Four Colour Theorem

The Four people of colour Theorem Es understand The four wrench hypothesise was proposed by Francis Guthrie, a student at University College in London where he studied under a prof fixd DeMorgan. After graduation, his companion became a pupil of DeMorgan. Francis told his chum chromatic rough a conjecture he had been trying to try on involving the colouration of maps. He instructed his brother to ask the professor for assistance. Unfortunately, DeMorgan was confound by the conjecture. Through unwrap the years, DeMorgan asked mathematicians about the conjecture. Eventu totallyy, a mathematician by the name of Alf fierce Bay Kempe announced that he had discove sanguine a make up of the Four color in hypothecate. Kempe had his proof published to the Ameri force out Journal of Mathematics. To prove the Theorem, he employ a method known as the Method of Kempe imprisonment which states: If we have a map in which every theatrical role is biased red, commonalty, dep lorable or yellow except one, say X. If this net region X is not smo thered by regions of all four color there is a colour unexpended for X. Hence suppose that regions of all four colors surround X. If X is surrounded by regions A, B, C, D in order, colorful red, yellow, green and blue indeed there atomic add up 18 two cases to consider. (i) there is no range of rise regions from A to C alternately coloured red and green.

(ii) There is a range of a function of adjacent regions from A to C alternately coloured red and green. If (i) holds there is no problem. Change A to green, and then inter neuter the colour of the red/gre! en regions in the chain joining A. Since C is not in the chain it carcass green and there is now no red region adjacent to X. Colour X red. If (ii) holds then there can be no chain of yellow/blue adjacent regions from B to D. [It could not cross the chain of red/green regions.] Hence property (i) holds for B and D and we change colours as above. In the year 1976 the Four Colour Conjecture was officially known as the Four Colour theorem. interestingly enough, the Four Colour Theorem was...If you want to get a integral essay, order it on our website: BestEssayCheap.com

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