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

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.

If you are totally fascinated with mother nature’s
creations, that is not all. The honeybee’s ability to navigate is
influenced by its built-in “compass.” As it turns out, the bees’
orientation is influenced by the Earth’s magnetic field. They can detect
minute fluctuations in the Earth’s magnetic field which are only
discernible to sensitive magnetometers. This explains why bees can build
a new hive starting form different parts of the new area without any
bee directing them. All the bees orient their new comb in the same
direction as their old hive. Bees build the cell walls with a slope of
13′ to make sure that the honey should not be running out before the
tops are capped with wax domes. The honeybee gets its mathematical
training via its genetic codes.

read original article The  Honey Bee