Euler's equation. If you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces, E the number of edges and V the number of vertices, you will always get V – E + F = 2,"
The Hard Sphere Monte Carlo Model performs canonical Monte Carlo simulations of 256 or 500 hard spheres covering the fluid and solid states. The results are analysed through the radial distributions functions from which the equation of state (EOS) is estimated. This is done by fitting a polynomial to the radial distribution functions in order to exrapolate them to the hard spheres distance of contact.