What is the sequence of the diagonals of a polygon?

1 Answer
Apr 20, 2017

Answer:

#{ (a_1 = 0), (a_2 = 0), (a_n = (n(n-3))/2" for "n >= 3) :}#

Explanation:

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,...#