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  "body": "\n## Summary\n\nA polygon triangulation cuts a simple polygon into triangles by drawing diagonals between its vertices.\nEvery simple polygon with $n$ vertices has one, and each triangulation has exactly $n - 2$ triangles and $n - 3$ diagonals.\nTriangulations reduce questions about a complicated polygon to questions about triangles.\nThey are a basic tool of [[computational geometry|KAT7K2NE9Z]], used for area computation, guarding problems such as the [[art gallery theorem|G4WSPQJ6W1]], and graphics.\n\n## Explanations\n\n### L1 human\n\nTake a polygon drawn on paper whose sides do not cross.\nDraw straight cuts from corner to corner, staying inside the polygon, until no more cuts fit without crossing.\nThe polygon is then split into triangles whose corners are corners of the polygon.\nFor a convex hexagon, the three cuts from one corner to the three non-adjacent corners give $4$ triangles.\nIt is a planar cousin of the [[triangulation|YH170WBQ6M]] of a space in topology.\n",
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