Honeycomb
58258
224759007
2008-07-10T08:32:20Z
79.41.125.51
/* External links */ added a new interesting link about the mathematics of the honeycomb
{{alternateuses}}
[[Image:Honey comb.jpg|thumb|Honeycomb]]
A '''honeycomb''' is a mass of [[hexagon]]al [[wax]] cells built by [[honey bee]]s in their nests to contain their [[larva|larvae]] and stores of [[honey]] and [[pollen]].
[[beekeeping|Beekeepers]] may remove the entire honeycomb to harvest [[honey]]. Honey bees consume about 8.4 pounds of honey to secrete one pound of wax (Graham 1992), so it makes economic sense to return the wax to the hive after harvesting the honey, commonly called "pulling honey" or "robbing the bees" by beekeepers. The structure of the comb may be left basically intact when honey is extracted from it by uncapping and spinning in a centrifugal machine—the [[honey extractor]]. 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. Honeycomb is edible all by itself, and has been called "the beekeeper's lunch".
[[Brood (honeybee)|Brood]]comb becomes dark over time, because of the cocoons embedded in the cells and the tracking of many feet, called ''travel stain'' by beekeepers when seen on frames of [[comb honey]]. Honeycomb in the "[[honey super|super]]s" that are not allowed to be used for brood stays light coloured.
[[Image:Honeycomb-Process.png|thumb|left|The bees begin to build the comb from the top of each section. When filled with honey, the bees seal the cells with wax.]]
Numerous [[wasp]]s, especially [[polistinae]] and [[vespinae]], construct hexagonal prism packed combs made of paper instead of wax; and in some species (like ''[[Brachygastra mellifica]]''), honey is stored in the nest, thus technically forming a paper honeycomb. However, the term "honeycomb" is not often used for such structures.
==Honeycomb geometry==
[[Image:Apis_florea_nest_closeup2.jpg|thumbnail|270px|right|Close up of an abandoned ''[[Apis florea]]'' nest, [[Thailand]]. The hexagonal grid of wax cells on either side of the nest are slightly offset from each other. This increases the strength of the comb and reduces the amount of wax required to produce a robust structure.]]
The axes of honeycomb cells are always quasi-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 cells [[slope]] slightly upwards, between 9 and 14 degrees, towards the open ends.
There are two possible explanations for the reason that honeycomb is composed of hexagons, rather than any other shape. One, given by [[Jan Brożek]], is that the hexagon [[hexagonal tiling|tiles the plane]] with minimal [[surface area]]. Thus a hexagonal structure uses the least material to create a lattice of cells within a given [[volume]]. Another, given by [[D'Arcy Wentworth Thompson]], is that the shape simply results from the process of individual bees putting cells together: somewhat analogous to the boundary shapes created in a field of [[soap bubble]]s. In support of this he notes that queen cells, which are constructed singly, are irregular and lumpy with no apparent attempt at efficiency.
The closed ends of the honeycomb cells are also an example of geometric efficiency, albeit three-[[dimension]]al and little-noticed. The ends are trihedral (i.e., composed of three planes) [[pyramid (geometry)|pyramidal]] in shape, with the [[dihedral angle]]s 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)).)
<div style="text-align:center;">[[image:honeycomb cell 3d rot.png|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]]<br>''The three-dimensional geometry of a honeycomb cell.''</div>
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.
<div style="text-align:center;">[[image:honeycomb 3d rot.png|A computer-generated model of two opposing honeycomb layers, showing three cells on one layer fitting together with three cells on the opposing layer]]<br>''Opposing layers of honeycomb cells fit together.''</div>
[[Image:Honeycomb_on_tree.jpg|thumb|right|350px|Honeycomb of the Giant honey bee ''[[Apis dorsata]]'' on a tree in Srirangapatnna near [[Bangalore]]]]
Individual cells do not, of course, show this geometric perfection: in a regular comb, there are deviations of a few [[percent]] from the "perfect" hexagonal shape. In transition zones between the larger cells of drone comb and the smaller cells of worker comb, or when the bees encounter obstacles, the shapes are often distorted.
In 1965, [[László Fejes Tóth]] discovered that the trihedral pyramidal shape (which is composed of three [[rhombus|rhombi]]) 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. This difference is too minute to measure on an actual honeycomb, and irrelevant to the hive economy in terms of efficient use of wax, considering that wild comb varies considerably from any mathematical notion of "ideal" geometry.
==References==
{{Nofootnotes|date=February 2008}}
*Graham, Joe. The Hive and the Honey Bee. Hamilton/IL: Dadant & Sons; 1992; ISBN
*Thompson, D'Arcy Wentworth (1942). ''On Growth and Form''. Dover Publications. ISBN.
*"The [[Mathematics]] of the Honeycomb" (June 1985). ''Science Digest'', pp. 74-77.
*"The Royal Institution of Great Britain Christmas Lectures"
==External links==
*[http://www.archimedes-lab.org/monthly_puzzles_72.html The solved angular puzzle of the honeycombs' cells]
*[http://www.b-visible.co.uk/article/honeycombe.html Honeycomb article]
[[Category:Beekeeping]]
[[Category:Bees]]
[[Category:Elementary geometry]]
[[Category:Entomology]]
[[de:Bienenwabe]]
[[es:Panal]]
[[fr:Alvéole d'abeille]]
[[io:Alveolo]]
[[it:Favo]]
[[ja:ハニカム構造]]
[[sw:Sega]]
[[nl:Bijenraat]]
[[pl:Plaster (pszczelarstwo)]]
[[ru:Пчелиные соты]]
[[simple:Honeycomb]]
[[tr:Petek]]
[[zh:蜂巢]]