Bees have never learned the mosaic theory, and neither have rotary spiders learned the logarithmic spiral. But like many things in nature, the buildings of insects and beasts can often be analyzed by mathematical methods. Nature uses the most effective form-the form that requires the least energy and materials. Isn't this the connection between nature and mathematics? Nature has mastered the art of solving minimax problems, linear algebraic problems and finding the optimal solution of constraint problems.
Focusing our attention on bees, we can observe many mathematical concepts.
Square, regular triangle and regular hexagon are the only three kinds of self-inlaid regular polygons. Among them, for a given area, the circumference of a hexagon is the smallest. This means that bees can use less wax and do less work to close the same space when building hexagonal columnar nests in honeycombs compared with the case of using square or triangular prisms embedded in spaces. The wall of the hive is about 1/80 inches (British unit of length, 1 inch equals 2.54 cm). The thick nest wall can support 30 times its own weight. This is also the reason why the hive gives people a heavy feeling. A hive of about 14.5 inches× 8.8 inches can store more than 5 pounds of honey, while the wax required for construction is only about 1.5 ounces (British weight unit, 1 ounce is 28.3495 grams). -translator's note). Bees use three oblique prism sections to form hexagonal columns, and the joint of nest walls forms an angle of120. Bees work in different parts at the same time, seamlessly building a hive. Beehives are built vertically downward, and bees use part of their bodies as measuring instruments. In fact, their heads act as measuring hammers.
Another fascinating "tool" owned by bees is a compass. The direction of bees is influenced by the earth's magnetic field. They can detect tiny fluctuations in the earth's magnetic field, which can only be distinguished by sensitive magnetometers. This is why when a group of bees occupy a new place, they can start building hives in different parts of this new field at the same time without any bees leading them. All bees put their new hives and old hives in the same direction.
In the picture on the next page, you can see that the beehives are closely arranged, and the bees have covered both ends with a half-diamond dodecahedron. In addition, the inclination of the cavity wall built by bees is 13, which can prevent honey from flowing out before sealing the end cover with wax cover.
Communication is another interesting field. When worker bees return to the hive after a long-distance reconnaissance, they will send out a series of codes in the form of "dancing" to indicate the direction of the food source they found. They can convey the direction and distance of food. The orientation of dancing relative to the sun indicates the direction of food, and the duration of dancing indicates the distance. It is also surprising that bees "know" that the shortest distance between two points is a straight line. Maybe this is a "straight line" (a straight line between two points). Possible sources of this term. The worker bee comes and goes freely among the flowers. After collecting a lot of nectar, it knows to take the most direct route back to the hive. Bees get math training through their genetic code. It is interesting to analyze all aspects of nature from a mathematical point of view. This glimpse of bee life is no exception. Here we found the optimization of materials and work, the mosaic pattern of plane and space, hexagon, hexagon column, rhombic dodecahedron, geometric theorem, magnetic field, code and amazing engineering technology.