The first recollection I have of the hives as they were opened was the organisation of the comb into regular hexagonal cells, showing a repeating, symmetrical mathematical pattern. Such a pattern could be equally well achieved by cells based on the equilateral triangle or square.

So why the hexagon?

By comparing the area enclosed by these regular shapes, each with a perimeter of one unit, it is possible to see why the hexagon is the most efficient.

Area of a single cell (square units)

equilateral triangle

0.048

square

0.063

hexagon

0.075


Considering that for each gram of wax produced the bee needs to consume 6 - 7 grams of honey, it is to the bees' advantage that the shape providing the maximum area has the minimum expenditure of materials and energy.

Engineers will confirm that a hexagonal structure also provides the maximum strength. Although the wax cell walls may be only about 0.05mm thick, each cell can support 25 times its own weight.

Mathematicians are still conjecturing as to whether in fact bees have hit on the optimum honeycomb. A bee's honeycomb cell has an hexagonal cross-section but the bottom of the cell consists of 3 equal rhombi. Considering this three dimensional shape, the Hungarian mathematician Fejes Tóth has formulated the "isoperimetric problem for honeycombs" to determine what dimensions would actually yield the "optimal design". Although a definitive solution has not been reached, it has been shown that the bees' design is close to but not quite the optimal one.

If accessed directly, this page should be viewed as part of the series starting here.

Micscape Magazine September 1998.



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