When you think of beehive, your first thought may be of honey oozing out of the iconic hexagonal cells. Remarkable as the honey may be, though, the cells themselves are just as interesting. The hexagons, shaped so because they perfectly balance an efficient use of resources and structural stability, are where female workers rear and tend the offspring produced by the queen.
If the colony was made only of workers, each hexagon would be identical, but, as the colony grows, they begin to invest into reproductives, such as drones, the male bees. Males are larger than workers, and so they require a larger hexagon in which to grow. However, if you try to connect a larger hexagon to a smaller one, there will be gaps. This could create an unstable structure or force the bees to fill those gaps with additional wax, wasting precious resources.
Scientists, though, have discovered that bees and wasps have figured out a mathematically sound response to this problem. Using a semi-automated image processing software, the scientists measured over 22,000 cells, and noticed that what other studies has assumed were random, misshapen cells were actually regular pairings of a pentagonal with a heptagonal cell. Whenever the insects transitioned from worker cells to reproductive ones, they switched to this unique pair of non-hexagonal cells. When placed together, the two shapes, just like two hexagons, have 10 open sides, meaning they won’t disrupt the pattern. This allows the bees and wasps to transition into making larger hexagonal cells without wasting precious resources. The scientists say that this solution is a nearly perfect mathematical solution to the bees’ conundrum!