Perfect packing of squares

2022/12/08 by Antal Joós, Joós, Antal
Engineering · Mathematics · #52C15 #52C20 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Optimization and Packing Problems #graph theory and CDMA systems

paper · doi:10.48550/arxiv.2212.04121

openalex publication_date 2022/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that ∑_{i =1}^∞ 1/ i²=π²/6. Meir and Moser asked what is the smallest ε such that all the squares of sides of length 1, 1/2, 1/3, … can be packed into a rectangle of area π²/6+ε. A packing into a rectangle of the right area is called perfect packing. Chalcraft packed the squares of sides of length 1, 2^-t, 3^-t, … and he found perfect packing for 1/2

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