Abstract: The Madelung constant of the double atomic system on a circle with radius R is calculated. It has been proved numerically that the Madelung constant for the circle case is identical to that for the linear chain case under the condition of infinite number of primitive cells,which demonstrates intuitively the physical base of periodic boundary conditions. Based on such results,two identical relations are obtained.

Key words: Madelung constant, circle, periodic boundary condition, identical relations