Why Do Bees Make Their Honeycombs Hexagonal?
Social animal breeds, such as bees and ants, really have amazing abilities. Most of the time, thanks to their brains, which are quite large compared to their body size, they can handle serious and surprising tasks that are not expected of them. Perhaps the most interesting of these are the cells that bees use in their honeycombs and their architecture. We want to talk about this through Darwin:
Darwin knew before publishing The Origin of Species in 1859 that if he was going to announce such a theory, the theory should also be able to answer such seemingly detailed but important questions: If everything in general is evolving from simple to complex, how can bees build their honeycombs in the hexagonal and most efficient way known so far? What are the previous steps? Do all bees build hexagonal nests?
Darwin conducted numerous studies on this subject in his house, called Down House. Until the time of Darwin, scientists thought that all bees built hexagonal cells. Lord Brougham, one of the respected biologists of the time, suggested that no bee had a honeycomb structure other than a hexagon in order to Decry Darwin’s Theory of Evolution, and therefore bees had never undergone such an evolution. Darwin, on the other hand, knew that there were bees that built honeycombs, which are necessarily more cylindrical in structure and simple in nature, thanks to his extensive and age-old predictions; but he had no idea where to find it.
However, as a result of long correspondence and research, Darwin found the creature he was looking for: Melipona domestica. This bee, known as the Mexican Bee, was building honeycomb cells that, unlike other bees, were quite round and could be Decribed as more “rough”. The honeycombs of these bees also eventually converged to a hexagon, but they were much more rounded and cursory than the honeycombs produced by other bees (for example, the honeycomb in the top image). It was almost like a Decoupling type between a round design and a full hexagonal design!
All natural scientists know that it is much easier to build a round and angular structure than it is to build a angular structure. For example, the nests of birds are circular for this reason. On the other hand, hexagonal geometry is the geometry that provides the most and most frequent packing by making the least space consumption. But of course the earliest ancestors of bees, especially bees, had no way of knowing this.
2 Possibilities in the Evolution of Hexagonal Honeycombs
Therefore, there were two possibilities: Either The Bees build honey combs which they were most likely the ancestors of the shape is round, and, over time, rectangular, pentagonal, hexagonal architecture, which is the most advantageous among those who build different shapes such as hexagonal honeycomb shape were selected genes that cause; or in any way the bees, especially honey so it is round they build their combs, but the laws of physics, these forms are inevitably making hexagons. Or both of these two possibilities worked Decently together.
Possibility 1: It is Physics That Builds Bees’ Honeycombs; Not Biology!
Proceeding from this point, Darwin again made a proposition beyond his age: he suggested that, in fact, the honeycomb cells of all bees are circular. But most bees built these honeycombs so close and often to each other that the honeycombs bend and bend under physical pressure and become a hexagonal and Decaying pattern due to a regular distribution. The steps of this can be seen below:
If you follow the sequence above, you will see that the circles pressed against each other are always packed geometrically at 120-degree angles under physical forces. There is only one geometric figure, each of the internal angles of which is 120 degrees:
In other words, bees do not need to have much knowledge; honeycombs naturally turn into a hexagonal shape under physical forces. Indeed, in the time-lapse video below it is seen that the honeycombs built by a Dec Dec hornet-type bee are not specifically made hexagonal by the bee (they are even built in a rather rough round shape), but simply turn into hexagons under physical forces when neighboring pores are forced into a cramped space:
If you have the opportunity to visit the Cosmo Caixa Museum of Science and History in Barcelona, Spain in person, you can find out why and how bees produce hexagonal cells there with a visual and interactive experiment. Since there is no record of this, let’s try to explain it to you:
Imagine a container. This container stands vertically, and its width is very small, about 5 millimeters. Its structure is circular. Imagine that you drop small, spherical water bubbles into it from above. Bubbles will fall down from the top and begin to accumulate below, as the bottom of the container is closed. When you continue in this way constantly, after a while, the bubbles and the water will begin to fill up your cup for a long time to appear after your global, shake, and the water bubbles around them to each other to increase their forces together as you will see a hexagonal start taking shape.
That is why the cells in the honeycombs are hexagonal. Honeycombs, which are essentially built in a circular shape, take on a hexagonal shape because they are frequently woven. This phenomenon is called “self-organization” and this form can only occur under the laws of physics. It is possible to see this situation in soap bubbles:
During the production of bees’ honeycombs, the hexagonal geometry is more vague in the outermost parts; however, as the construction continues, the hexagonal structure of these parts becomes more obvious:
Because the parts where the wax is built are still hot, and the wax melts under the temperature, easily changes shape and takes on the most efficient hexagonal shape. In studies, it has been shown that the geometry in honeycombs deviates a few degrees from what we expect to see in mathematics. Also in a study by László Fejes Tóth in 1965, it was shown that the trihedral pyramidal forms of honeycombs are theoretically not the most efficient geometric shape, originally a more efficient packing could be obtained with 2 smaller rhombuses. However, the difference between the two geometries is around 0.035%; therefore, the difference between these two geometric advantages in the evolutionary process may be Dec Decipherable. Because the geometry that we already see in beehives is not perfect, and the margins of error are much larger than this small advantage. Decapitation is not a problem.
Possibility 2: Hexagonal Honeycombs Are the Product of Evolution!
But not all biologists agree with the above statement yet. Some argue that bees evolved to have a hexagonal geometry in the evolutionary process and that they are already building their honeycombs in a hexagonal shape today. In other words, the evolutionary advantage behind the hexagonal shape should not be forgotten. Indeed, shapes that converge to the hexagon may have been chosen in the evolutionary process.
The hexagonal design uses the least amount of wax. Therefore, those who try to build in a different structure (for example, pentagonal, as you said, etc.), will be disadvantaged by using more building materials; because the amount of honey to be accumulated as nutrients will decrease. Similarly, among the bees that build circular honeycombs from the very beginning, those that are more prone to hexagonal architecture (those that have a tendency in this direction in their behavior due to genes) will be more advantageous and selected Decently in the evolutionary process, as they will build more efficient nests.
This also makes sense, because honeycombs have an incredibly large role for the survival of bees. But building honeycombs using beeswax is a very difficult task: a bee needs to Decant 225 grams of honey to be able to produce 28 grams of beeswax. But a single honey bee can produce only 0.35 grams of honey in its lifetime, and for this, on average, 50,000 bees in each swarm need to fly a total of 90,000 kilometers and visit about 4 million flowers per kilogram of honey. Dec. Therefore, it is an evolutionary and vital necessity for bees to optimize their waist combs (to make them the most compatible); there is no alternative.
Therefore, modern bees do indeed build hexagonal honeycombs, because the genes that give them this tendency have been selected over generations.
Point of Agreement: Hexagon, The Most Efficient Shape
Yet these two possibilities, which is not biologically accurate; however, there is one point they agree with the mathematicians bees: how each occurs, the hexagonal geometry of spending the least amount of wax with the highest number of pores and the most made of tightly packed is the most efficient way. In mathematics, this is called the honeycomb conjecture. Let us look at it a little:
The Honeycomb Conjecture: Packing in 2 Sizes
Important theorems, equations, theories, proofs, paradoxes and conjectures in the history of mathematics are referred to by the name of the person who carried out the first idea about it. However, although it is not clear who put forward the honeycomb conjecture, it is a mathematical conjecture that has been studied for hundreds of years.
One question: What do a grocery store and honey bees have in common? Of course, both are quite resourceful in providing food for others. But to give a richer and more technical answer to this question: Grocery and honey bees may “know” how to efficiently pack their resources.
Honeycombs made of beeswax secreted by bees are used to store honey, pollen and larvae. For thousands of years, the honeycomb hexagon has been researched and admired. Today, however, honeycomb structures have numerous engineering and scientific applications, including in the aerospace industry.
Why do honeycombs have a hexagonal structure? One of the first to question this question was Pappus of Alexandria, who said that bees “have a divine sense of symmetry”. The reason underlying this discourse, to be expressed in simple mathematical terms: Pappus found that the perimeter of a square with an area of 1 is 4, the perimeter of an equilateral triangle with an area of 1 is larger, approximately 4.6. He determined that the circumference of a hexagon with an area of 1 is equal to the lowest value, about 3.7. In other words, hexagonal geometry is the geometric shape that has the shortest perimeter among these three possibilities (square, equilateral triangle and hexagon). Decimation of the hexagon
So what about other varieties of polygons (for example, circle, heptagon, etc.) if you say why not: Except for a square, an equilateral triangle and a hexagon, polygons with n-sides can not be Decoupled side by side, so that there are no gaps between them.
In other words, if we return to the hexagon again, if you draw an equilateral triangle, square and hexagon with the same area on a piece of paper, the shape you will spend the least pencil on will be a hexagon.
But were the statements of Pappus of Alexandria completely true? The honeycomb conjecture states that the most reasonable way to divide a piece of paper into cells of equal sizes is a set of hexagons. This statement was coined by the mathematician Thomas C. in 1999, 1650-odd years after Pappus. It is proved by a 22-page article by Hales. In other words, hexagon is indeed the most efficient packaging method in 2-dimensional geometries.
The Kelvin Problem: Packing in 3 Sizes
But the work did not end in 2 dimensions. You also need to think about the 3 dimensions. Here in 1887, William Thompson, better known as Lord Kelvin, thought a little deeper about this question and examined it in three dimensions.
“How do we divide the space with the least surface area (it can be a cube, a prism of dictatograms, or a room for us to imagine better) into small cells of equal volume?” he asked his question, so what was the most efficient form? This problem has been called the Kelvin Problem ever since.
Although the first efficient design that came to mind was cube-shaped cells, Kelvin thought about this problem and came to the conclusion that the optimal solution is the shape that will be called a Kelvin cell. Although this shape is a foam based on a cut cubic honeycomb, the shape of the tetradecahedron, consisting of eight hexagons and six squares, was indicated with all faces slightly curved.
But Lord Kelvin was not the only one who studied it in three dimensions; the honeycomb consists of cells in two layers, similar to the shape of a tube, with one end open. These layers are connected one after the other. Of course, although the bees seem to have found the simplest and most economical design (they close the end of each tube with four rhombuses, which allows the two layers to intertwine more effectively), László Fejes Tóth found an even more economical method than the bees used in 1953. He has shown that sealing each tube with two hexagons and two small squares makes bees spend less wax than a rhombus.
If we return to Kelvin’s assumption, it seems that the problem has been solved, and although it is believed that there has been no counterexample for about 100 years. However, Denis Weaire and Robert Phelan developed the Kelvin cell and thus refuted Kelvin’s assumption. After making the necessary calculations by suggesting a shape known as the Weaire-Phelan Foam, they determined that the surface area of the Weaire-Phelan structure is 0.3% less than the Kelvin structure.
The Weaire-Phelan structure has not been proven to be optimal, that is, it is the shape that is the best we have so far. The Weaire-Phelan cell is the shape with six 14-sided shapes and two 12-sided curved faces. Despite this, this design was successfully used in the design of the National Aquatics Center at the 2008 Beijing Olympics.
With these results, it is difficult to say that the honeycombs starting with Pappus of Alexandria are completely correct, even if they are examined in three dimensions until they come to our days. Maybe the person who will continue this journey started by Pappus after Kelvin, Fejes Toth, Denis Weaire and Robert Phelan will come out of the readers of this article, who knows?
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References:
- T. C. Hales. (1999). The Honeycomb Conjecture. Discrete & Computational Geometry, sf: 1–22. | Arşiv Bağlantısı
- D. Weaire, et al. (1993). A Counter-Example To Kelvin’s Conjecture On Minimal Surfaces. Philosophical Magazine Letters, sf: 107–110. | Arşiv Bağlantısı
- F. Nazzi. (2016). The Hexagonal Shape Of The Honeycomb Cells Depends On The Construction Behavior Of Bees. Nature Scientific Reports. | Arşiv Bağlantısı
- G. Sarcone. The Geometry Of The Bees…. (19 Şubat 2020). Alındığı Tarih: 19 Şubat 2020. Alındığı Yer: Archimedes Lab | Arşiv Bağlantısı
- D. Bauer, et al. (2012). Hexagonal Comb Cells Of Honeybees Are Not Produced Via A Liquid Equilibrium Process. Naturwissenschaften, sf: 45–49. | Arşiv Bağlantısı
- C. W. W. Pirk, et al. (2004). Honeybee Combs: Construction Through A Liquid Equilibrium Process?. Naturwissenschaften, sf: 350–353. | Arşiv Bağlantısı
- F. Morgan. (2016). The Hexagonal Honeycomb And Kelvin Conjectures. Geometric Measure Theory, sf: 159–172. | Arşiv Bağlantısı
