In reference to a question I got in a test, I asked a teacher how many long and short diagonals were in a 15-sided regular polygon. Considering a long diagonal to be any diagonal with a minimum of 2 vertices in between the vertices joined to make the diagonal, and a short diagonal made such that only 1 vertex lies in between, he replied 15 for both.

My question is can we generalise this result? n long and n short diagonals for an n sided regular polygon? It definitely doesn't work for smaller values of n, but I guess the picture seems to blur at bigger values. If not, what's the correct answer? Please do let me know.