Honeycomb

From TheBestLinks.com

A honeycomb is a mass of hexagonal wax cells built by honeybees in their nests to contain their larvae and stores of honey and pollen. The term is also used for manmade materials that resemble it in appearance or structure.

Honeycomb is essentially the furniture in the bees' home. Beekeepers may remove the entire honeycomb to harvest honey. The honey is removed from the comb by uncapping and extracting in a centrifugal machine. Fresh, new comb is sometimes sold and used intact as "comb honey", especially if the honey is being spread on bread rather than used in cooking or to sweeten tea. Some believe that this benefits one's physical and mental health.

Broodcomb becomes dark over time, because of the cocoons embedded in the cells and the tracking of many feet. Honeycomb in the "supers" that is not allowed to be used for brood stays light colored.

Honeycomb geometry

The axes of honeycomb cells are always horizontal, and the non-angled rows of honeycomb cells are always horizontally (not vertically) aligned. Thus, each cell has two vertical walls, with "floors" and "ceilings" composed of two angled walls.

The reason that honeycomb is composed of hexagons, rather than any other shape, is that the hexagon tiles the plane with minimal perimeter per piece area. Thus a hexagonal structure uses the least material to create a lattice of cells with a given volume. It is likely that the honeybee constructs the honeycomb based on instinct, and the prevailing theory of biology is that the appearance of such efficient shapes in nature is a result of natural selection.

The closed ends of the honeycomb cells are also an example of geometric efficiency, albeit three-dimensional and little-noticed. The ends are trihedral (i.e., composed of three planes) pyramidal in shape, with the dihedral angles of all adjacent surfaces measuring 120°, the angle that minimizes surface area for a given volume. (The angle formed by the edges at the pyramidal apex is approximately 109° 28' 16" (= 180° - arccos(1/3)).)

A computer-generated model of a honeycomb cell, showing a hexagonal tube terminating in three equal rhombuses that meet at a point on the axis of the cell

The three-dimensional geometry of a honeycomb cell.

The shape of the cells is such that two opposing honeycomb layers nest into each other, with each facet of the closed ends being shared by opposing cells.

A computer-generated model of two opposing honeycomb layers, showing three cells on one layer fitting together with three cells on the opposing layer

Opposing layers of honeycomb cells fit together.

In 1965, L. Fejes Tóth discovered that the trihedral pyramidal shape (which is composed of three rhombuses) used by the honeybee is not the theoretically optimal three-dimensional geometry. A cell end composed of two hexagons and two smaller rhombuses would actually be .035% (or approximately 1 part per 2850) more efficient, but there may have been no viable evolutionary path leading to this geometry, or the minuscule difference in efficiency may not have been enough to justify the greater complexity.

References

Thompson, D'Arcy Wentworth (1942). On Growth and Form. Dover Publications. ISBN 0-486-67135-6.
"The Mathematics of the Honeycomb" (June 1985). Science Digest, pp. 74-77.

Honeycomb or cinder toffee is also the name of a kind of confectionery, which somewhat resembles a honeycomb. In New Zealand it is known instead as Hokey Pokey. It is a kind of crunchy toffee made of sugar, honey or golden syrup, butter (optional) and water, and contains gas bubbles made by adding vinegar and bicarbonate of soda.

--- Honeycomb is also a cereal that is made by Post.

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