Honeybees and the Hexagon

hexagon and honeycomb Near perfect symmetry!

How honeybees came to be mathematicians.

The home of a honeybee is a palace of gold.  Wall to wall, honey gleams through the hive, casting with it the aroma of sweet earth, the nectar of two million flowers, and fresh warm beeswax.  Architecturally, a beehive’s perfect repeating hexagonal pattern is constructed more precisely than any human could ever dream of creating without the assistance of advanced technology.  How do these small little insects, with brains the size of a crumb, know how to create such perfectly symmetrical shapes?  Why did they decide to create the honeycomb out of hexagons?  These are 2,000-year-old questions that have only recently been answered.  I should also add that even though the actual brain size of the honeybee is quite small, the neural density per micrometer of honeybee brain tissue is greater than any other animal on Earth!

hexagon and honeycomb. A cross-section of freshly cut honeycomb. Notice the granules of bee pollen.

Why the hexagon?

Honeycomb, made of beeswax, is a tessellation of tiny hexagons which is used to store honey, larvae, and pollen.  This is their home; where the queen lays all of her eggs, workers raise and care for the brood, and the foragers bring in all of the colony's food resources collected from various nearby plants.  A hexagon is a six-sided shape (think of a stop sign) not as commonly seen in our daily lives as say the square, circle, or the triangle. Each of the six angles of the hexagon is 120º for a total of 720º.  Why did the honeybees choose to employ such a complex shape? Wouldn’t a square or a triangle be more efficient for them? Square cells seem like they would be much easier to build, stack and organize. But, the answer is no, and honeybees have developed their design strategy like tiny master craftsmen. As it turns out, the hexagon is the most efficient of all shapes and they actually gain strength under compression.

Producing beeswax is a lot of work and requires huge amounts of energy. The honeybees collectively have to consume six pounds of honey to generate one pound of beeswax. That's a tough ratio no matter how you look at it! For this reason, honeybees had to figure out (over millions of years) how to store the greatest amount of honey using the least amount of beeswax possible.  This is called the “Honeybee Conjecture” which was confirmed in 1999 by mathematician Thomas Hales.  Hales, through a mathematical proof, found the hexagon to have the greatest surface area while covering the smallest distance (in comparison to all other shapes).

Alan Lightman writes in his essay The Symmetrical Universe, “If we think of nature as a vast ongoing experiment, constantly trying out different possibilities of design, then those designs that cost the least energy or that require the fewest different parts to come together at the right time will take precedence”.  This principle of Lightman’s is true not only for humankind but even the smallest of insects.  It continues to amaze me the various roles a honeybee plays in her short life.  She pollinates, makes honey, makes beeswax, is a nurse, a master of navigation, an exquisite communicator, a fierce warrior, and  now we can add mathematician and engineer to that amazing list!  It's funny, the more I learn about honeybees, the more I want to know!

For an up close and personal view (and taste) of this amazing structure try one of our delicious raw honeycomb varieties!

Submitted By: Rayne MacPhee