The cosmic microwave background (CMB) anisotropy constrains the geometry of the Universe because the positions of the acoustic peaks of the angular power spectrum depend strongly on the curvature of three-dimensional space. In this Letter we exploit current observations to determine the geometry in the presence of isocurvature modes. Most previous analyses assumed that the primordial perturbations were adiabatic. A priori one might expect that allowing isocurvature modes would substantially d...