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Four Colors Suffice: How the Map Problem Was Solved (Princeton Science Library) [Paperback]

Robin Wilson , Ian Stewart

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Table of Contents

Foreword by Ian Stewart xi
Preface to the Revised Color Edition xiii
Preface to the Original Edition xv
1The 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
2The Problem Is Posed 12
De Morgan Writes a Letter | Hotspur and the Athenaeum | Möbius and the Five Princes | Confusion Reigns
3Euler's Famous Formula 28
Euler Writes a Letter | From Polyhedra to Maps | Only Five Neighbors | A Counting Formula
4Cayley 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
6A Chapter of Accidents 71
A Challenge for the Bishop | A Visit to Scotland | Cycling around Polyhedra | A Voyage around the World | Wee Planetoids
7A Bombshell from Durham 86
Heawood's Map | A Salvage Operation | Coloring Empires | Maps on Bagels | Picking Up the Pieces
8Crossing the Atlantic 105
Two Fundamental Ideas | Finding Unavoidable Sets | Finding Reducible Configurations | Coloring Diamonds | How Many Ways?
9A New Dawn Breaks 124
Bagels and Traffic Cops | Heinrich Heesch | Wolfgang Haken | Enter the Computer | Coloring Horseshoes
10Success! 139
A Heesch-Haken Partnership? | Kenneth Appel | Getting Down to Business | The Final Onslaught | A Race against Time | Aftermath
11Is 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

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