Critical curves of a binary fluid mixture are usually plotted as a function of pressure and temperature (p, T projection), temperature and composition (T, x projection) or as a function of the reduced densities of the two components (y1, y2 projection). In these three ways of representation, we will show the structure of the critical curves around a mathematical double point. Moreover, it will be shown that mathematical double points can conveniently be divided into two groups : the (meta)stable and unstable mathematical double points. To date, the (meta)stable mathematical double points have not been investigated with a pressure-explicit equation of state. In this paper, it will be shown how the two types of mathematical double points can be calculated. We will digress on the thermodynamic conditions to be obeyed for the calculation of the two types of mathematical double points.