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April 1, 1966American Mathematical Monthly

Packing and Covering.

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Authors

HZHans ZassenhausUniversity of Notre Dame CRC. A. RogersChromoLogic (United States)

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Implication

Theoretical analysis reveals existence bounds and density limits for geometric packings and coverings, highlighting fundamental constraints in discrete geometry.

Key Points

Investigate theoretical existence criteria, asymptotic bounds, and density limits for geometric packings and coverings of convex bodies, including simplices and spheres.
Formulated mathematical frameworks to analyze packing and covering densities across Euclidean spaces.
Evaluated existence criteria and bounds for both general and lattice-based geometric arrangements.
Derived analytical limits on the maximum density of simplex packings and the economic efficiency of sphere coverings.
Established existence theorems for dense packings and economical coverings across general and lattice structures.
Demonstrated that simplex packings face fundamental theoretical limits that prevent them from achieving high density.
Showed that geometric coverings formed with spheres cannot achieve high economic efficiency under asymptotic constraints.

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Zassenhaus et al. (1966) studied this question.

synapsesocial.com/papers/6a7c03bf84d0f3193c7613bd https://doi.org/10.2307/2315450

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Implication

Theoretical analysis reveals existence bounds and density limits for geometric packings and coverings, highlighting fundamental constraints in discrete geometry.

Packing and Covering.

Discussion

Member takes

Implication

Key Points

Cite This Study

Packing and Covering.

Discussion

Member takes

Implication

Key Points

Cite This Study

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