An avian nest box in North Mountain Park (Ashland OR) was taken over by a colony of bees. Although the creators of these honeycombs were not to be found, by elimination I assume the combs were constructed by one of the honeybee or Apis species, since they are made of wax. Additionally, other bees are solitary and live in wood, under the ground or other habitat. Bumble bees, also social species that live in colonies, construct their nest under the ground. The elegant wax honeycomb shapes piqued my curiosity.
Pappus of Alexandria, a Fourth Century geometer, suggested that the repeating pattern of six-sided cells is the most efficient geometric form for honey storage, requiring the least amount of wax to store the most honey. Pappus’ “guess” became known as the Honeycomb Conjecture and resisted all attempts at a mathematical proof.
In 1999 Thomas Hales at the University of Michigan finally produced a nineteen page paper filled with advanced mathematics that finally showed that the honeycomb pattern was indeed the most efficient design for honey storage.
A special class of worker bees forms flakes of wax on their abdomens. These “builder” bees take the wax from their abdomens, knead and chew it to make it soft then apply it in layers around themselves to form the characteristic six-sided cells. I was surprised to learn that when the cells are initially constructed they are round in cross section. Heat from the bodies of the construction workers softens the wax to 45° C (about 113° F). As the cells cool the wax gets pulled into their hexagonal shape by surface tension at the joints where the walls meet. The “heater” or construction bees are specialized to warm the wax. Other bees in the hive do not raise the temperature in the hive above its normal temperature of about 35° C (95° F). Bhushan Karihaloo (University of Cardiff, UK) demonstrated in 2013 that the honeycomb cells begin round in cross section.
Ignoring the science and mathematics, honeycombs with their staggered layers of hexagonal cells are amazing feats of architecture.