Square packing with graph
Year: 2025
Type: article
Abstract: It introduces a symbolic formula for estimating the number of axis-aligned squares of fixed side lengthx that can be fully packed within a circle of radius r. The formula is constructed to ensure that eachsquare lies entirely within the circle and provides a conservative approximation of the total packed area.We prove that this area converges to πr2as x → 0, and that all square placements satisfy chord-basedcontainment constraints. A convergence graph is included to illustrate the accuracy of the method. Thisresult contributes a discrete symbolic framework to the study of geometric packing problems.
Author: Haileab, Haileab
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6911928246
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