Exploring Discrete Geometry

Explore discrete geometry by starting with familiar challenges like polygon triangulations and art gallery problems, then venturing into variants that encourage rethinking established answers. Vivid illustrations and intuitive reasoning fuse high school algebra and geometry into an engaging journey.
Together with its clear mathematical exposition, the problems in this book take the reader from an introduction to discrete geometry all the way to its frontiers. Investigations start with easily drawn figures, such as dividing a polygon into triangles or finding the minimum number of ""guards"" for a polygon (""art gallery"" problem). These early explorations build intuition and set the stage. Variations on the initial problems stretch this intuition in new directions. These variations on problems together with growing intuition and understanding illustrate the theme of this book: ""When you have answered the question, it is time to question the answer."" Numerous drawings, informal explanations, and careful reasoning build on high school algebra and geometry.

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