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Concave

Course: 
5th Grade

Used to describe a polygon with at least one angle measurig more that 180 degrees; One or more line segments that are outside the polygon can always be drawn between two vertices.

Meaning

Informally, a concave 2-dimensional shape is any shape that has "indentations" in it.

A way to "test" for such indentations leads to a better definition for concavity: A shape is concave if, for some choice of two points on the boundary of the figure, a line segment that connects those two points lies partially or entirely outside 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 Image:concave.png, a line segment that connects a different selection of two points on this figure lies partially outside of the figure Image:concave2.png. Therefore, this figure is concave. Similarly, Image:ChevronSmallTan.png is concave.



This potato-like figure Image:convex.png, even though it is irregular, seems to have 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.