Volumen centralne krogle pri enostavnem kubičnem pakiranju - Škvarč, Teja (Matrika, 2019)
The article discusses the ratio between volume of the central sphere of simple cubic packing and volume of the hypercube. In the paper, one can find something about sphere packing in general, some historical background, the best structure for 3-dimensional space and the relatable problem of kissing number. Later on, the paper provides more information about simple cubic packing, that is one of the simplest packings of spheres in the cube, presented in 2-, 3-, 4- and n-dimensional space. The central sphere, its radius and volume will be mostly discussed. In article one can also find a proof of the theorem that tells us that the ratio between volume of the central sphere and volume of the hypercube rises to infinity while dimension rises to infinity. In the end, one can find usage of sphere packing in communication systems.
Keywords: central sphere; centralna krogla; hiperkocke; hypercubes; pakiranje krogel; sphere packing