Sunday, July 01, 2012

The famous four colour theorem

The famous four colour theorem seems to have been first proposed by Möbius in 1840, later by DeMorgan and the Guthrie brothers in 1852, and again by Cayley in 1878. The problem of proving this theorem has a distinguished history, details of which abound in the literature. The statement of the theorem may be introduced as follows. In colouring a geographical map it is customary to give different colours to any two countries that have a segment of their boundaries in common. It has been found empirically that any map, no matter how many countries it contains nor how they are situated, can be so coloured by using only four different colours. The map of India requires four colours in the states bordering Madhya Pradesh. The fact that no map was ever found whose colouring requires more than four colours suggests the mathematical theorem.