### Challenge Problem – Polygon Diagonal Formula

Here’s a challenge problem for anyone who’d like to try it.

On Monday I will post the answer and the names of the first five people who got this right. So good luck, everyone.

A regular polygon is a polygon all of whose sides are congruent and all of whose angles are congruent. For any polygon, a “diagonal” is defined as a line segment that runs from one vertex of the polygon to another, and which runs through the interior of the polygon.

Find a formula that tells how to determine the number of diagonals there are in any regular convex polygon with n sides.

Once you have the formula, use it to figure out the number of diagonals in a regular convex polygon with 1,000 sides (don’t try this by hand! — that’s why algebra was invented).

Good luck!