On the relative packing densities of pistachios and pistachio shells

Ruben Zakine; Michael Benzaquen

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arXiv · 2406.18386

On the relative packing densities of pistachios and pistachio shells

Ruben Zakine·Michael Benzaquen

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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.

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Ruben Zakine, Michael Benzaquen. 2024-06-26. On the relative packing densities of pistachios and pistachio shells. https://arxiv.org/abs/2406.18386

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