On the relative packing densities of pistachios and pistachio shells

TL;DR

This paper investigates the optimal container size for pistachio shells based on packing density, revealing that densely packed shells require a container slightly over half the original bowl size, while loosely packed shells need about 73%.

Contribution

It provides empirical measurements of pistachio shell packing densities and relates these findings to existing packing theories.

Findings

Densely packed shells fit in a container about 0.57 times the original size.

Loosely packed shells require a container about 0.73 times the original size.

Results align with theories on packing ellipsoids and spherical caps.

Abstract

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 we find that, provided the shells are densely packed, such container needs only be slightly more than half ($\approx 0.57$) that of the original pistachio bowl. If loosely packed this number increases to $\approx 0.73$. Our results are discussed in light of existing literature on packing ellipsoids and spherical caps.