What’s the most efficient way to pack a group of identical spheres? It is to stack them like your grocer stacks oranges, which Kepler conjectured would yield a packing density of 74%, and Thomas Hales proved Kepler right in 1998.
What’s the most efficient way to pack a group of identical, regular tetrahedron? Here answers have been all over the board. Aristotle thought they would pack together perfectly. That’s false; it turns out they don’t pack together very easily at all. Is their packing density greater than that of the sphere problem? Around 2006, the answer appeared to be negative. Now we know it is positive, and the race is on to find the upper limit.
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That’s really neat! Especially the way that simulations and physical models were able to quickly find solutions that were much better than the theoretical ones, but that new periodic ones do better than the quasi-periodic ones showing up in the simulations.
Also, a minor point, but I’m sure Kepler could prove that the density of his particular sphere packing was 74% – what he conjectured was that no other packing was better.
Exactly! Isn’t this nice?
This is kind of neat, too.