Abstract

A close examination of a honeybee hive reveals a structure which is much more complicated than one would expect. Moreover, a simple analysis shows that the observed angle of the honeycomb hexagon cells is consistent with a minimum of surface area per constant volume. The angle turns out to appear at other seemingly unrelated fields, such as problems of minimal packing, and soap bubble surfaces. The present paper treats the mathematical problem of the hexagon cells, and gives a brief overview of the rich history of this problem. The physical and/or biological "motivation" of the complex geometric structure of the honeybee hive is investigated. It is suggested that the surface is not a minimal surface, and therefore biological 'saving' considerations can be ruled out. Alternative mechanisms are suggested, and further research suggestions are offered.

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