An iterative method for finding the center of a linear programming polytope is presented. The method assumes that we start at a feasible interior point and each iterate is obtained as a convex combination of the orthogonal projection on the half spaces defined by the linear inequalities plus a special projections on the same half spaces. The algorithm is particularly suitable for implementation on computers with parallel processors. We show some examples in two dimensional space to describe geometrically how the method works. Finally, we present computational results on random generated polytopes and linear programming polytopes from NetLib to compare the centering quality of the center using projections and the analytic center approach.