A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by nonintersecting diagonals is C_(n - 2) (with C_(n - 3) diagonals), where C_n is a Catalan number. This is Euler's polygon division problem. Counting the number of regions determined by drawing the diagonals of a regular n-gon is a more difficult problem, as is determining the number of n-tuples of concurrent diagonals.
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