04/07 -- Junior Circle: Three solutions to one problem. (Oleg Gleizer)

At the end of the previous quarter, we considered the following problem. Prove that medians of any triangle in the Euclidean plane intersect at one point and that the intersection point divides them in the ratio 2:1 counting from the corresponding vertex. We are going to give three different proofs to the theorem, each coming from a distinct, and very important, branch of mathematics. In the process, we will learn a bit of geometry of masses and barycentric coordinates, linear algebra, and classical (Greek-style) geometry of the Euclidean plane.