Polygon

[Bladesofhalo]

For a problem, Im supposed to figure out the max number of diagonals possible in a polygon. The teacher told us there is an equation involved.

 

[galactus]

See here:

http://www.freemathhelp.com/forum/viewtopic.php?t=17759

 

[soroban]

Hello, Bladesofhalo!

I'm supposed to figure out the max number of diagonals possible in a polygon.
The teacher told us there is an equation involved.

Your teacher is correct . . . and you can derive the formula yourself.

Suppose the polygon has \(\displaystyle n\) sides and vertices.
Let's say the vertices are: \(\displaystyle A,\,B,\,C,\,D,\,.\,.\,.\,N\)

Pick a vertex. .There are \(\displaystyle n\) choices.
It can be connected to any of the other \(\displaystyle n\,-\,1\) vertices.
It seems that there are: \(\displaystyle \,n(n\,-\,1)\) choices of diagonals.

But our list would contain, for example, \(\displaystyle A\tex{-to-}B\) and \(\displaystyle B\text{-to-}A\)
. . and they represent the same diagonal.
And this happens with every pair on our list.

Hence, our list is twice as long as it should be.

Therefore, the maximum number of diagonals is: \(\displaystyle \L\,\frac{n(n\,-\,1)}{2}\)

 

[galactus]

Ahhh....Soroban....I think you have a typo. Are you sure about that?.

I believe it's \(\displaystyle \frac{n(n-3)}{2}\)