Four Colors Suffice
Princeton University Press (Verlag)
978-0-691-12023-2 (ISBN)
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On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history - one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps.In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron.
It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution - which involved no fewer than 1,200 hours of computer time - was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.
Robin Wilson is Head of the Pure Mathematics Department at the Open University and Fellow of Keble College, Oxford University. He is Gresham Professor of Geometry at Gresham College, London, and is a frequent visitor to Colorado College. He has written and edited about 25 books on topics ranging from graph theory via philately, to the Gilbert and Sullivan operas, to the history of mathematics.
Preface xi 1. The four-colour problem 1 WHAT IS THE FOUR-COLOUR PROBLEM? | WHY IS IT INTERESTING? | IS IT IMPORTANT? | WHAT IS MEANT BY 'SOLVING 'IT? | WHO POSED IT,AND HOW WAS IT SOLVED? | PAINTING BY NUMBERS | TWO EXAMPLES 2. The problem is posed 16 DE MORGAN WRITES A LETTER | HOTSPUR AND THE ATHENAEUM | MOBIUS AND THE FIVE PRINCES | CONFUSION REIGNS 3. Euler's famous formula 38 EULER WRITES A LETTER | FROM POLYHEDRA TO MAPS | ONLY FIVE NEIGHBOURS | A COUNTING FORMULA 4. Cayley revives the problem ... 60 CAYLEY'S QUERY | KNOCKING DOWN DOMINOES | MINIMAL CRIMINALS | THE SIX-COLOUR THEOREM 5. ... and Kempe solves it 73 SYLVESTER'S NEW JOURNAL | KEMPE'S PAPER | KEMPE CHAINS | SOME VARIATIONS | BACK TO BALTIMORE 6. A chapter of accidents 95 A CHALLENGE FOR THE BISHOP | A VISIT TO SCOTLAND | CYCLING AROUND POLYHEDRA | A VOYAGE AROUND THE WORLD | WEE PLANETOIDS 7. A bombshell from Durham 116 HEAWOOD'S MAP | A SALVAGE OPERATION | COLOURING EMPIRES | MAPS ON DOUGHNUTS | PICKING UP THE PIECES 8. Crossing the Atlantic 143 TWO FUNDAMENTAL IDEAS | FINDING UNAVOIDABLE SETS | FINDING REDUCIBLE CONFIGURATIONS | COLOURING DIAMONDS | HOW MANY WAYS? 9. A new dawn breaks 169 DOUGHNUTS AND TRAFFIC COPS | HEINRICH HEESCH | WOLFGANG HAKEN | ENTER THE COMPUTER | COLOURING HORSESHOES 10. Success! ... 190 A HEESCH -HAKEN PARTNERSHIP? | KENNETH APPEL | GETTING DOWN TO BUSINESS | THE FINAL ONSLAUGHT | A RACE AGAINST TIME | AFTERMATH 11. ... but is it a proof? 214 COOL REACTION | WHAT IS A PROOF TODAY? | MEANWHILE ... | ANEWPROOF | THE FUTURE ... Notes and references 229 Chronology of events 245 Glossary 249 Picture credits 255 Index 257
| Zusatzinfo | 24 halftones. 173 line illus. |
|---|---|
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 140 x 203 mm |
| Gewicht | 340 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Naturwissenschaften ► Geowissenschaften ► Geografie / Kartografie | |
| ISBN-10 | 0-691-12023-4 / 0691120234 |
| ISBN-13 | 978-0-691-12023-2 / 9780691120232 |
| Zustand | Neuware |
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