What are the stories of Archimedes?

Archimedes (287 BC - 212 BC), a great ancient Greek philosopher, encyclopedic scientist, mathematician, physicist, mechanics, static mechanics and hydrostatics The founder of mathematics and known as the "Father of Mechanics", Archimedes, Gauss and Newton are among the three major mathematicians in the world. Archimedes once said: "Give me a fulcrum and I can lift the entire earth."

(1) Determination of Archimedes' lever principle: People have been using it since ancient times. Leverage, and knowing how to use it skillfully. When the pyramids were being built in Egypt, slaves used levers to lift heavy stones. Shipbuilders used levers to erect masts on ships. People used water booms to get water from wells, etc. But why does leverage do this? Before Archimedes discovered the law of the lever, no one could explain it.

At that time, when some philosophers talked about this issue, they insisted that it was "demonic nature". Archimedes did not admit that there was any "demon nature". He understands that various phenomena in nature always have natural reasons to explain them. Leverage had its natural causes, too, and he was determined to explain them. After repeated observations, experiments and calculations, Archimedes finally established the law of balance of levers. That is, "the moment arm is inversely proportional to the force (weight)." In other words, the small weight is one-thousandth of the large weight, and the long moment arm should be several times as long as the short moment arm.

After Archimedes established the law of the lever, he concluded that as long as the appropriate lever length can be obtained, any weight can be lifted with very little force.

It is said that he once said such heroic words: "Give me a fulcrum, and I can lift the earth!" After hearing this, King Syracuse said to Archimedes: "With that, I can lift the earth!" "I swear by Zeus (Zeus is the king of the gods in Greek mythology, responsible for the sky, thunder, lightning and rain), what you said is really strange, Archimedes!" Archimedes explained the characteristics of the lever to the king. Later, the king said: "Where can I find a fulcrum to lift the earth?" "There is no such fulcrum." Archimedes replied. "Then it is impossible to convince people of the power of mechanics?" said the king. "No, no, you misunderstood, Your Majesty, I can give you other examples." Archimedes said. The king said: "You are too boastful! You can push a heavy thing for me and see what you say."

The king was having a difficult problem at that time, which was that he built a heavy object for the king of Egypt. A very big ship. After the ship was built, the entire city of Syracuse was mobilized, but they could not push it into the water. Archimedes said: "Okay, let me push this boat for you." After Archimedes left the king, he designed and built a set of ingenious machinery using the principles of levers and pulleys. After everything was ready, Archimedes invited the king to watch the ship being launched. He handed the end of a thick rope to the king and asked him to pull gently. Suddenly, the big ship slowly moved and slid into the water smoothly. The king and ministers were amazed to see such a miracle, as if they were watching a magic trick! So, the king believed in Archimedes and issued a proclamation to the whole country: "From now on, no matter what Archimedes says, you must believe in him..."

(2) Archimedes' Principle : In the eyes of ordinary people, Archimedes is a "weird". In the words of the Roman historian Plutarch: "He seemed to be a man bewitched and didn't care about food or his own body." Sometimes, when rice was placed on the table and he was asked to eat, he seemed to He didn't hear it and continued to draw his geometric figures in the ashes of the brazier. His wife must watch over him at all times. For example, when he was rubbing his body with oil, he would just sit there and draw patterns on his body with oil, forgetting what he was doing. His wife was even more afraid of sending him to the bathhouse to take a bath. This joke was caused by the king's new crown.

Not long ago, the king asked a craftsman to make a gold crown for him. The king gave the craftsman as much gold as he needed. The craftsman's skills are very skillful, and the crown made is exquisite and unique, and it weighs as much as the gold given by the king.

However, someone reported to the king: "When the craftsmen were making the crown, they secretly swallowed part of the gold and mixed the same weight of silver into it." After hearing this, the king also became suspicious, so he called Archimedes and asked him for ideas. Determine whether the gold crown is mixed with silver, and whether the craftsman has embezzled the gold.

This time, Archimedes was stumped. He returned home and thought hard for a long time, but could not come up with a solution. He could not eat, sleep well, or take a shower every day, as if he was possessed by a demon. One day, the king sent someone to urge him to report to the palace. His wife saw that he was too dirty and forced him to take a bath. When he was taking a bath in the bathhouse, he was still thinking about the problem of weighing the crown. Suddenly, he noticed that as his body sank in the tub, some of the water overflowed from the edge of the tub. At the same time, he felt that the deeper he went into the water, the lighter his body became.

So he immediately jumped out of the bathtub, forgot to put on his clothes, and ran into the street where there were people. While running, he shouted: "I figured it out, I figured it out, the solution to the crown has been found!" After entering the palace, he said to the king: "Please allow me to do an experiment first, and then I can report the results to you. "The king agreed. Archimedes placed a piece of gold, a piece of silver, and the crown, which were as heavy as the crown, in a basin one by one. He saw that the amount of water displaced by the gold piece was less than that of the silver piece, and that the amount of water drained by the crown was less than that of the gold piece. A lot of water. Archimedes said to the king: "The crown is mixed with silver!" The king saw the experiment and didn't understand it, so he asked Archimedes to explain it.

Archimedes said: "Comparing one kilogram of wood with one kilogram of iron, the volume of wood is larger. If they are put into water respectively, the amount of water displaced by the larger wood will be greater than that of the smaller one. Iron displaces more water. I apply this principle to gold, silver and crowns. Because gold has a high density and silver has a low density, the volume of gold and silver must be greater than the volume of gold. Therefore, if gold and silver nuggets of the same weight are put into water, the amount of water displaced by the gold nugget will be less than that of the silver nugget. The experiment just proved that the crown displaces more water than the gold nugget, indicating that the density of the crown is greater than the density of the gold nugget. Small, this proves that the crown is not made of pure gold.”

Archimedes’s logical explanation convinced the king. The results of the experiment proved that the craftsman had embezzled the gold. This experiment of Archimedes is the embryo of "hydrostatics". But he did not stop at this point and continued to study the problem of floating bodies in depth. The result was the discovery of an important principle in natural science - Archimedes' law. That is: when an object is immersed in a liquid, the volume of liquid displaced is equal to the volume of the object immersed; maintaining the buoyancy of the floating body is equal to the weight of the liquid displaced by the floating body.

The king made a gold crown. He suspected that the craftsman had secretly exchanged some silver for some gold, so he asked Archimedes to identify whether it was made of pure gold and not to damage the crown. Archimedes held the crown and thought hard all day long. One day, Archimedes went to the bathroom to take a bath. He stepped into the tub, and as his body immersed in the tub, part of the water overflowed from the edge of the tub. Archimedes Seeing this phenomenon, a flash of lightning flashed in my mind, "I found it!". Archimedes took a gold nugget and a silver nugget of equal weight and placed them in a container filled with water. He found that the silver nugget displaced much more water.

So Archimedes took a gold nugget that was equal to the weight of the crown, put it into a container filled with water, and measured the amount of water discharged; then he put the crown into a container filled with water and saw. See if the amount of water discharged is the same, the problem will be solved. With further research, Archimedes' law, the most important cornerstone of fluid mechanics that is still used today, was born.

In addition, he used mirrors to burn enemy warships. The story of telling the enemy to wait and letting him finish a math problem before being killed is also popular. Birthday wishes for colleagues, Two thousand one hundred and ninety years ago, in Syracuse, Sicily, ancient Greece, a great physicist appeared. His name was Archimedes (287-212 BC).

. Throughout his life, Archimedes was diligent and studious, dedicated himself to science, and was loyal to his motherland. He was respected and praised by people. Archimedes discovered the law of the lever and Archimedes' law is named after him.

And used these laws to design a variety of machinery to serve the people and the motherland. The details of his life cannot be verified. But the stories about his inventions and defense of the motherland have been passed down to this day.

(3) Discovery of the principle of buoyancy: It is said that once, Hieron II made a gold crown, but he always suspected that the goldsmith had stolen his gold and mixed it with gold. silver. So he invited Archimedes to appraise it, on the condition that the crown would not be damaged. At that time, people did not know that different substances had different proportions. Archimedes thought hard for many days, but there was no good way. One day, he went to take a bath. As soon as he lay down in the tub filled with warm water, the water overflowed and he felt his body floating slightly.

So he suddenly thought that objects of the same weight would discharge different amounts of water due to different volumes... He stopped taking a bath, jumped out of the tub, and ran home naked from the street. . When his servant rushed home panting, Archimedes was already conducting experiments; he put the crown into a basin filled with water, measured the overflowing water, and put the same weight of pure gold into a basin filled with water. but the water that overflowed was less than what had just overflowed, so he concluded that the goldsmith had mixed silver into the crown. From this, he discovered the principle of buoyancy and recorded this principle in his famous book "On Floating Bodies". People today call it Archimedes' principle.

(4) Battle of Syracuse: Archimedes: Battle of Syracuse In the later years of Archimedes, the Roman army invaded Syracuse, and Archimedes guided his compatriots to create Lots of offensive and defensive combat weapons. When Marcellus, the leader of the invading army, led his troops to attack the city, he designed a trebuchet that beat the enemy to tears.

The iron claw crane he built could lift and reverse enemy ships... Another incredible legend is that he once led the people of Syracuse to hold a concave mirror and focus the sunlight on the Roman army. wooden warships and set them on fire. The Roman soldiers were frightened by these frequent blows, and the grass and trees were all soldiers. When they saw ropes or logs being thrown from the city, they exclaimed "Archimedes is coming" and ran away with their heads in their hands.

The Roman army was blocked from entering the city for three years. Finally, in 212 BC, the Romans took advantage of the slight laxity in the defense of the ancient city of Syracuse and launched a massive attack into the city. At this time, the 75-year-old Archimedes was concentrating on studying a profound mathematical problem. A Roman soldier broke in and trampled on the figure he had drawn. Archimedes argued with him angrily. The cruel and ignorant soldier raised his knife. With a wave of his hand, a bright scientific star fell.