The article studies the convergence of a sequence of iterated polygons. If we consider a polygon in RN, another polygon may be constructed by connecting the mid-points of the edges of the initial polygon. If we iterate this construction we get a sequence of polygons, for which we prove, by using elementary computations, that is convergent. Moreover, if we consider other ”weighted points” instead of mid-points we obtain that the corresponding sequence of iterated polygons converges to the centre of gravity of the initial polygon.

Author: Tudor Mihai