Piecewise linear curve in the context of "Simple polygon"

In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments. These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons.

The sum of external angles of a simple polygon is ${\displaystyle 2\pi }$. Every simple polygon with ${\displaystyle n}$ sides can be triangulated by ${\displaystyle n-3}$ of its diagonals, and by the art gallery theorem its interior is visible from some ${\displaystyle \lfloor n/3\rfloor }$ of its vertices.