Los Angeles Math Circle

11/11 -- Junior Circle: The triangle inequality and the shortest paths between points. (Oleg Gleizer)

For the first hour, we will solve a variety of problems, including taking roots of numbers, drawing a graph of a function, constructing a right angle by means of a rope, and figuring out the winners of a fencing competition. In the second part of the class, we will prove the triangle inequality for the Euclidean plane. We will further use it as a tool for finding the shortest paths between points in the Euclidean plane and on a cylinder.