On non-parallel cylinder packings

2023/10/10 by Ofek Eliyahu, Eliyahu, Ofek
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2310.06943

openalex publication_date 2023/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we will discuss optimal lower and upper density of non-parallel cylinder packings in R³ and similar problems. The main result of the paper is a proof of the conjecture of K. Kuperberg for upper density (existence of a non-parallel cylinder packing with upper density π/√(12)). Moreover, we prove that for every ε > 0 there exists a nonparallel cylinder packing with lower density greater then π/6 - ε.

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