Puzzles/Four colour map

From Wikibooks, open books for an open world
< Puzzles
Jump to navigation Jump to search
Bodleian Libraries, Wallis's new geographical game exhibiting a tour through England & Wales (title on slip case) (cropped).jpg

The four color map theorem mentions that you only need four colors to color all the regions of any map without the intersection or touching of the same color as itself.

As seen on the old maps of Britain on the right, we can see that district all Britain are coloured with red , yellow, green and blue. We can scrutinize the map itself and found that the map itself don't have any areas with same colour which touches side by side.

The first proposal of such puzzle's theory was made by Francis Guthrie on October 23, 1852. The proposal occurred while trying to color the map of England, when it was noticed that only four different colors were needed. (See the map on right). He asked his brother Frederick if it was true that any map can be colored using four colors in such a way that adjacent regions (i.e. those sharing a common boundary segment, not just a point) receive different colors. Francis Guthrie showed his brother some results he had been trying to prove about the colouring of maps and asked Frederick to ask De Morgan about them.

In 1860, De Morgan (lecturer of Francis Guthrie) to showcase the problem and its proof to the United States of America. In America, Benjamin Price (1809-1880) a famous mathematician and astronomer, chose to develop logical methods to investigate this conjecture. De Morgan used the fact that in a map with four regions, each touching the other three, one of them is completely enclosed by the others. Since he could not find a way of proving this, he used it as an axiom, the basis of his proof. His argument was considered correct until 1890 when Percy John Heawood discovered a flaw. Work by many people continued and the conjecture was finally proved true in 1976 by Kenneth Appel and Wolfgang Haken.

Bibliography[edit]