On the Relative Packing Densities of Pistachios and Pistachio Shells

Given an appetizer bowl full of N pistachios, what is the optimal size of the container � neither too small, nor too big � needed for accommodating the resulting 2N non-edible pistachio shells? Performing a simple experiment the authors find that, provided the shells are densely packed, such a container needs only be slightly more than half (� 0.57) that of the original pistachio bowl. If loosely packed this number increases to � 0.73. The results are discussed in light of existing literature on packing ellipsoids and spherical shells.