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### 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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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