Bees and Math
“Bees…by virtue of a certain geometrical forethought…know that the hexagon is greater than the square and the triangle, and will hold more honey for the same expenditure of material. — Pappus of Alexandria
Bees have not studied tessellations theory. However, some of their behavior patterns can be explained mathematically. One such phenomena which mother nature instilled in the bee is the nature to use the least expenditure of energy and materials. The bees somehow know that the square, the triangle and the hexagon are the only three self-tessellating regular polygons. Of the three, the hexagon has the smallest perimeter for a given area. So, when bees are constructing hexagonal prism cells in the hive, they use less wax and do less work to enclose the same space than if tessellating space with prisms of square or triangular bases. The honeycomb walls are made up of cells which are 1/80 of an inch thick, yet can support 30 times their own weight. A honeycomb of 14.5”x8.8” can hold more than five pounds of honey. That also explains why they are so heavy. The bees are creating hexagonal prisms in three rhombic sections, and the walls of the cell meet at exactly 120 degree angles. What is even more amazing, is the fact that the bees work simultaneously on different sections forming a comb with no visible seams. It is built vertically downward, and the bees use parts of their bodies as measuring instruments. In fact, their heads act as plummets.”
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Click above to see some fun kids activities - one of which helps to illustrate why bees build hexagons via thedeltacs.com.