2024-07-04 21:17:40
at the Paris Polytechnic School (French Polytechnic university) Ruben Zakine and Michael Benzaquen often discuss science while eating pistachios in a cafeteria. Naturally, they began to wonder about the mathematical best way to collect the remains of their snacks.
The researchers placed 613 pistachios in a cylindrical container – to determine “packing density”, the fraction of space occupied by whole nuts in their shells. Separately, they measured the packing density of the nut shells alone. In one experiment, the researchers poured peanut shells into a container and allowed them to expand, while in another they shook them into a denser, more efficient configuration.
Without shaking, the shells occupied about 73 percent. of the initial packing density. The shake-up brought that number down to 57 percent. This suggests that with any pistachio container, an extra half-size container will hold the shell waste as long as you shake the container occasionally while eating.
Zakine and Benzaquen based their findings by modeling pistachios and their shells as ellipsoids – three-dimensional figures resembling compressed spheres – and calculating their “packing density” based on mathematical rules. These results confirmed the results of real experiments and suggested that the same relations can be applied to other shapes of capacitors.
Despite these similarities, the researchers found that the calculations and actual measurements differ by about 10 percent. Zakine says this is not surprising, as pistachios are not perfect ellipsoids and their shape naturally varies. And calculating the best way to pack objects into containers is difficult – so far, mathematical researchers have only been able to do calculations with spheres and uniform shapes – such as M&M’s.
In the future, scientists want to perform more complex calculations on a computer. But for now, they’re hoping to get some math questions – at least when pistachios are served at parties, New Scientist writes.
Research published on arXiv.
2024-07-04 21:17:40