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In this work, we emphasize that it is possible using a personal computer to perform a Monte Carlo simulations in a reasonable computing time, and find the equilibrium structure of a hardsphere gas for a Euclidean multi-dimensional spaces. We study the properties of equilibrium and  determine the equation of state of gas of hard spheres in Euclidean spaces from two to seven  dimensions. The results show that the pressure is in agreement with different theoretical models  based on virial expansion in spaces from two to five dimensions, also our results are extended for  seven dimensions. As expected, it was found that the system of hard spheres loses its structure  and the pressure of the system decreases when the dimension of the space increases.

Monte Carlo simulation for a gas of hard spheres in d-dimensional space: Equilibrium structure and state equations