Random Sequential Packing in Euclidean Spaces of Dimensions Three and Four and a Conjecture of Palasti

摘要

A conjecture of Palasti that the limiting packing density beta sub d is a space of dimension d equals beta superscript d where Beta is the limiting packing density in one dimension continues to be studied, but with inconsistent results. Some recent correspondence to this Journal, as well as some other papers, indicate a lively interest in the subject. In a prior study, we demonstrated that the conjectured value in two dimensions was smaller than the actual density. Here we demonstrate that this is also so in three and four dimensions and that the discrepancy increases with dimension.