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Let $P$ be a pointset consisting of $n$ uniformly random elements of $[0,1]^2$. It is known that the diameter (greatest number of edges in any shortest path between two points) of the Delaunay ...

This is a variant on Polya's orchard problem.1,2 Suppose trees are planted randomly in the plane. The question is: How many trees are visible from the origin as their radii grow? More precisely, ...

Although the MO question Limit of lights in rooms was quickly closed, it suggests a related question: Q0. What is the probability that a random quadrilateral $Q$ is entirely illuminated from a ...