The hexagonal versus the square lattice

The hexagonal versus the square lattice

Math. Comp. 73 (2004), 451-473 We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p. 201), motivated by considerations from hyperbolic geometry, conjectured that in dimensions 2 to 8 th...

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Bibliographische Detailangaben
Hauptverfasser: Moree, Pieter, Riele, Herman J. J. te
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Metric Geometry
Mathematics - Number Theory
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Zusammenfassung:Math. Comp. 73 (2004), 451-473 We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p. 201), motivated by considerations from hyperbolic geometry, conjectured that in dimensions 2 to 8 the best known lattice sphere packings have `maximal lengths' and goes on to write: "In dimension 2 the conjecture means in particular that the hexagonal lattice is `better' than the square lattice. More precisely, let 0
DOI:10.48550/arxiv.math/0204332