We give a proof of the planar case of a longstanding conjecture of Kneser (1955) and Poulsen (1954). In fact, we prove more by showing that if a finite set of disks in the plane is rearranged so that the distance between each pair of centers does not decrease, then the area of the union does not decrease, and the area of the intersection does not increase.

Click here for a PDF version, here for a ps version, here for a dvi file, and here for a tex file. The following are ps files for the figures. Figure 1, figure 2, figure 3.