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# Four Colors Suffice:How the Map Problem Was SolvedRobin WilsonWith a new foreword by Ian Stewart

 TABLE OF CONTENTS:Foreword by Ian Stewart xiPreface to the Revised Color Edition xiiiPreface to the Original Edition xv1The Four-Color Problem 1What 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 Examples2The Problem Is Posed 12De Morgan Writes a Letter | Hotspur and the Athenaeum | Möbius and the Five Princes | Confusion Reigns3Euler's Famous Formula 28Euler Writes a Letter | From Polyhedra to Maps | Only Five Neighbors | A Counting Formula4Cayley Revives the Problem . . . 45Cayley's Query | Knocking Down Dominoes | Minimal Criminals | The Six-Color Theorem5. . . and Kempe Solves It 55Sylvester's New Journal | Kempe's Paper | Kempe Chains | Some Variations | Back to Baltimore6A Chapter of Accidents 71A Challenge for the Bishop | A Visit to Scotland | Cycling around Polyhedra | A Voyage around the World | Wee Planetoids7A Bombshell from Durham 86Heawood's Map | A Salvage Operation | Coloring Empires | Maps on Bagels | Picking Up the Pieces8Crossing the Atlantic 105Two Fundamental Ideas | Finding Unavoidable Sets | Finding Reducible Configurations | Coloring Diamonds | How Many Ways?9A New Dawn Breaks 124Bagels and Traffic Cops | Heinrich Heesch | Wolfgang Haken | Enter the Computer | Coloring Horseshoes10Success! 139A Heesch-Haken Partnership? | Kenneth Appel | Getting Down to Business | The Final Onslaught | A Race against Time | Aftermath11Is It a Proof? 157Cool Reaction | What Is a Proof Today? | Meanwhile . . . | A New Proof | Into the Next Millennium | The Future Chronology of Events 171Notes and References 175Glossary 187Picture Credits 193Index 195 Return to Book DescriptionFile created: 4/21/2017 Questions and comments to: webmaster@press.princeton.eduPrinceton University Press