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Natural Hexagons

Honeybee’s Pursuit of Perfection and Revered Mystery

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Abstract

The absolute perfection with which honeybees construct their hexagonal comb cells has astonished human beings since ancient times. The deep mystery is not why hexagons, but how such a perfect geometrical shape is fabricated, without any geometrical portrait or tools. Do they possess divine intelligence? Recent studies shed light on this revered mystery and show beyond doubt that it is the thermo-mechanical properties of beeswax and the knitting mechanism of bees that remould fresh circular cells into rounded hexagonal shape. How does this remoulding happen? In this article, we describe the inner mechanism involved in such spontaneous transformation of shapes, and explore the hidden mystery behind honeybee’s architecture.

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Suggested Reading

  1. R H Hepburn, Honeybees and Wax: An experimental natural history, Springer-Verlag, Berlin (1986).

  2. H R Hepburn and S P Kurstjens, The combs of honeybees as composite materials, Apidologie, Vol.19, 25, 1988.

    Article  Google Scholar 

  3. T C Hales, Cannonballs and honeycombs, Notices of the AMS, Vol.47, 440, 2000.

    Google Scholar 

  4. E G Klarreich, Foams and honeycombs, Am. Sci. 88, 152 (2000).

    Article  Google Scholar 

  5. T C Hales, The honeycomb conjecture, Discrete Comput. Geom., Vol.25, PP.1–22, 2001.

    Article  Google Scholar 

  6. George G Szpiro, Kepler’s Conjecture, John Wiley & Sons, New Jersey (2003).

    Google Scholar 

  7. R Buchwald, M D. Breed, and A R Greenberg, The thermal properties of beeswaxes: unexpected findings, J. Exp. Biol., Vol.211, No.121, 2008.

  8. S P. Kurstjens, H R Hepburn, F R L Schoening and B C. Davidson, The conversion of wax scales into comb wax by African honeybees, J. Comp. Physiol. B, Vol.156, No.95, 1985.

  9. D F Siemens Jr, Of bees and mathematicians, The Mathematics Teacher, Vol.60, PP.758–761, 1967.

    Article  Google Scholar 

  10. B L Karihaloo, K Zhang and J Wang, Honeybee combs: how the circular cells transform into rounded hexagons, J. R. Soc. Interface, Vol.10, p.20130299, 2013.

    Article  Google Scholar 

  11. F Nazzi, The hexagonal shape of the honeycomb cells depends on the construction behavior of bees, Sci. Rep., Vol.6, p.28341, 2016.

    Article  Google Scholar 

  12. D Talukdar and K Dutta, A simplified thermomechanical approach to visualize hexagonal honeycomb construction, SN Applied Science, Vol.1, p.1220, 2019.

    Article  Google Scholar 

  13. R Buchwald, A R Greenberg and M D Breed, A biomechanical perspective on beeswax, American Entomologist 51, 39, 2005.

    Article  Google Scholar 

  14. K Zhang, H L Duan, B L Karihaloo and J Wang, Hierarchical, multilayered cell walls reinforced by recycled silk cocoons enhance the structural integrity of honeybee combs, Proc. Natl Acad. Sci., USA Vol.107, 9502, 2010.

    Article  Google Scholar 

  15. C W W Pirk, H R Hepburn, S E Radloff and J Tautz, Honeybee combs: construction through a liquid equilibrium process? Naturwissenschaften, VVol.91, PP.350–353, 2004.

    Article  Google Scholar 

  16. A P Tulloch, Beeswax — composition and analysis, Bee World, Vol.61, 47, 1980.

    Article  Google Scholar 

  17. S P Kurstjens, E McClain, and H R Hepburn, The proteins of beeswax, Naturwissenschaften, Vol.77, 34, 1990.

    Article  Google Scholar 

  18. R Buchwald, M D Breed, L Bjostad, B E Hibbard and A R Greenberg, The role of fatty acids in the mechanical properties of beeswax, Apidologie, Vol.40, 585, 2009.

    Article  Google Scholar 

  19. S Sinaringati et al., The utilisation of paraffin and beeswax as heat energy storage in infant incubator, ARPN J. Eng. Appl. Sci., Vol.11, 800, 2016.

    Google Scholar 

  20. R G Craig, J D Eick and F A Peyton, Properties of natural waxes used in dentistry, J. dent. Res., Vol.44, 1308, 1965.

    Article  Google Scholar 

  21. M E Hossain et al., Experimental studies on physical and mechanical properties of natural and synthetic waxes using uniaxial compressive strength test, Proc. ICCST’09, 41–44246, 2009.

  22. R Buchwald, M D Breed, A R Greenberg and G Otis, Interspecific variation in beeswax as a biological construction material, J. Exp. Biol., Vol.209, p.3984, 2006.

    Article  Google Scholar 

  23. M. Kleinhenz et al., Hot bees in empty broodnest cells: heating from within, J. Exp. Bio., Vol.206, 4217, 2003.

    Article  Google Scholar 

  24. D Bauer and K Bienefeld, Hexagonal comb cells of honeybees are not produced via a liquid equilibrium process, Naturwissenschaften, Vol.100, 45, 2013.

    Article  Google Scholar 

  25. Elmer web pages: http://www.csc.fi/elmer/.

  26. R Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 2004.

    Google Scholar 

  27. T H Shellhammer, T R Rimsey, and J M Krochta, Viscoelastic properties of edible lipids, J. Food Eng., Vol.33, 305, 1997.

    Article  Google Scholar 

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Acknowledgement

The present article is published as a requirement of scientific social responsibility policy under the MATRICS scheme, granted by Science and Engineering Research Board (SERB), Govt. of India (Grant No. MTR/2019/000044).

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Correspondence to Kishore Dutta.

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Kishore Dutta is working in the Department of Physics, Handique Girls’ College, Guwahati. His research interests include nonlinear dynamics, critical phenomena in strongly correlated magnetic systems, quantitative social sciences, to name a few.

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Dutta, K. Natural Hexagons. Reson 26, 399–413 (2021). https://doi.org/10.1007/s12045-021-1138-8

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  • DOI: https://doi.org/10.1007/s12045-021-1138-8

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