# Math Help - Polygon Center Point

1. ## Polygon Center Point

Hello .

How can I calculate the polygon center point using its vertexes?

Thanks

2. Originally Posted by rat
Hello .

How can I calculate the polygon center point using its vertexes?

Thanks
are these regular polygons?

3. No, they also can be irregular...

4. Originally Posted by rat
No, they also can be irregular...
Then don't we need to know what type of centre you are
interested in?

Centre of mass of unit weights at the vertices.

Centre or mass of rods of unit mass per unit length making
up the sides of the polygon.

Centre of mass of a lamellar of unit mass per unit area in
the form of the polygon.

Or some other centre?

5. Since the polygon may be irregular, rat must mean the center of mass, when every vertex point $\vec r_1,\ldots,\vec r_n$(plural: vertices ) has nonzero mass $m_1,\ldots,m_n.$ Then the center of mass lies at the tip of the vector

$\vec r=\frac{m_1\vec r_1+\dots+m_n\vec r_n}{m_1+\ldots+m_n}$.

Hope this is ok.