Why bees are the architects of nature

Writing in The Globe and Mail, Canadian science journalist Deflin said that after 1,600 years of hard work, mathematicians have finally proved that bees are the most efficient builders in the world. In the fourth century, the ancient Greek mathematician Pepos proposed that the beautiful shape of the honeycomb is the most efficient representation of labor in nature.

He speculated that the hexagonal honeycombs that people saw were built by bees using the least amount of beeswax. This conjecture of his is called the "honeycomb conjecture", but no one has been able to prove it. A few weeks ago, Hale, a mathematician at the University of Michigan, claimed that he had cracked the conjecture.

Honeycomb is a very delicate construction project. When bees build their nests, young worker bees secrete flakes of fresh beeswax, each the size of a needle. Other worker bees are responsible for carefully placing the beeswax in a position to form a vertical six-sided cylinder.

The thickness of each beeswax partition wall is less than millimeters, and the error is only millimeters.

The 6 partition walls are exactly the same width, and the angle between the walls is exactly 120 degrees, forming a perfect geometry. People have long wondered why bees don't make their nests triangular, square or other shapes? Why is the partition wall flat and not curved?

Although the honeycomb is a three-dimensional building, each honeycomb is a six-sided cylinder, and the total area of the beeswax wall is only related to the cross-section of the honeycomb. This leads to the mathematical problem of finding a plane figure with the largest area and the smallest circumference.

In 1943, the Hungarian mathematician Taos ingeniously proved that the circumference of a regular polygon is the smallest of all the regular polygons connected to each other. But what happens if the edges of a polygon are curves? Taos believed that the regular hexagon had the smallest circumference compared to any other shape, but he could not prove it.

Hale, on the other hand, considers that the perimeter is curved, whether the curve protrudes outwards or is concave inward, proving that the circumference of a figure composed of many regular hexagons is minimal.

1. In the building, when the hexagonal honeycomb structure is composed of diamond-shaped surfaces at how many angles, the materials are the most economical, and the capacity obtained is the largest. 2. People are amazed by the bees' superb construction skills. This hexagonal columnar honeycomb not only consumes less material, but also has a large capacity and is strong and strong.

Bees are nature's most brilliant architects. 3. There is a kind of lightweight plastic plate with honeycomb structure, which can be used to build a house with light weight and high strength. Its density is only 1 3 to 1 5 of ordinary building materials, but it is durable, not easy to deform, and also has sound insulation, heat insulation and other properties.

The hive is the necessary "furniture" and "pantry" of the bee home. Beekeepers will tear down entire hives to get honey. Honey can be extracted by opening the hive, removing the hive, and then placing it in a centrifuge that separates the honey and spinning it.

In addition, new hives are sometimes sold in the form of unartificial honeycomb honey, especially honey used to coat bread rather than honey that is cooked or flavored with tea. The nest that hatches the bee larvae becomes dim over time because the cocoons get embedded in the nest chamber and leave a lot of footprints, which the beekeeper calls "moving stains" when seen on the honeycomb honey frame. The hives on the "nest board" cannot be used to hatch bee larvae, so they retain their bright color.

Darwin marvelled at the bee's nest as one of nature's most amazing and magical buildings. The nest house is composed of a regular hexagonal hollow column chamber, arranged symmetrically back to back. The hexagonal chambers are parallel to each other, and each chamber is equally spaced apart.

The building of each nest is based on the middle and horizontal to the sides, with an elevation angle of 13° from the bottom of the chamber to the opening, in order to avoid the outflow of honey. The bottom of the chamber on the other side joins the bottom of this side and consists of three congruent diamonds.

In addition, each chamber of the nest has exactly the same width on all six partition walls, and the angle between the two walls is exactly 120 degrees, forming a perfect geometric shape. People always wonder why the hive chamber is not triangular, square or other shapes. Why is the partition wall flat and not curved?

Research has confirmed that such a hive is the most space-saving, the most material-saving, the largest and the most scientific.

Worker bees nurse their larvae in the hive, store honey and pollen, and the hive forms an angle of about 9 to 14 degrees to prevent the honey from flowing out. The ecology of bees and the structure of the hive are truly astonishing, and it can be said that nature is a miracle. It can be seen that not to mention the bee world, which is still unknown, just from the view of the beehive, it can be seen that human wisdom is far inferior to them in terms of natural creativity.

As an insect with excellent social characteristics, bees have survived and thrived from the past that is older than human history, and have brought us many blessings such as honey, royal jelly, propolis, pollen, and beeswax. At the beginning of the new century, in the process of making nest frames, the creativity and wonder of bees made us think deeply.

The bee nest is an amazing and magical natural structure. The nest is a hexagonal chamber. The nest is covered with naturally ripened honey and reddish-brown with pollen.

The bee hive is a strictly hexagonal columnar body with a flat hexagonal opening at one end and a closed hexagonal rhombic base at the other, consisting of three identical rhombic shapes. The diamond shape that makes up the chassis has an obtuse angle of 109°28 and all acute angles of 70°32, which is both strong and material-efficient. The hive has a thick nest wall and a minimal error.

The internal structure of the hive is called the hive, and the hive is composed of a series of hexagonal cylindrical hives made of beeswax, which are closely arranged, and this hexagonal arrangement is called a honeycomb structure. The inner and outer nests (called nests) are just half staggered from each other, and the point where the sides of the hexagonal shape intersect is the center of the inner hexagon. This is to increase the strength and prevent the bottom of the nest from breaking.

In addition, from the cross-sectional view, it can be seen that the direction of the nest on both sides is facing upwards.

The honeycomb is strictly hexagonal cylindrical. It has a hexagonal opening at one end and the base of a closed hexagonal pyramid at the other, consisting of three identical diamonds. At the beginning of the 18th century, the French scholar Malaarche had specifically measured the size of a large number of beehives, and he was very surprised that all the obtuse angles of the diamond shape of these honeycombs forming the chassis were 109°28, and all the acute angles were 70°32.

Later, after the French mathematician König and the Scottish mathematician Mark Lorraine theoretically calculated, if the least amount of material is to be consumed, the largest diamond container is made from this angle. In this sense, bees can be called "genius mathematicians and designers".

Yes, and bees are architects by nature.