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Explorations in Topology by David Gay

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3

Maps Data

This chapter introduces the reader to collecting data from maps. This is an important notion that is utilized throughout the book. The basic items of data are the number of vertices, borders (edges), and countries of a map. The reader and the story characters are led to observe patterns in this data, one of which is Euler’s formula. An argument for this formula is given in the chapter. The formula appears first for maps on an island, then extended to a formula for maps on the sphere. This leads to a formula for polyhedra where the data are vertices, edges, and faces. Counting arguments used to calculate the data for certain polyhedral will reappear frequently in subsequent chapters. In addition to vertices, borders, and countries, ...

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