The Packing Properties of spheres
by Fabien Paillusson 08/10/2025
Ever struggled to fit all your coffee beans in a jar or level out ingredients in a cup when baking? It turns out that this everyday frustration links directly to a fascinating problem in Mathematics.
Fabien Paillusson first introduced the packing fraction (eta equals N subscript v over V) which describes how much space is actually filled by a material inside a container. The discussion then led to reveal that hexagonal arrangements are the most effective in both 2D and 3D planes proved by The Kepler Conjecture in 2017 [1].
A common way to make a substance more compact in its jar is to tap the sides of the container. But a shocking fact mentioned by Fabien Paillusson in the 2006 study by Yu et al [2] reveals that only tapping the sides of a container is much more effective than tapping the bottom! Fabien further described that gentle vibrations of a container result in a higher density than harder vibrations, and that harder taps can actually decrease the packing fraction from findings in a study by Mueggenburg in 2012 [3].
Fabien then outlined the historical development of this timeless problem and mentioned a Scott, Nature study in 1960 [4] provided one of the earliest papers and used extrapolation in his findings. He then left us pondered, describing how randomness is not really random its just events that happen with some probability and that there’s no such thing as perfect packing
[1] Hales, T. (2005). A proof of the Kepler conjecture. Annals of Mathematics, 162(3), pp.10651185. doi:https://doi.org/10.4007/annals.2005.162.1065.
[2] Yu, A. B., & Hall, J. S. Packing of fine powders subjected to tapping. Powder Technology, 78(3), 247-256. https://doi.org/10.1016/0032-5910(93)02790-H
[3] Mueggenburg, N. (2012). Granular compaction under confinement. Physical Review E, 85(4). doi:https://doi.org/10.1103/physreve.85.041305.
[4] SCOTT, G. Packing of Spheres: Packing of Equal Spheres. Nature 188, 908909 (1960). https://doi.org/10.1038/188908a0
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You have presented your blog fairly well, including the seminar title, the speaker’s name, and the date at the beginning of your report. Your grammar could do with some work; more use of commas in sentences would definitely help it read better, and there were also a couple of instances where you completely missed out words that would help sentences make sense. You reported and contextualised the seminar’s message well, but you could have gone into more detail when explaining your findings and included a direct quote from any of your references. The writing style was appropriate, but the technical level should be higher.
A couple of things to improve upon, but overall it’s a decent effort. :)