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.
One of the most detailed discussions of living things is Karl von Frisch’s book Dance Language and Orientation of Bees. Von Frisch spent 40 years studying how bees communicate to other bees information about pollen sources. He referred to the honeycomb as a dance floor and described the bee making a “waggle dance” which gave other bees information where to find nectar. The bee dance indicates the direction to this food source and an alteration of the shape of the dance indicates the distance to the source. If the food source was close, the bee uses a round dance instead of the waggle dance. Von Frisch’s study catalogs what the bee does, but it doesn’t tell you how the bee does it.
Barbara Shipman is a mathematician with an interest in bees. There is a mathematical concept known as “manifolds.” Manifolds can have two dimensions, but they can have an infinite number of dimensions. One type of manifold called the “flag manifold” has six dimensions. As Shipman worked with flag manifolds, she saw patterns that were similar to the patterns of the waggle dance of the bees. Physicists use flag manifolds in dealing with subatomic particles called quarks which are the building blocks of protons and neutrons. Shipman believes that bees are sensitive to quarks and the sensitivity appears to be a reaction to a quantum field acting on the membranes of selected cells in the bees. It has been demonstrated that bees are sensitive to Earth’s magnetic field and the polarization of sunlight. Shipman is seeking to add the dimension of quantum fields to the bee’s repertoire of tools for location and communication.