Q is an abelian group. Prove that G is complete and that every connected component of G is a single element. Let R be the set of real numbers. Let X be a bounded subset of the real line. P is a prism all of whose edges are tangent to a unit sphere.
T is a triangle of unit area.
Choose two points in T independently, each with the uniform distribution. The line joining the points almost certainly divides the triangle into a triangle and a quadrilateral. Find their expected areas.