Bee geometric talent

Bee is the most admirable architectural expert in the universe. Based on the innate instinct given by God, they adopted the "economic principle"-building the largest space (beehive) with the least materials (beeswax)-to build the home of bees.

Regular hexagonal building structure has the highest sealing performance, the simplest materials needed and the largest available space. It has compact structure, equal stress on all sides, easy to disperse stress, and can bear greater impact than other structures.

Honeycomb-the most economical and effective building in nature

Darwin praised the beehive as the most amazing and magical building in nature. The nest room is composed of regular hexagonal hollow cylinders, which hit the court directly and are symmetrically arranged back to back. Hexagonal atria are parallel to each other, and the distance between each atrium is equal. The building of each nest room is horizontally spread to both sides based on the middle, and the elevation angle from the bottom of the middle court to the opening is 13 to avoid the outflow of honey. The atrioventricular bottom on the other side is connected with the bottom on this side and consists of three identical diamonds. In addition, the width of the six partition walls in each room of the Bird's Nest is exactly the same, and the included angle between the two walls is exactly 120 degrees, forming a perfect geometric figure. People always want to know, why don't bee nests take the shape of triangles, squares or other shapes? Why is the partition flat, not curved?

In fact, as early as 180 BC, the ancient Greek mathematician Zhi Nuo Dorothy proved:

(1). For an N-polygon with a fixed perimeter, the regular N-polygon has the largest area. The greater the n, the larger the area.

(2) When the perimeter is fixed, the circular area is larger than all regular polygons.

The ancient Egyptians also knew for a long time that only regular triangles, squares and regular hexagons can be paved into planes.

17 12 At the request of naturalist Reaumur, the Swiss mathematician Samuel Konig proved that the bottom of a modified hexagonal cylinder consists of three congruent diamonds, and the method of saving materials is that the adjacent angles of the diamonds are109 26' and 70 34' respectively, so that the minimum surface area can be obtained under a certain volume. The adjacent angles of the diamond at the bottom of the honeycomb are109 28' and 70 32' respectively, which is only 2' different from Samuel Koenig's theoretical proof.

Recently (65438+1September 1999), Canadian science journalist Devlin wrote an article: "After 1600 years of efforts, mathematicians finally proved that bees are the most efficient builders in the world. American mathematician Hale declared that he had solved the "honeycomb conjecture". Bei Bo, an ancient Greek mathematician in the 4th century, pointed out that the beautiful shape of honeycomb is the most efficient and economical architectural representative in nature. He guessed that the honeycomb with hexagonal cross section was built by bees with the least amount of beeswax. His conjecture is called "Honeycomb conjecture", but it was not proved by Hale until 1999.

Although the beehive is a three-dimensional building, each beehive is a hexagonal cylinder, and the total area of beeswax wall is only related to the cross section of the beehive. This leads to a mathematical problem, that is, "finding the plane figure with the largest area and the smallest perimeter". 1943, the Hungarian mathematician Taos skillfully proved that the circumference of a regular polygon is the smallest of all regular polygons connected end to end. But what if the edges of a polygon are curves? Taos thinks that a regular hexagon has the smallest circumference compared with other figures, but he can't prove it. However, when Hale thinks that the periphery is a curve, it is proved that the circumference of a figure composed of many regular hexagons is the smallest, no matter whether the curve protrudes outward or sinks inward.

The most outstanding architect-bee

Bee hives are unique in shape and ingenious in structure, which has long attracted great interest of scientists.

Bees build houses for themselves. They are the most outstanding architects in the world.

Honeycomb structure

The basic structure of a beehive is a building composed of regular hexagonal cells, with all openings facing down or to one side and symmetrically arranged back to back. Each atrium is uniform in size and equal in distance from top to bottom. The honeycomb is about 0.5 cm in diameter, and the rooms are closely connected, neat and orderly, as if carefully designed.

When the climate is hot and the temperature in the hive rises, worker bees will flap their wings at the entrance of the hive to make the air in the hive circulate and become cool.

Because beeswax is white and soft; Therefore, the hive is translucent and milky white; After air drying, it gradually turns yellow and hardens.

It is estimated that worker bees need to consume 16 kg of nectar to secrete 1 kg of beeswax; To collect 1 kg nectar, bees have to fly 320 thousand kilometers to complete it; It's equivalent to circling the earth eight times. So beeswax is precious to bees.

Scientists have found that regular hexagonal buildings have the highest structural compactness, the simplest materials needed and the largest available space. Therefore, it can accommodate tens of thousands of bees.

This regular hexagonal honeycomb structure shows amazing mathematical talent, which makes many architects sigh!

Bees are the most admirable architectural experts in the universe. Based on the innate instinct given by God, they adopted the "economic principle"-building the largest space (beehive) with the least materials (beeswax)-to build the home of bees.

Darwin (1809- 1882), a famous contemporary biologist (literature), said: "A person must be a fool if he doesn't appreciate the exquisite beehive. 」

Pappus (300-350 BC), an ancient Greek mathematician, carefully observed and studied the exquisite and wonderful structure of beehives. He wrote in the book "Mathematical Highlights": "Honeycombs are full of regular polygonal patterns with equal sides and angles, which are very symmetrical and regular. 」

With the wisdom given to it by God, the bees chose the regular hexagon with the largest number of angles. With the same amount of raw materials, the honeycomb has the largest volume, so it can hold more honey.

In other words, the hive is not only exquisite and magical, but also very realistic, and it is the most economical spatial structure.

The hive built by bees is really an amazing natural building. As early as the beginning of18th century, French astronomer Mallardi personally measured many beehives and found that the holes and bottom of each beehive were hexagonal prisms.

If the bottom of the whole honeycomb is divided into three rhombic sections, the angles of each acute angle and each obtuse angle are equal (acute angle is about 72, obtuse angle is about l09).

What is even more surprising is that in order to prevent honey from flowing out, the structure of each hive is horizontally unfolded from the middle to the two sides; Each hive presents an elevation angle of 13 o from the bottom of the inner chamber to the opening.

Historically, the wisdom of bees has also caused the famous astronomer Kepler (literature) to point out: "The angle of this honeycomb full of spatial symmetry should be the same as that of the rhombic dodecahedron. The bottom of each regular hexagonal honeycomb consists of three congruent diamonds, and the obtuse angle of each diamond is equal to 109 o28' and the acute angle is equal to 70 o32'. 」

/kloc-at the beginning of the 8th century, French scientist René de Reaumur (1683- 1757) (literature) speculated: "The honeycomb built at this angle must be the most material-saving construction method in the same volume. 」

The hexagon of the honeycomb is the densest structure, and the forces on all sides are equal, which is easy to disperse.

The airframe parts of the American B-2 stealth bomber mostly adopt sandwich structure, that is, a honeycomb layer with extremely low density is glued between two high-strength thin plates, so that the airframe strength is increased and the weight is reduced.

The nozzle of the engine is deeply placed in the wing and is honeycomb-shaped, so that radar waves can only enter but not exit.

The graphite in a pencil is composed of carbon atoms arranged in hexagonal honeycomb sheets. If these carbon atoms recombine, they can become diamonds.

Whether it is as big as a "hive warship" or as small as a "cellular mobile phone", its inspiration comes from the structure of the hive.

The proverbs of Solomon, the wise king, say, "Wisdom cries out in the streets and makes a sound in the wide places. (Proverbs 1:20) Solomon's wisdom is unparalleled. His wisdom is obtained by praying to God, and God is willing to give him wisdom.

The incarnation of Jesus Christ is a wiser Lord than Solomon. He has gone through 33 and a half years in human history, and he is the source of wisdom of "the most outstanding wisdom worker bee". Because Jesus Christ is the wisdom of God.

"The fear of the Lord is the beginning of wisdom; Knowing the most holy is wisdom. " (Proverbs 9: 10)

"A wise man stores knowledge; A fool's mouth will soon be ruined. " (Proverb 10: 14)

If the life of the most outstanding architect in the world-bee is a masterpiece created by God; The spirit of all things, with the image and style of God, should not know the source of wisdom of all things in the universe-God, who is the creator and the only true God.