**Bees are master engineers of the storing of dense fluids.** Their fluid is honey, and they store it in a way that shows excellent honeybee engineering.

Worker bees gorge on honey and excrete slivers of wax. Other workers take that wax and position and mold it into a column of six-sided cells. The bees cluster to keep the temperature of the wax at 35 degrees C (95 degrees F) so that it’s firm but malleable. Each wax partition is less than .1 mm thick with a tolerance of .002 mm. The cell walls must be at a 120-degree angle in relation to each other to make a lattice of regular hexagons.

**There are only three regular polygons which pack together snugly without leaving gaps–equilateral triangles, squares, and regular hexagons.** The perimeter of a hexagonal cell that encloses an area is less than that of a square or a triangular cell making it the most economical shape. Using the same quantity of wax, hexagonal cells can hold more honey than square or triangular cells. Mathematicians have tried other options, such as using curved sides or a mixture of polygons. They have confirmed that curved polygons could not do as well as straight-line hexagons. **Mathematicians can’t beat honeybee engineering.**

**How do the bees keep the honey in the cells?** They tip the cells upward at an angle of 13 degrees from the horizontal. That is precisely the angle needed to stop the honey from dripping out. There is one more problem. How can the bees seal off the bottom of the columns? A flat bottom would not do. Bees construct the base with three, four-sided diamond shapes that meet in a point. Two rows of cells are placed back-to-back and offset so that they interlock. With the cells backing up each other, only one layer of wax acts as the bottom for both cells. Mathematicians have proven that the angles of the diamond-shaped cell bottoms (109.5 and 70.5 degrees) give the maximum volume for storage.

It’s difficult to believe that the honeycomb structure is an accident or the final product of trial and error. **Mistakes are usually lethal or at least result in a loss of vital energy resources.** Honeybee engineering has fascinated and amazed philosophers and mathematicians since the time of ancient Greece. We think the honeybee engineers learned the principles of structural math from the Master Engineer.

–John N. Clayton and Roland Earnst © 2018