Four colours suffice : how the map problem was solved

著者

書誌事項

Four colours suffice : how the map problem was solved

Robin Wilson

Allen Lane, an imprint of Penguin Books, 2002

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注記

Includes bibliographical references (p. 229-244) and index

内容説明・目次

内容説明

The problem is simply stated, and involves the colouring of maps. Can every map be coloured with at most four colours so that neighbouring countries are coloured differently? First posed 150 years ago, it took more than a century of colouring maps and developing the necessary theoretical machinery before the result was established with certainty. Even then, difficult philosophical questions remained. With elegance and clarity, Robin Wilson explains the problem and the proof.

目次

  • Part 1 The four-colour problem: 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. Part 2 The problem is posed: De Morgan writes a letter
  • Hotspur and the Athenaeum
  • Mobius and the five princes
  • confusion reigns. Part 3 Euler's famous formula: Euler writes a letter
  • from Polyhedra to maps
  • only five neighbours
  • a counting formula. Part 4 Cayley revives the problem: Cayley's query
  • knocking down dominoes
  • minimal criminals
  • the six-colour theorem. Part 5 And Kempe solves it: Sylvester's new journal
  • Kempe's paper
  • Kempe chains
  • some variations
  • back to Baltimore. Part 6 A chapter of accidents: a challenge for the bishop
  • a visit to Scotland
  • cycling around Polyhedra
  • a voyage around the world
  • wee planetoids. Part 7 A bombshell from Durham: Heawood's map
  • a salvage operation
  • colouring empires
  • maps on doughnuts
  • picking up the pieces. Part 8 Crossing the Atlantic: two fundamental ideas
  • finding unavoidable sets
  • finding reducible configurations
  • colouring diamonds
  • how many ways?. Part 9 A new dawn breaks: doughnuts and traffic cops
  • Heinrich Heesch
  • Wolfgang Haken
  • enter the computer
  • colouring horseshoes. Part 10 Success!: a Heesch-Haken partnership?
  • Kenneth Appel
  • getting down to business
  • the final onslaught
  • a race against time
  • aftermath. Part 11 But is it a proof?: cool reaction
  • what is a proof today?
  • meanwhile
  • a new proof
  • the future.

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