It is believed that flat maps of the cortex facilitate the recognition of individual differences in cortical organization and the localization of activated foci in functional neuroimages. It is impossible to flatten a curved surface in 3D space without metric and areal distortion. However, the Riemann Mapping Theorem implies that it is theoretically possible to preserve conformal (angular) information under flattening. I am using a novel computer realization of the Riemann Mapping Theorem that uses circle packings to create quasi-conformal flat maps of the cortical surface obtained from MRI scans. This approach offers a number of advantages including maps can be created in the Euclidean and hyperbolic planes and on a sphere and the maps are mathematically unique. I will discuss this method and present some of the flat maps of the cerebellum that I have created using this approach.