Bees as good at math as any other animal

Despite their reputation for honeycomb patterns, bees are not actually brilliant mathematicians.

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Note the similarities between the honeycomb and the film—perhaps nature is the mathematician after all.

Ella Whalen, Staff Writer

If there is one animal well known for being mathematical, it would be the honeybee. Their hives use the most efficient packing of shapes when comparing the area of a cell to its perimeter (i.e. the lowest perimeter of a given area of any tiling). The conjecture that proved that these hexagons were the most efficient (with math too complicated for a school newspaper) was even called the honeycomb conjecture! Surely, they must have some knowledge of geometry, right? Unfortunately, as with many things in nature, the bees do not really know mathematics, and their efficiency in building hives is more incidental than intentional.

Bees produce their wax through specialized glands that process the sugars from honey. The wax gets chewed by workers until it is soft and malleable, then gets added to cells. Initially, the cells are actually cylindrical, stacked in a staggered manner much like oranges at the grocery store. This pattern is still somewhat efficient, as circles have the best area-to-perimeter of any single shape, but stacking (or tessellating) them leaves gaps between the cells. As bees work inside the cells, they both press on the cells’ walls and heat them up, making them malleable again. Two bees in adjacent cells like this force the wall between them to be straight instead of curving as a circle. This pressure across the entire hive leads to the iconic hexagonal pattern.

A similar pattern can be seen in soap bubbles in a film—making straight lines wherever two bubbles come into contact. Since a bubble needs to be the minimal surface area for its volume, they tend to be spherical by themselves for the same reason bees start with cylinders. When bubbles collide in a film, they experience the same pressures as two bees pressing on opposite sides of a wall, and likewise form a straight line.

That is not to say that bees are as dumb as soap bubbles (or that there’s bubblebees out there constructing soap films for that matter). Wild bees choose the locations of their hives meticulously to protect them from the elements, and will just up and leave a location if they are unsatisfied (including bee farms). They also use a disinfectant collected from plant buds, propolis, on their legs before entering the hive, in a hive’s construction, and to embalm invaders so they do not decompose inside the hive and threaten the colony. They may be construction workers or epidemiologists, but they are not geometrists.