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How many ways can you triangulate a regular polygon?

  • For a regular square, there are two ways to triangulate it: by connecting the NW and SE corners, or by connecting the SW and NE corners.
  • For a regular pentagon, there are five ways to triangulate it by choosing a vertex and connecting it to both non-adjacent vertices.
  • For a regular hexagon, there are 14 ways to triangulate it, including connecting every other vertex, creating an equilateral triangle, or creating a zig-zag pattern.
  • The number of ways to triangulate a regular (n + 2)-gon is given by the nth Catalan number, which has various applications in mathematics.

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