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 Everyday Examples
 Concave:  If, when you join any two points inside a figure, the resulting line segment goes outside the figure, then the figure is concave. Also called nonconvex.

Image source: http://www.cosc.brocku.ca/Offerings/3P98/boomerang.jpg

A boomerang is concave so that the curvature in the boomerang helps it return back to you after you throw it.

Image source: http://www.m-b.com/acatalog/stapler.gif

A stapler is concave so that a stack of papers can squeeze between two of the metal plates.

Image source: http://www.canesgalore.com/images/cane.gif

The handle of a walking cane is concave so that it is easier to hold.