This document summarizes research on modeling the equilibrium shape of a dielectric droplet placed in a uniform electric field. The researchers used a third-order polynomial approximation to represent the shape of the droplet and calculated the total energy as a function of surface energy and electrostatic energy. They were able to determine the shape of the droplet for given dielectric properties and electric field strength. Their results showed that pointed ends develop when a parameter reaches zero, and there is hysteresis in the system depending on the starting point of the energy minimization calculation. The relationship between electric field strength and the angle of pointed ends was found to be nonlinear.