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Explorations in Topology by David Gay

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1

Acme Does Maps and Considers Coloring Them

The reader is introduced to coloring maps on a sphere and on an “island.” Coloring rules are presented and refined. Several examples of “real” and “imagined” maps are examined. For coloring purposes, it is shown that the exact shape of countries is not important. A map can be distorted, as if made of rubber, but the problem of its coloring remains the same. Problems are introduced: (1) Find the fewest number of colors needed to color a given map. (2) Answer the question: Can one find a number N so that all maps (on an island) can be colored in N or fewer colors? (3) Then, if such an N exists, find it! A partial solution to these problems is found: All of a certain simple class of maps can be colored ...

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