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Wilson R.Four Colors Suffice.How The Map Problem Was Solved 2014
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. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved. Cover Page Half-title Page Title Page Copyright Page Dedication Page Foreword Preface to the Revised Color Edition Preface to the Original Edition The Four-Color Problem 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 The Problem Is Posed De Morgan Writes a Letter Hotspur and the Athenaeum Möbius and the Five Princes Confusion Reigns Euler’s Famous Formula Euler Writes a Letter From Polyhedra to Maps Only Five Neighbors A Counting Formula Cayley Revives the Problem Cayley’s Query Knocking Down Dominoes Minimal Criminals The Six-Color Theorem . . . and Kempe Solves It Sylvester’s New Journal Kempe’s Paper Kempe Chains Some Variations Back to Baltimore A Chapter of Accidents A Challenge for the Bishop A Visit to Scotland Cycling around Polyhedra A Voyage around the World Wee Planetoids A Bombshell from Durham Heawood’s Map A Salvage Operation Coloring Empires Maps on Bagels Picking Up the Pieces Crossing the Atlantic Two Fundamental Ideas Finding Unavoidable Sets Finding Reducible Configurations Coloring Diamonds How Many Ways? A New Dawn Breaks Bagels and Traffic Cops Heinrich Heesch Wolfgang Haken Enter the Computer Coloring Horseshoes Success! A Heesch-Haken Partnership? Kenneth Appel Getting Down to Business The Final Onslaught A Race against Time Aftermath Is It a Proof? Cool Reaction What Is a Proof Today? Meanwhile . . . A New Proof Into the Next Millennium The Future Chronology of Events Notes and References Glossary Picture Credits Index
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Wilson R.Four Colors Suffice.How the Map Problem Was Solved 2014.pdf
