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. |