, W. W. Rouse 1850-1925 Verfasser (DE-588)122792718 aut Mathematical recreations & essays Walter W. Ball ; Harold S. Coxeter 12. ed. Toronto [u.a.] Univ. of Toronto Press 1974 XVII, 428 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 1. - 3. Aufl. u.d.T.: Ball, Walter W.: Mathematical recreations and problems of past and present times Chiffres (Cryptographie) Cryptographie Géométrie - Problèmes et exercices Jeux mathématiques Recreatieve wiskunde gtt Ciphers Cryptography Geometry Famous problems Mathematical recreations Coxeter, Harold S. M. 1907-2003 Verfasser (DE-588)118522507 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005703511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ball, W. W. Rouse 1850-1925 Coxeter, Harold S. M. 1907-2003 Mathematical recreations & essays Chiffres (Cryptographie) Cryptographie Géométrie - Problèmes et exercices Jeux mathématiques Recreatieve wiskunde gtt Ciphers Cryptography Geometry Famous problems Mathematical recreations |
| title | Mathematical recreations & essays |
| title_auth | Mathematical recreations & essays |
| title_exact_search | Mathematical recreations & essays |
| title_full | Mathematical recreations & essays Walter W. Ball ; Harold S. Coxeter |
| title_fullStr | Mathematical recreations & essays Walter W. Ball ; Harold S. Coxeter |
| title_full_unstemmed | Mathematical recreations & essays Walter W. Ball ; Harold S. Coxeter |
| title_short | Mathematical recreations & essays |
| title_sort | mathematical recreations essays |
| topic | Chiffres (Cryptographie) Cryptographie Géométrie - Problèmes et exercices Jeux mathématiques Recreatieve wiskunde gtt Ciphers Cryptography Geometry Famous problems Mathematical recreations |
| topic_facet | Chiffres (Cryptographie) Cryptographie Géométrie - Problèmes et exercices Jeux mathématiques Recreatieve wiskunde Ciphers Cryptography Geometry Famous problems Mathematical recreations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005703511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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