Aristotle mistakenly thought that identical regular tetrahedrons packed together perfectly, as identical cubes do, leaving no gaps in between and filling 100 percent of the available space. They do not, and 1,800 years passed before someone pointed out that he was wrong. Recent research on how efficiently they do pack has come up with some interesting results.
By way of contrast is the problem of how best to pack identical spheres.Johannes Kepler conjectured in 1611 that the best packing density was just larger than 74 %. But proving the obvious took almost four centuries until Thomas Hales of the University of Pittsburgh proved it in 1998 with the help of a computer.
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