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The Hexagonal Honeycomb Conjecture


Author: Frank Morgan
Journal: Trans. Amer. Math. Soc. 351 (1999), 1753-1763
MSC (1991): Primary 52A38, 49Q20, 28A75
DOI: https://doi.org/10.1090/S0002-9947-99-02356-9
Published electronically: January 26, 1999
MathSciNet review: 1615934
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Abstract | References | Similar Articles | Additional Information

Abstract: It is conjectured that the planar hexagonal honeycomb provides the least-perimeter way to enclose and separate infinitely many regions of unit area. Various natural formulations of the question are not known to be equivalent. We prove existence for two formulations. Many questions remain open.


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Additional Information

Frank Morgan
Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
Email: Frank.Morgan@williams.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02356-9
Keywords: Hexagonal honeycomb, bees, perimeter-minimizing, isoperimetric
Received by editor(s): November 5, 1996
Published electronically: January 26, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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