Marvelous Engineering !
|[Note Guidelines] Photographer's Note|
|Clicked this honey loaded honeycomb (partly broken due to weight) hanging on roadside cliff near Panchgani while descending down towards Pune.|
A honeycomb is a mass of hexagonal wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen.
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 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 bubbles. 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-dimensional and little-noticed. The ends are trihedral (i.e., composed of three planes) sections of rhombic dodecahedra, 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)).)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.
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 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.
1. Graham, Joe. The Hive and the Honey Bee. Hamilton/IL: Dadant & Sons; 1992; ISBN.
2. Thompson, D'Arcy Wentworth (1942). On Growth and Form. Dover Publications. ISBN.
ramthakur, NinaM, oanaotilia, haraprasan, eng55, CeltickRanger, gannu, peter_stoeckl has marked this note useful
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Yes, it is a coincidence. You too have posted a Honeycomb today, but without Bees on it. Apparently, it is an abandoned one.
You have handled the light very effectively in this shot. The Comb has a natural look to it and the details on it are very sharp and clear.
Well done and TFS.
Looks like this colony was invaded by uninvited guests called the moths. If you observe closely you can see the X mark on the comb and so the bees leave their priceless possession and disappear. tfs.
- [2009-03-19 7:13]
very fortunate to find one like this, good image, hope you got a real closeup of those honeycomb structure. tfs.
- [2009-03-19 7:25]
Oh, I can feel the was and sweet honey crackling under my teeth, wow. This is beautiful and so interesting, along with the great notes, Thank you, a great find to photograph and post on TN,
- [2009-03-19 7:49]
Nice capture of a honeycomb well seen against the dark BG with good sharpness and lighting.
Yes, a marvel of engineering! It seems the hexagonal shape of the cells follows the hexagonal shape of each compound eye of the bee.
Thanks and best regards,
Ah, with this picture you opened my appetite. Indeed, these are engineering masterpiece, well showed in this picture. Thanks for sharing this.
Hi Mr. Subhash,
A nice capture of this honey comb full of honey. Excellent shot with good details and composition. Thanks a lot for sharing.
- [2009-03-19 11:11]
It's realy great engineering.Well caught,framed and composed.Excellent note too!
Thanks for posting.
excellent photo of the honeycomb, fine POV,
excellent focus on it, excellent sharpness and details,
- [2009-03-20 8:18]
very beautiful information doctor. Excellent view and lovely composition. Ganesh
interesting documentation coming with very thoughtful words on "ideal" geometry. Thank you for this fine contribution of high educational value.
With best regards,