In “Exploring the Art Gallery Theorem and Variations,” I dive into a whole field of mathematics that stems from Victor Klee’s 1973 question: how many guards are needed to protect a polygonal art gallery with n walls? I both state and prove the Art Gallery Theorem following Steven Fisk’s method, which includes the Three-Color Theorem and the Triangulation Theorem. I then discuss the variants of this method, such as the constrained case, the orthogonal constrained case, and galleries with holes, and many more.
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