References & Sources

The Honeycomb Conjecture

Proving mathematically that honeybee constructors are on the right track

A hexagonal grid represents the best way to divide a flat surface into regions of equal area with the least total perimeter.

References:

Hales, T.C. Preprint. The honeycomb conjecture. Available at http://xxx.lanl.gov/abs/math.MG/9906042.

Morgan, F. 1999. The hexagonal honeycomb conjecture. Transactions of the American Mathematical Society 351(May):1753.

Further Readings:

Ball, P. 1999. The Self-Made Tapestry: Pattern Formation in Nature. Oxford, England: Oxford University Press.

Bleicher, M.N., and L.F. Toth. 1965. Two-dimensional honeycombs. American Mathematical Monthly 72(November):969.

Morgan, F. 1999. Hales proves hexagonal honeycomb conjecture. Available at http://www.maa.org/features/mathchat/mathchat_6_17_99.html.

Peterson, I. 1998. Cracking Kepler’s sphere-packing problem. Science News 154(Aug. 15):103.

______. 1995. Toil and trouble over double bubbles. Science News 148(Aug. 12):101.

______. 1994. Constructing a stingy scaffolding for foam. Science News 145(March 5):149.

Thompson, D.W. 1952. On Growth and Form. Cambridge, England: Cambridge University Press.

Tóth, L.F. 1964. What the bees know and what they do not know. Bulletin of the American Mathematical Society 70(July):468.

Weaire, D., and R. Phelan. 1994. Optimal design of honeycombs. Nature 367(Jan. 13):123.

Sources:

Thomas C. Hales
University of Michigan
Department of Mathematics
Ann Arbor, MI 48109
Web site: http://www.math.lsa.umich.edu/~hales

Frank Morgan
Williams College
Department of Mathematics
Williamstown, MA 01267
Web site: http://www.williams.edu/Mathematics/fmorgan

John M. Sullivan
University of Illinois at Urbana-Champaign
Department of Mathematics
1409 W. Green Street
Urbana, IL 61801-2975
Web site: http://www.math.uiuc.edu/~jms/narrative.html

Denis Weaire
Trinity College Dublin
Department of Pure and Applied Physics
Dublin 2
Ireland
Web site: http://www2.tcd.ie/Physics/People/Denis.Weaire/foams/index.html

From Science News, Vol. 156, No. 4, July 24, 1999, p. 60. Copyright © 1999, Science Service.