The answer to this month’s puzzle is π−1.

The loops can be dissected into overlapping rectangles, quarter-circles, and a central square as shown. Furthermore, it can be shown that the diameters of the seven circles are 670, 671, 672, 673, 674, 675, 676. From here it is a matter of properly adding (and occasionally subtracting) the various component areas to get the correct answer.