On the Packing Density Bound in 3-Space

TL;DR

This paper presents a straightforward method to improve the upper bound on packing density in three-dimensional space, refining previous estimates to a higher value.

Contribution

It introduces a simple approach to enhance the known packing density bound in three-dimensional Euclidean space.

Findings

Improved packing density bound from 0.53835 to 0.54755

Demonstrates an accessible method for density bound enhancement

Provides a tighter estimate for sphere packing density in 3D

Abstract

The note shows an easy way to improve E.H. Smith's packing density bound in $\mathbb{R}^3$ from $0.53835...$ to $0.54755...$ .