Abstract
Geometrical investigations of honeycombs and speculations on how honeybees measure and construct the hexagons and rhombi of their cells are centuries old. Here we show that honeybees neither have to measure nor construct the highly regular structures of a honeycomb, and that the observed pattern of combs can be parsimoniously explained by wax flowing in liquid equilibrium. The structure of the combs of honeybees results from wax as a thermoplastic building medium, which softens and hardens as a result of increasing and decreasing temperatures. It flows among an array of transient, close-packed cylinders which are actually the self-heated honeybees themselves. The three apparent rhomboids forming the base of each cell do not exist but arise as optical artefacts from looking through semi-transparent combs.
References
Bartholin E (1660) De Figure Nivis. In: Georgi Gordiani (1674) De Naturae Mirabilibus, Quaestiones Academicae. Hafniae
Bénard H (1900) Les tourbillons cellulaires dans une nappe liquide. Rev Gen Sci 12:1261–1271, 1309–1328
Boltzmann L (1905) Populäre Schriften. Barth, Leipzig, Germany
Bonanni APP (1681) Ricreatione dell’occhio e della mente, nell’ Osservatione delle Chiocciole. Rome
Bujok B, Kleinhenz M, Fuchs S, Tautz J (2002) Hot spots in the bee hive. Naturwissenschaften 89:299–301
Darchen R (1959) Un des rôles des chaînes d’abeilles: la torsion des rayons pour les rendre parallèles entre eux. Ann Abeilles (Paris) 2:193–209
Fröhlich B (2000) Wachse der Honigbiene Apis mellifera carnica Pollm.: chemische und physikalische Unterschiede und deren Bedeutung für die Biene. PhD thesis, Beegroup, Universität Würzburg, Germany
Hales TC (2000) Cannonballs and honeycombs. Not AMS 47:440–449
Hepburn HR (1986) Honeybees and wax: an experimental natural history. Springer, Berlin Heidelberg New York
Hepburn HR, Kurstjens SP (1988) The combs of honeybees as composite materials. Apidologie 19:25–36
Hepburn HR, Muller WJ (1988) Wax secretion in honeybees: thermal integrity of the festoon. Naturwissenschaften 75:628–629
Hunter J (1792) Observations on bees. Philos Trans R Soc 82:128–196
Kepler J (1611) De Nive Sexangula (see Aiton EJ, Duncan AM, Field JV (1997) The harmony of the world. American Philosophical Society, Philadelphia)
Lau D (1959) Beobachtungen und Experimente über die Entstehung der Bienenwabe (Apis mellifica L.). Zool Beitrag 4:233–306
Leduc S (1911) The mechanism of life. Rebman, London
Martin H, Lindauer M (1966) Sinnesphysiologische Leistungen beim Wabenbau der Honigbiene. Z Vergl Physiol 53:372–404
Müllenhof K (1883) Über die Entstehung der Bienenzellen. Pfluegers Arch 32:589–618
Remnant RA (1637) Discourse or historie of bees. Young, London
Thomson J (1881–1882) On a changing tessellated structure in certain liquids. Proc Glasgow Philos Soc
Thompson DW (1917) On growth and form. Cambridge University Press, Cambridge
Tóth F (1964) What the bees know and what they do not know. Bull Am Math Soc 70:468–481
Vogt H (1911) Geometrie und Ökonomie der Bienenzelle. Trewend Granier, Breslau, Germany
Waterhouse GR (1864) On the formation of the cells of bees and wasps. Trans Entomol Soc. Lond Ser III 2:115–129
Weaire D, Phelan R (1994) Optimal design of honeycombs. Nature 367:123
Acknowledgements
We thank H. Kragh (Denmark), T. Seeley (USA), E. Rademacher (Germany) and S. Ripley (South Africa) for constructive suggestions, Strahl & Pitsch (USA) for the gift of waxes and C. Hepburn (South Africa) for technical assistance. Financial support came from the Deutsche Forschungsgemeinschaft (GK 200 to C.W.W.P., SFB 554 to J.T.). The experiments performed comply with the current laws of Germany and South Africa.
Author information
Authors and Affiliations
Corresponding author
Electronic Supplementary Material
Rights and permissions
About this article
Cite this article
Pirk, C.W.W., Hepburn, H.R., Radloff, S.E. et al. Honeybee combs: construction through a liquid equilibrium process?. Naturwissenschaften 91, 350–353 (2004). https://doi.org/10.1007/s00114-004-0539-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00114-004-0539-3