Mean line segment length
In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen. Even for simple shapes such as a square or a triangle, solving for the exact value of their mean line segment lengths can be difficult because their closed-form expressions can get quite complicated. As an example, consider the following question: What is the average distance between two randomly chosen points inside a square with side length 1? While the question may seem simple, it has a fairly complicated answer; the exact value for this is . (Wikipedia).
