TABLE OF CONTENTS: Foreword by Ian Stewart xi Preface to the Revised Color Edition xiii Preface to the Original Edition xv 1 The Four-Color Problem 1 What Is the Four-Color 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 12 De Morgan Writes a Letter | Hotspur and the Athenaeum | Möbius and the Five Princes | Confusion Reigns 3 Euler's Famous Formula 28 Euler Writes a Letter | From Polyhedra to Maps | Only Five Neighbors | A Counting Formula 4 Cayley Revives the Problem . . . 45 Cayley's Query | Knocking Down Dominoes | Minimal Criminals | The Six-Color Theorem 5 . . . and Kempe Solves It 55 Sylvester's New Journal | Kempe's Paper | Kempe Chains | Some Variations | Back to Baltimore 6 A Chapter of Accidents 71 A Challenge for the Bishop | A Visit to Scotland | Cycling around Polyhedra | A Voyage around the World | Wee Planetoids 7 A Bombshell from Durham 86 Heawood's Map | A Salvage Operation | Coloring Empires | Maps on Bagels | Picking Up the Pieces 8 Crossing the Atlantic 105 Two Fundamental Ideas | Finding Unavoidable Sets | Finding Reducible Configurations | Coloring Diamonds | How Many Ways? 9 A New Dawn Breaks 124 Bagels and Traffic Cops | Heinrich Heesch | Wolfgang Haken | Enter the Computer | Coloring Horseshoes 10 Success! 139 A Heesch-Haken Partnership? | Kenneth Appel | Getting Down to Business | The Final Onslaught | A Race against Time | Aftermath 11 Is It a Proof? 157 Cool Reaction | What Is a Proof Today? | Meanwhile . . . | A New Proof | Into the Next Millennium | The Future Chronology of Events 171 Notes and References 175 Glossary 187 Picture Credits 193 Index 195 Return to Book Description File created: 4/27/2015 |