Polygon Diagonal Formula

Date: 8/20/96 at 0:26:41
From: Myer Moses
Subject: Use of Polygon Diagonal Formula

I know the formula for the number of diagonals in a polygon is
d = [s(s - 3)]/2. Does this same formula apply to other parts of 
geometry?

Date: 8/20/96 at 11:2:29
From: Doctor Anthony
Subject: Re: Use of Polygon Diagonal Formula

For a convex n-sided polygon, there are n vertices, and from each 
vertex you can draw n-3 diagonals.

So the total number of diagonals that can be drawn is n(n-3).  
However this method means that each diagonal will be drawn twice, 
(to and from each vertex), so the expression must be divided by 2, 
to give:

   number of diagonals of polygon = n(n-3)/2  

You can see that the formula arises from the nature of the diagram and 
the construction of the diagonals.  There is no reason why this 
formula should fit any other property of polygons, like the number of 
triangles formed when you draw in the diagonals.  Each of these 
questions must be reasoned out on its own merits.


-Doctor Anthony,  The Math Forum
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