TABLE OF CONTENTS: 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
Return to Book Description File created: 4/23/2008 | 
