The bees cluster in large numbers, maintaining a hive temperature of 35 C, which keeps the wax firm but malleable during cell construction. This energetic, piecemeal activity produces a strong, remarkably precise structure. Each wax partition, less than 0.1 millimeter thick, is fashioned to a tolerance of 0.002 mm. Moreover, the cell walls all stand at the correct 120 angle with respect to one another to form a lattice of regular hexagons. Observers throughout recorded history have marveled at the hexagonal pattern of the honeybee's elaborate storage system.
Biologists assume that bees minimize the amount of wax they use to build their combs.
Mathematician Thomas C. Hales of the University of Michigan at Ann Arbor has now formulated a proof of the so-called honeycomb conjecture, which holds that a hexagonal grid represents the best way to divide a surface into regions of equal area with the least total perimeter. In his mathematical analysis, he focused on the hexagonal arrangement of cells. Although honeycomb cells are three-dimensional structures, each cell is uniform in the direction perpendicular to its base. Hence, its hexagonal cross section matters more than other factors in calculating how much wax it takes to construct a comb. Mathematicians of ancient Greece asked what choices bees might have if they wanted to divide a flat surface into identical, equal-sided cells.