Write a conjecture as to the number of sides as compared to the number of triangles formed when drawing diagonals from one vertex to the other vertices

If we connect all vertices of a regular N-sided polygon we obtain a figure with (N/2) = N(N - 1)/2 lines.

All triangles are formed by the intersection of three diagonals at three different points. There are five arrangements of three diagonals to consider. We classify them based on the number of distinct diagonal endpoints. We will directly count the number of triangles with 3, 4 and 5 endpoints (top three figures). We will count the number of potential triangles with 6 endpoints, then correct for the false triangles. In each of the following five figures, a sample triangle is highlighted.

NOTE: See picture attached.

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