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In many cases we could use a lot more colors if we wanted to but a maximum of four colors is enough.
Coloring maps four colors. The theorm states that. Student francis guthrie notices that four colors su ce to color a map of the counties of england. Given any separation of a plane into contiguous regions producing a figure called a map no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment not merely a corner where.
Coloring maps history the history of the four color theorem 1852. This result has become one of the most famous theorems of mathematics and is known as the. Map created by fibonacci on wikimedia. Guthrie poses the four color problem to his brother frederick a student of augustus de morgan a big shot of 19th century british mathematics.
The next obvious question to ask is whether any maps actually require four colors. Recap some facts about maps and coloring. In mathematics the four color theorem or the four color map theorem states that given any separation of a plane into contiguous regions producing a figure called a map no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. In some cases like the first example we could use fewer than four.
Four color theorem guthrie kempe tait and other people and stuff stefanuttimaps coloring java. Should we really have a 3 color. The first results about graph coloring deal almost exclusively with planar graphs in the form of the coloring of mapswhile trying to color a map of the counties of england francis guthrie postulated the four color conjecture noting that four colors were sufficient to color the map so that no regions sharing a common border received the same color. The map shows the four colour theorem in practice.
After all before there was a 4 color theorem there was a 5 color theorem. It seems that any pattern or map can always be colored with four colors. History in mathematics the four color theorem or the four color map theorem states that given any separation of a plane into contiguous regions producing a figure called a map no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
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