14 DAY TRIAL // While it may be of little interest to some, mathematicians and physicists are extremely interested in learning which shapes would fill a container best. Studies about packing all sorts of things into given spaces are nothing new, and a wide variety of algorithms exist to inform packing companies. Still, when it comes to filling a space randomly, as in without intervention, things change. It would appear now that the shapes which best fill a given space are tetrahedrons, pyramids with four triangular faces.
A group of researchers used a series of containers to run the new experiments. They took small tetrahedrons, placed them inside the test vessels, and then shook them for a while. They determined that these structures have the ability to occupy as much as 76 percent of the container's interior, which is a very high percentage when considering that the filling is done randomly. For comparison, spheres can only fill about 64 percent of a container, whereas ellipsoids can occupy about 74 percent. The pyramids were simulated using game dice, the researchers say.
The team behind the new investigation is based at the New York University. It was led by graduate student Alexander Jaoshvili, who was the one to set up the experiments. Together with NYU physics professor and adviser Paul Chaikin, the student even imagined a host of applications for the work that exceed the boundaries of packing per se. The two believe that the study could, for example, be used to create new and stronger materials. While analyzing the way various shapes distributed themselves in the test containers, the team determined that tetrahedrons tend to lock each other in, and not accept too many external influences.
This was not true for spheres, which were found to be highly-susceptible to influences coming from as far as the length of six sphere diameters away. “If, for instance, you wanted to make a very dense, rigid, hard ceramic, you would probably be better off making the powder from tetrahedra,” Chaikin explains. “Nobody knows whether the densest packing is ordered or random,” he detailed for NewScientist. “People tend to think that the densest packings are always ordered, but there's no fundamental reason why that has to be true. We can't rule out the possibility that the densest packings of tetrahedra will be disordered,” concludes Princeton University expert Salvatore Torquato, who was not involved in the new work, but who conducts this type of research as well.