Each circle marked with a number N has a radius 1/N of the outer circle. An infinite number of circles can be packed this way, and amazingly, N is always a whole number! We begin by placing the largest possible two equal circles into the outer circle. Then in each space bounded by three circles, we place the largest possible circle. We can repeat this forever, in principle. With the radius of the outer circle = 1, if a square grid of spacing 1/N is overlaid with a grid intersection at the center of the outer circle, the center of any circle marked N will always fall on a grid intersection.