The diligence of bees is most appreciated by people. It has been calculated that if a bee wants to brew 1 kg honey, it must collect the raw materials of 1 10,000 flowers. If the average distance from the flowers to the hive is 1.5km, the bees will fly 450,000 km every time they collect 1kg honey, which is almost equivalent to flying around the equator of the earth 1 1 circle.

In fact, bees are not only hardworking, but also extremely clever. They showed amazing mathematical talent when building beehives, and even made many architects in the world feel ashamed!

Darwin, a famous biologist, even said, "If a person doesn't praise the beehive, he must be a fool."

Beehives are warehouses where bees store honey. It consists of many regular hexagonal beehives, one next to the other, closely arranged, with no gap in the middle. As early as more than 2,200 years ago, an ancient Greek mathematician named Baptist made a detailed observation and study on the exquisite and wonderful structure of beehives.

In his book "Mathematical Compilation", Baptist wrote: Honeycombs are covered with regular polygonal patterns with equal sides and angles, which are very symmetrical and regular. Mathematically, if the whole plane is a regular polygon, then there are only three such regular polygons, namely regular triangle, square and regular hexagon. With instinctive wisdom, bees choose the regular hexagon with the largest number of angles. In this way, they can use the same amount of raw materials to make the hive have the largest volume, thus storing more honey.

In other words, the honeycomb is not only exquisite and wonderful, but also meets the demand and is the most economical structure.

Historically, the wisdom of bees has attracted the attention of many scientists. The famous astronomer Kepler once pointed out that the angle of this symmetrical honeycomb full of space should be the same as that of the rhombus 12 polyhedron. French astronomer Marathi personally measured many beehives. He found that the bottom of each regular hexagonal honeycomb is composed of three congruent diamonds, and the obtuse angle of each diamond is equal to 109 28', and the acute angle should be 70 32'.

/kloc-At the beginning of the 8th century, the French natural philosopher Leo Miao La speculated that under the same volume, the honeycomb built at this angle must be the most material-saving. In order to confirm this speculation, he consulted Koenig, an academician of the Paris Academy of Sciences and a Swiss mathematician.

This kind of problem is called extreme value problem in mathematics. Koenig did a lot of calculations by means of advanced mathematics, and finally came to the conclusion that the obtuse angle of each rhombus should be109 28'16 "and the acute angle should be 70 31'44".

This conclusion is only 2' from the actual value of the hive.

The circumference is 360, and every 1 is 60'. The error of 2' is very small. People think generously: it is good that bees can do this step. As for the small error of 2', it is completely understandable.

But things are not over. 1743, the famous mathematician Ma Kraulin studied the shape of beehives again and came to a shocking conclusion: to build the most economical beehives, the obtuse angle of each rhombus should be109 28'16 "and the acute angle should be 70 31'44".

This conclusion is consistent with the actual value of beehives. It turned out that it was not the bees that were wrong, but the mathematician Koenig's calculation!

How can mathematicians make mistakes? Later, it was found that the logarithm table used in Koenig's calculation was wrongly printed.

Bee is really not simple. Mathematicians didn't work out and confirm this problem until the middle of18th century. It has been applied to beehives before human history.