In this post the central point of the theme is the convex region, which are fundamentals for a plane in geometry. Notions of convex region Definition (Convex Region): a set of points $\Gamma$ is convex if, and only if, any two distinct points $A$ and $B$ of these sets are one of the possibilities: endpoints of a line segment ($\overline{AB}$) contained in this set $\Gamma$ $\Gamma$ is unitary $\Gamma$ is empty