How do the bees a perfect hexagon?

"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. 

 

According to Pappus , bees , by geometric intuition , know that of the three regular shapes ( hexagon, square, triangle ) the hexagon is the most efficient way to store honey figure. It can be shown mathematically that the hexagon , given the three indeed is the perfect figure to make this work , but how can bees tell? You might think you have some natural intuition for geometry , however this is not what happens in reality. Bees, with some help from the laws of physics , construct hexagonal honeycombs not because it is the most effective way to store their honey , among other things, use that figure because they can not build another .The circular and spherical forms are abundant in nature , we can see flowers, fruits , celestial bodies, among many other things that take such forms , on the other hand it is difficult, if not impossible, to find in the objects nature or living organisms take forms perfectly square or triangular .
A little help from the physical lawsAs already mentioned , the bees do not know that , among the three evaluated , the hexagon is the perfect way for the construction of the cells that make up the honeycomb, if we seek efficient ways the circle would be the perfect form , the form that is bees just built, but do not because the most efficient way for your purposes , because it is erected one of the most easy to make shapes . .If the bees do not build hexagons how can we explain the hexagonal shapes of the cells in the right figure ?

The laws of physics provide the answer , the bees build their cells of circular shape. Being each other together and found the wax in a state midfluid while bees rotate about a fixed point for shaping the cell adhesion force , cause the cells ( circles) adopt the hexagonal shape

Since the material used by the wasps to build their nests is less semifluid the wax that bees use the cells of the combs of the first hexagonal often less than the bees