There's a fun puzzle (chemistry / math) hidden in the Wikipedia entry for Peaberry coffee beans, which are hypothesized to:

roast more evenly, because of their rounder shape minimizes sharp edges, and rolls about the roasting chamber more easily, as well as the alleged **higher bean density** may improve heat transfer in the roasting process.(sic)

To a chemist, the question resembles the prediction problem: *how do atoms in a solid sit and if you cram them , how can they sit closer?*

From the coffee roaster's point of view, the special thing here is that normal coffee beans are sort of flat but the Peaberry, born untwinned, is a spherical bean. College chemistry students will recognize the implied problem of *how many neighbors does a given object have when packed as tightly as possible*? Coffee roasters will simply think of it as *how many beans and how much air is in my roaster?*

If objects are spherical, some chemistry textbook solutions are *cubic close packed, hexagonal close packed, and face centered cubic*. If the objects are flattish, it must be much more complicated to model.

UPDATE: Someone else who thinks about closest-packing was interviewed in last week's paper, a self-described Recreational Mathematician was sitting down to lunch and the Times reporter described the food:

...a small table, about two and a half feet square, was jammed with a teapot, two plates of curry, a bowl of soup, two cups of tea, two glasses of water, a plate with two egg rolls, a plate of salad *“There’s a packing puzzle here,”* (Vi Hart) said. *“This is the kind of thing where if you’re accustomed to thinking about these problems, you see them in everything.”*

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