What is the four color theorem?
Q: What is the four color theorem?
A: The four color theorem is a mathematical theorem that states that in any plane surface with regions, the regions can be colored with no more than four colors. Adjacent regions must not get the same color.
Q: How was the first proof of the four color theorem established?
A: The first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This means that it was established by dividing it into cases and proving each one separately.
Q: Are mapmakers interested in this problem?
A: No, mapmakers are not very interested in this problem as maps utilizing only four colors are rare and usually require only three colors. Books on cartography and history of map making do not mention the four-color property.
Q: What is the five color theorem?
A: The five color theorem states that five colors are enough to color a map and it has a short, elementary proof which was proven in late 19th century.
Q: How difficult was it to prove that only 4 colors were needed for coloring maps?
A: Proving that only 4 colors were needed for coloring maps turned out to be much more difficult than expected as many false proofs and false counterexamples have appeared since its first statement in 1852.
Q: Is there an example of a map where 5 or more colors would be necessary to properly colour all regions?
A: Yes, one such example is when one region is surrounded by an odd number of others which touch each other in a cycle - 5 or more colours may be necessary to properly colour all regions in this case.
