This talk aims to study a method for computing the discrepancy of any given distribution of points on the sphere. Studying distributions of points on the sphere has a long history and Thomson’s Problem, inspired by early atomic theory dating back to 1904, was a landmark. While Thomson’s Problem is based on the Coulomb potential, the discrepancy measures the deviation of the number of points in a set from the expected value.

In this talk, the Polar Coordinates method was introduced in the context of Thomson’s problem and the order of the growth of the discrepancy for this method is investigated. Applying tiny modifications to this method leads to the best-known rate. Besides, a new algorithm is introduced that enables one to determine whether the discrepancy of a given distribution is greater than any given number or not, and in the latter case, it specifies the location where a high discrepancy occurs.