Honeycomb Geometry .


Karunakar Rayker (CC BY 2.0)

Bees have encouraged mathematical speculation for two millennia, since classical scholars tried to explain the geometrically appealing shape of honeycombs. How do bees tackle complex problems that humans would express mathematically? In this series we’ll explore three situations where understanding the maths could help explain the uncanny instincts of bees.

Honeycomb geometry

Honeybees collect nectar from flowers and use it to produce honey, which they then store in honeycombs made of beeswax (in turn derived from honey). A question that has puzzled many inquiring minds across the ages is: why are honeycombs made of hexagonal cells?

The Roman scholar Varro, in his 1st century BC book-long poem De Agri Cultura (“On Agriculture”), briefly states

“Does not the chamber in the comb have six angles, the same number as the bee has feet? The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space1.”

This quote is the earliest known source suggesting a link between the hexagonal shape of the honeycomb and a mathematical property of the hexagon, made more explicit a few centuries later by Pappus of Alexandria (sometimes considered to be the last Ancient Greek mathematician). Writing after the Roman Empire’s glory days, Pappus points out that there are three regular polygons that tile the plane without gaps—triangles, squares and hexagons—and bees, in their wisdom, choose the design that holds the most honey given a set amount of building material2.

 

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