Functional information from the brain is available from a variety of modalities including functional magnetic resonance imaging (fMRI) and positron emission tomography (PET). Individual variability in the size, shape and extent of the folding patterns of the the human brain makes it difficult to compare functional activation differences across subjects. I will discuss a method that attempts to address this problem by creating flat maps of the cortical surface. These maps are produced using a novel computer realization of the Riemann Mapping Theorem that uses circle packings. These maps exhibit conformal behavior in that angular distortion is controlled. They are mathematically unique and canonical coordinate systems can be imposed on these maps. Some of the maps of the cortical surface that I have created in the Euclidean and hyperbolic planes and on a sphere will be presented.