The Miraculous Space Efficiency of Hexagons

Slate/Science   July 22, 2016

Hexagons and the Science of Packing

By Marc Chamberland

Excerpted from Single Digits: In Praise of Small Numbers by Marc Chamberland. Out now from Princeton University Press.

What do grocers and honeybees have in common? The obvious answer is that they are both adept at providing food for others. But there is a richer, more technical answer to this question: These two groups know how to efficiently pack their resources.

Honeycombs, made from the wax secreted by bees, are used to store honey, pollen, and larvae. For thousands of years, the honeycomb’s hexagonal structure has been noted and admired. It is wondered whether this entomological architecture inspired the interior ribbing and hidden chambers in the dome of the Pantheon in Rome. Today honeycomb structures have numerous engineering and scientific applications, including in the aerospace industry.

Why do honeycombs have a hexagonal structure? Pappus of Alexandria declared that bees “possessed a divine sense of symmetry,” and Charles Darwin described the honeycomb as a masterpiece of engineering that is “absolutely perfect in economizing labor and wax.” A mathematical rationale was given by the Polish polymath Jan Brożek (1585–1652): The hexagon tiles the plane with minimal boundary. Stated another way, Brożek conjectured that the optimal way to cover a large region with shapes of the same area while minimizing the boundary is to use the hexagonal structure. This problem resisted a solution for centuries but was finally positively settled by Thomas Hales in 1998.

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Cleaning Honeycombs with Ozone

ARS: News & Events   March 2014

Sometimes, even honey bees need help with “housekeeping”—especially when it comes to tidying up their combs once the honey’s been removed. Research by Agricultural Research Service scientists has shown that fumigating combs with ozone gas can eliminate pests and pathogens that threaten honey bee health and productivity. Recent results suggest that ozone fumigation may also help reduce pesticide levels in combs.

The findings stem from a two-part study led by Rosalind James, an entomologist in ARS’s Pollinating Insect—Biology, Management, and Systematics Research Unit in Logan, Utah. Results from the first part of her team’s study, published in 2011 in the Journal of Economic Entomology, demonstrated that fumigating combs with ozone gas...

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http://www.ars.usda.gov/is/AR/archive/mar14/honeycombs0314.htm

Secret of Bees' Honeycomb Revealed

The Nation   7/23/13

PARIS, France: For thousands of years, thinkers have marvelled at the feat of engineering that is the honeycomb.Each waxy cell is a perfect hexagon, its six wafer-thin sides providing not only strength to the honeycomb structure but also the smartest way to store honey.

“By virtue of a certain geometrical forethought... (bees) know that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material in constructing each,” wrote a 4th-century Greek geometer, Pappus of Alexandria.

For Charles Darwin, the honeycomb was “absolutely perfect in economising labour and wax.”
But how do bees do it?

The answer, according to a new study, is that the cells do not start out as hexagons but as circles.
They gradually form into hexagons by a subtle flow of the wax, which is turned semi-molten by the heat from a special class of worker bee.

The solution is proposed by a trio of scientists in Britain and China, led by Bhushan Karihaloo of Cardiff University.–AFP