Discriminant Coamoebas in Dimension 2 via Homology Coamoebas of reduced A-discriminants arise when studying the convergence of Mellin-Barnes integrals for the solutions to the associated A-hypergeometric system. Nilsson and Passare described these coamoebas, in dimension 2, as topological chains in the 2-torus T^2 with piecewise-linear boundary. This boundary, with opposite orientation, is the boundary of a natural centrally symmetric zonotope in T^2, and they showed that the union of these two chains is a cycle equal to vol(A)\cdot[T^2], i.e., it covers T^2 vol(A)-many times. Their proof could not be generalized to higher dimensions, and it gave no intuition about the multiplicity. In this talk, which is joint work with Passare, we give a new, simpler, and elementary proof of these facts which identifies the multiplicity from the pushforward of a homology cycle in a torus T^A to T^2. The ingredients of this proof generalize to all dimensions, giving hope for a complete understanding of A-discriminant coamoebas.