When you look at a map, you are probably lost or trying to find the easiest route from Liverpool Street to the Waterloo. When cartographers look at a map, they are admiring their own handiwork. When printers look at a map, they are thinking, “That cartographer should have come to me, I would have done a much better job.” However, when mathematicians look at maps, they speculate, “I wonder what is the fewest number of colours I can use to colour this map, such that no two bordering countries share a colour.”
What’s the answer?
The answer is a surprisingly low four – but it took over 150 years to prove it. Mathematicians had been trying to solve the ‘four colour problem’ since 1840, but it had to wait for the invention of the computer. In fact, the four colour theorem was the first major theorem to be proved using computers.
Why did the problem take so long to solve?
The number of possible arrangements of countries on a map is essentially infinite. It only takes one of those configurations to require five colours to disprove the conjecture. In 1989, after thousands of hours of computer time, Kenneth Appel and Wolfgang Haken found that they could replace the infinity of individual arrangements with just 1,936 “reducible configurations” - designs from which all other configurations could be deduced. These could then be checked individually. The computer reported back that none of the maps required more than four colours to meet the specification.
Of course, if you want a map printed, you are going to want to be using more than four colours anyway. Happily, we are printers not mathematicians and are happy to oblige. For any advice about colour printing, please contact us on 01603 488001 or drop us an email at websales@col-print.co.uk.
