Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Hexagonal Honeycomb Conjecture


Author: Frank Morgan
Journal: Trans. Amer. Math. Soc. 351 (1999), 1753-1763
MSC (1991): Primary 52A38, 49Q20, 28A75
Published electronically: January 26, 1999
MathSciNet review: 1615934
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 52A38, 49Q20, 28A75

Retrieve articles in all journals with MSC (1991): 52A38, 49Q20, 28A75


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02356-9
PII: S 0002-9947(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