A finite collection of points of the complex plane lying in general position determines a polygonal shape. By extending each edge of the polygon into a line, these vertices describe certain intersections points of these lines. In general, the intersecting objects do not need to be lines nor need this to happen in the complex plane. In this talk, we want to give a taste of intersection problems in symplectic manifolds where the intersecting objects are a class of half-dimensional spaces, called Lagrangians. We will discuss (with examples) what this has to do with the method of Lagrangian multipliers and how such Lagrangian intersection problems reveal a path towards categorification.