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Description
The programme looks at the celebrated four colour map problem and at attempts to find a proof. It ends with an interview with the two mathematicians who finally solved the problem.
The programme looks at the celebrated four colour map problem and at attempts to find a proof. It ends with an interview with the two mathematicians who finally solved the problem.
| Module code and title: | TM361, "Graphs, networks and design" |
|---|---|
| Item code: | TM361; 12 |
| First transmission date: | 19-08-1981 |
| Published: | 1981 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:25:00 |
| + Show more... | |
| Producer: | John Stratford |
| Contributors: | Kenneth Appel; Wolfgang Haken; Robin Wilson |
| Publisher: | BBC Open University |
| Keyword(s): | Four colour problem; Reducible; Unavoidable |
| Footage description: | Robin Wilson, in the library at University College, London, introduces the programme. He reads from a story in the Times of 1976 which reported that two American mathematicians had worked out a proof for the four colour map problem. Wilson goes on to relate the early history of the four colour problem from Francis Guthrie to Augustus De Morgan. Shots of a map and still shot of De Morgan. With the aid of several coloured maps, Wilson briefly outlines the problem; a proof that no more than four are necessary to colour any map. The history of the four colour problem continues up to the point where Alfred Bray Kempe published his proof. Wilson explains that this, however, contained a fatal flaw which was not recognised for several years afterwards. Wilson goes on to look at the ideas central to Kempe's proof as these are also contained in the now accepted proof. He begins by defining the four types of 'countries' which are found in any map and calls these the unavoidable set. Wilson tests three of the four types of 'countries' (digons, triangles and squares) to see if, when they are found on a map, the map can be four coloured. He is able to do this easily for the digon and triangles. In order to do this with the square, he uses Kempe's chain argument. To show the fatal flaw of Kempe's proof, Wilson applies the chain argument to the fourth type of 'country', the pentagon. Kempe was forced to do two colour changes simulatneously and Wilson shows that this is not possible in certain cases. The flaw was first pointed out by Percy Heawood and Wilson looks at the counter example to Kempe's proof which Heawood formulated. Wilson briefly reviews the ideas presented in the programme so far. The rest of the programme consists of an interview with Professors Kenneth Appal and Wolfgang Haken of the University of Illinois who worked out the proof for the four colour map problem. They explain how they set about their task. |
| Production number: | FOUT082K |
| Videofinder number: | 1533 |
| Available to public: | no |
