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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