Abstract: We study the resistance between two tegral and get the general solution of the resistance arbitrary nodes in an infinite square lattice by mathematical inbetween two arbitrary nodes of the coordinate axis. Then we draw the contour line of the resistance to the origin and find out that this line is close to a circle. Finally, we give an approximate formula to calculate the equivalent resistance between two arbitrary nodes in the plane.

Key words: infinite square lattice, equivalent resistance, integral, approximate formula