Limits RegistryPUBLIC RECORDLimits RegistryResearch Console →The hexagonal packing is the densest congruent-circle packing in the Euclidean plane.
The question, scope, and sources behind this Registry record.
Determine the supremum density of packings of congruent circles in the Euclidean plane.
Current frontiers derived from accepted Claims.
The accepted equality closes this optimization result.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.