The math bees

A honeycomb is a structure formed by hexagonal cells made with wax. These share common walls and are built by bees to contain their larvae and deposit pollen and honey, which they themselves make, inside the hive. The bees seek to obtain a honeycomb form that is the most economical possible, that presents the largest volume for the smallest portion of material used. But, why do bees choose this hexagonal form? If the honeycomb cells were square they would optimize the space, but these living beings undergo a metamorphosis and need an adequate space for their new anatomy.

If the cells were cylindrical they would be perfect but the amount of wax used would not benefit them.

However, bees have a natural intuition that tells them that the most effective figure is the hexagon. This allows a distribution or lace such that it does not give rise to useless spaces, because all the faces of the hexagons of the honeycomb are joined to each other, with the maximum use of space. Maraldi, an astronomer at the Paris observatory, studied and measured the cells of the honeycomb, finding that they are approximately equal to each other. He measured the angles of the cells of a honeycomb, calculating with absolute precision the angles of that diamond and discovered 109º 28 'for the obtuse angle and 700º 32' for the acute angle.

"Las abejas..., en virtud de una cierta intuición geométrica..., saben que el hexágono es mayor que el cuadrado y que el triángulo, y que podrá contener más miel con el mismo gasto de material."

 Pappus de Alejandría.