Compact Packings are not always the Densest
Thomas Fernique, Daria Pchelina
TL;DR
This paper presents a counterexample to a longstanding conjecture, showing that compact packings of circles are not always the densest possible arrangements.
Contribution
It provides the first known counterexample to Connelly's conjecture regarding circle packing density.
Findings
Counterexample disproves the conjecture
Compact packings are not always densest
Advances understanding of circle packing configurations
Abstract
We provide a counterexample to a conjecture by B. Connelly about density of circle packings
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematics and Applications