Diagonals: Part I
5. Where do new problems come from?
This situation represents a polygon with holes, where the "holes" consist of segments and polygons which lie in the interior of a simple polygon. Questions addressing the triangulation of polygons with holes and the number of guards sometimes necessary and always sufficient to guard the interior have been posed. The solutions of these problems are not as straightforward as Fisk's solution to the case for a simple polygon.
In the next column, I will discuss how these ideas have enriched the rapidly developing subtopic of Art Gallery Theorems within computational geometry and led to new and interesting accessible geometry problems. The interested reader should consult Joseph O'Rourke's book of 1987, which summarizes what was known at that time.
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