In this paper we describe the Euclidean signature curves for two dimensional closed curves in the plane and their generalization to closed space curves. The focus will be on discrete numerical methods for approximating such curves. Further we will apply these numerical methods to plot the signature curves related to three-dimensional simulated DNA supercoils. Our primary focus will be on statistical analysis of the data generated for the signature curves of the supercoils. We will try to establish some relationships between the statistics and the shape of the signature curve. The hope is that these findings will provide a more efficient way for computers to search for and identify signature curves corresponding to similar DNA supercoils.