Our research experimentally, mathematically, and computationally investigated the singularity that forms at the tip of water droplets freezing on a flat surface (Snoeijer and Brunet, AJP 2012). We designed an apparatus to observe, video, and quantify the solidification of 10-μL drops of purified water. By making several simplifications about the freezing process, we used a geometric model to derive a system of differential equations that described the solidification rate and the unfrozen liquid’s volume, radius, and contact angle. Analysis of our equations revealed that the appearance of a singularity was dependent on the density ratio between the solid and liquid. This was also evident in the computer-based simulation that we created to predict frozen droplet shapes. While our model did demonstrate the formation of singularities in liquids with a density ratio <0.75, it inaccurately generated rounded solidified water droplets (density ratio 0.9) that were about 15% greater in volume than those experimentally observed.