Adventures in recreational mathematics: 1
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2022
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| Schriftenreihe: | ...
21,1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Bandzählung in der Serie fingiert |
| Beschreibung: | xiv, 300 Seiten Illustrationen |
| ISBN: | 9789811226007 |
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Datensatz im Suchindex
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| adam_text | Contents Preface ix xiii About the Author 1. What is Recreational Mathematics? 1 Bibliography............................................................................. 7 Part I. Ancient Puzzles 2. 3. 4. 9 Puzzles from The Greek Anthology 11 2.1 The Problems................................................................. 2.2 Solutions and Comments.............................................. Bibliography............................................................................. 12 15 16 Aryabhata and Other Early Indian Mathematicians 17 3.1 Pythagorean Recreations............................................... 3.2 Knowing What Each Pair Has...................................... 3.3 The Snail in the Well..................................................... Bibliography............................................................................. 18 28 31 34 Alcuin and his Propositiones 37 4.1 4.2 4.3 Alcuin.............................................................................. The Manuscripts........................................................... Managing the Text of Propositiones............................ V 38 41 43
Adventures in Recreational Mathematics vi 4.4 An Annotated Translation of Propositiones .................45 4.5 Summary and Discussions........................................... 75 Bibliography............................................................................. 82 5. The Problems of Abbot Albert 85 5.1 Summary......................................................................... 100 Bibliography................................................................................100 6. Pacioli: The First Book of MathematicalPuzzles 101 6.1 De Viribus Quantitatis.................................................... 106 6.2 Recreational Material in De Viribus Quantitatis . . . 109 Bibliography...................................................................... . . . 129 7. Pacioli’s Magic and Card Tricks 131 Bibliography................................................................................137 8. Some Early Topological Puzzles 139 The Chinese Wallet or Flick-Flack or Jacob’s Ladder................................................................ 140 8.2 The Alliance and Victoria Puzzle..................................143 8.3 Solomon’s Seal or AfricanBeads Puzzle........................ 144 8.4 The Cherries Puzzle ........................................................ 146 8.5 Six-Piece Burrs................................................................. 149 8.6 Borromean Rings.............................................................. 151 8.7 Chinese Rings.................................................................... 153 8.8 Puzzle
Grills........................................................................154 8.9 Conclusions........................................................................156 Bibliography................................................................................156 8.1 Interlude: Finding a Sardinian Maze 158 Part II. New Ideas about Old Puzzles 163 9. A Legacy of Camels 165 9.1 Some History................................................................... 166 9.2 Analysis of the 17 Camels Problem................................ 170 9.3 Analysis of the 13 Camels Problem................................ 174 Bibliography................................................................................179
Contents 10. Heronian Triangles vii 183 10.1 Determination of Pythagorean triples.......................... 184 10.2 Determination of Heronian triples................................. 185 Bibliography................................................................................187 11. The Ass andMule Problem 189 11.1 Analysis of the Original Problem................................. 190 11.2 Doslić’s Variation............................................................. 191 11.3 Another Simpler Variation.............................................. 193 Bibliography..................... 195 12. How to Count Your Chickens 197 12.1 Answers............................................................................209 Bibliography............................................................................... 210 13. The Monkey and the Coconuts 211 13.1 Determinate Versions...................................................... 212 13.2 Indeterminate Versions................................................... 218 13.3 A General Solution......................................................... 224 13.4 Other Variations............................................................ 230 13.5 Solutions and Some Comments................................... 232 Bibliography............................................................................... 233 14. Two River Crossing Problems 235 14.1 De Fontenay’s Generalization....................................... 237 14.2 Dudeney’s Solution......................................................... 240 14.3 Improved
Solutions......................................................... 241 14.4 Proof of Optimality......................................................... 244 14.5 Missionaries and Cannibals ......................................... 249 14.6 Other Cultures................................................................ 251 Bibliography............................................................................... 252 15. Sharing Barrels 15.1 15.2 15.3 15.4 255 The Barrels Problem...................................................... 256 Integral Triangles............................................................ 256 Triangular Coordinates...................................................257 The Number of Integral Triangles................................ 258
viii Adventures in Recreational Mathematics 15.5 The Number of Incongruent Integral Triangles .... 259 15.6 Relation to Partitions .................................................... 260 15.7 Other Versions ................................................................ 262 15.8 Fair Division of the First kn Integersinto к Parts . . 265 Bibliography............................................................................... 267 16. Vanishing Area Paradoxes 269 16.1 Early Examples................................................................ 274 Bibliography............................................................................... 278 Appendix A: Ancient and Important Sources 281 A.l Bibliography of Early Work........................................... 281 A.2 Sources Project................................................................. 295 A.3 Open Problems................................................................. 297
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| adam_txt |
Contents Preface ix xiii About the Author 1. What is Recreational Mathematics? 1 Bibliography. 7 Part I. Ancient Puzzles 2. 3. 4. 9 Puzzles from The Greek Anthology 11 2.1 The Problems. 2.2 Solutions and Comments. Bibliography. 12 15 16 Aryabhata and Other Early Indian Mathematicians 17 3.1 Pythagorean Recreations. 3.2 Knowing What Each Pair Has. 3.3 The Snail in the Well. Bibliography. 18 28 31 34 Alcuin and his Propositiones 37 4.1 4.2 4.3 Alcuin. The Manuscripts. Managing the Text of Propositiones. V 38 41 43
Adventures in Recreational Mathematics vi 4.4 An Annotated Translation of Propositiones .45 4.5 Summary and Discussions. 75 Bibliography. 82 5. The Problems of Abbot Albert 85 5.1 Summary. 100 Bibliography.100 6. Pacioli: The First Book of MathematicalPuzzles 101 6.1 De Viribus Quantitatis. 106 6.2 Recreational Material in De Viribus Quantitatis . . . 109 Bibliography. '. . . 129 7. Pacioli’s Magic and Card Tricks 131 Bibliography.137 8. Some Early Topological Puzzles 139 The Chinese Wallet or Flick-Flack or Jacob’s Ladder. 140 8.2 The Alliance and Victoria Puzzle.143 8.3 Solomon’s Seal or AfricanBeads Puzzle. 144 8.4 The Cherries Puzzle . 146 8.5 Six-Piece Burrs. 149 8.6 Borromean Rings. 151 8.7 Chinese Rings. 153 8.8 Puzzle
Grills.154 8.9 Conclusions.156 Bibliography.156 8.1 Interlude: Finding a Sardinian Maze 158 Part II. New Ideas about Old Puzzles 163 9. A Legacy of Camels 165 9.1 Some History. 166 9.2 Analysis of the 17 Camels Problem. 170 9.3 Analysis of the 13 Camels Problem. 174 Bibliography.179
Contents 10. Heronian Triangles vii 183 10.1 Determination of Pythagorean triples. 184 10.2 Determination of Heronian triples. 185 Bibliography.187 11. The Ass andMule Problem 189 11.1 Analysis of the Original Problem. 190 11.2 Doslić’s Variation. 191 11.3 Another Simpler Variation. 193 Bibliography. 195 12. How to Count Your Chickens 197 12.1 Answers.209 Bibliography. 210 13. The Monkey and the Coconuts 211 13.1 Determinate Versions. 212 13.2 Indeterminate Versions. 218 13.3 A General Solution. 224 13.4 Other Variations. 230 13.5 Solutions and Some Comments. 232 Bibliography. 233 14. Two River Crossing Problems 235 14.1 De Fontenay’s Generalization. 237 14.2 Dudeney’s Solution. 240 14.3 Improved
Solutions. 241 14.4 Proof of Optimality. 244 14.5 Missionaries and Cannibals . 249 14.6 Other Cultures. 251 Bibliography. 252 15. Sharing Barrels 15.1 15.2 15.3 15.4 255 The Barrels Problem. 256 Integral Triangles. 256 Triangular Coordinates.257 The Number of Integral Triangles. 258
viii Adventures in Recreational Mathematics 15.5 The Number of Incongruent Integral Triangles . 259 15.6 Relation to Partitions . 260 15.7 Other Versions . 262 15.8 Fair Division of the First kn Integersinto к Parts . . 265 Bibliography. 267 16. Vanishing Area Paradoxes 269 16.1 Early Examples. 274 Bibliography. 278 Appendix A: Ancient and Important Sources 281 A.l Bibliography of Early Work. 281 A.2 Sources Project. 295 A.3 Open Problems. 297 |
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| spelling | Singmaster, David 1939- Verfasser (DE-588)1106839536 aut Adventures in recreational mathematics 1 Singapore World Scientific 2022 xiv, 300 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier ... 21,1 Problem solving in mathematics and beyond Bandzählung in der Serie fingiert Unterhaltungsmathematik (DE-588)4124357-2 gnd rswk-swf Unterhaltungsmathematik (DE-588)4124357-2 s DE-604 (DE-604)BV047899450 1 ... 21,1 (DE-604)BV044751519 21,1 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033281405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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