Los Angeles Math Circle

4/7 -- Junior Circle: Three solutions to one problem. Geometry of masses. (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 will take time to give three different proofs to the theorem, each coming from a distinct, and very important, branch of mathematics. During this class, we will begin learning the geometry of weights that will take us from the workings of a lever to solving the original problem and beyond.