What and how can i find the sequence of the diagonals of a polygon

Kaylynn Cook

Kaylynn Cook

Answered question

2022-11-02

What and how can i find the sequence of the diagonals of a polygon

Answer & Explanation

Ismael Wilkinson

Ismael Wilkinson

Beginner2022-11-03Added 13 answers

I think you are wanting to know what the number of diagonals of a convex n sided polygon for any n, with the resulting sequence.
A diagonal runs from one vertex to a distinct non-adjacent vertex, of which there are n−3 possibilities.
Hence the formula for the number of diagonals of an n-sided convex polynomial is:
n ( n - 3 ) 2
which is valid for any n 3
So we can define a corresponding sequence by:
{ a 1 = 0 a 2 = 0 a n = n ( n - 3 ) 2 for n 3
The first few terms are:
0,0,0,2,5,9,14,20,...

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