# Convex

Course:

Used to describe a polygon with all interior angles measuring less than 180 degrees; all diagonals are inside the polygon.

## Meaning

Informally, a convex 2-dimensional shape is any shape that does not have indentations in it.

A way to "test" for such indentations leads to a better definition for convexity: A shape is convex if, for any choice of two points on the boundary of the figure, a line segment that connects those two points lies entirely inside the figure.

For example although it is possible to find two points on the edge of this figure that can be connected by a line segment that lies entirely inside the figure , a line segment that connects a different selection of two points on this figure lies partially outside of the figure . Therefore, this figure is not convex. Figures like this are called concave.

This potato-like figure , even though it is irregular, looks like it has no "indentations," places where a line segment connecting two points on the boundary would lie partially or entirely outside the figure. If, in fact, there are no such places, then it is convex.