The convexity coefficient 
of a planar region 
of finite positive area is the probability that the line
segment connecting two independently and uniformly chosen points in 
is contained entirely within 
. For a convex region,
.
Let 
denote the area of the part of 
visible from a point 
, and let 
be the area of 
. Then
 |
(Hodge et al. 2010).
The convexity coefficient is in general hard to compute exactly for concave regions even of simple shape. One closed
form is that of an annulus with inner radius 
and outer radius 
, where 
and 
, which has
 |
(Hodge et al. 2010).
