Thursday, February 7, 2008

Convex Polygon

In geometry, a convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity:

* Every internal angle is at most 180 degrees.
* Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon).

A polygon that is not convex is called concave.

A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two nonadjacent vertices of the polygon is strictly interior to the polygon except at its endpoints.

Every triangle is strictly convex.

The sum of the interior angles of a regular convex polygon with n sides is equal to 180°(n - 2).

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