Packing Tetrahedrons

see also: Geometric packing: honeycombs and soap bubbles

I checked out another book about math from the library. It is called Book of Mathematics: More than 100 years of writing by the numbers and it contains 110 articles from The New York Times, written from 1892 to 2010, that are related to math in some way. I am not reading this one cover-to-cover; I am just skipping through and looking at the articles that seem interesting.

One such article is called "Packing Tetrahedrons, and Closing in on a Perfect Fit" (link). It was written by Kenneth Chang and published in 2010. From it I have learned the following:

• That Aristotle thought that regular tetrahedrons pack perfectly with no spaces between them
• That this is incorrect, and that its incorrectness was pointed out almost two millenia after Aristotle
• That in the past several decades, mathematicians, physicists, chemists, and the students who work for them have found/developed increasingly dense packing structures for tetrahedrons, with the most dense packing taking up 85.63% of space at the time of the writing of the article

I found another article about the packing of tetrahedrons, from a few years before the NYT acrticle. It has a lot of information, much of which I do not understand, but which I hope to take a closer look at in the near future (link). I did not take any math classes beyond calculus when I was in school, so this may take some time and background research to read through. The idea is very interesting, though, which is why I am adding this page.

There is this blog post as well, also from 2010, which sums up the history even more nicely and has some illustrations and such to explain (link).