Legend has it that in 287 BC, King Syracuse won the battle. To celebrate his victory, he decided to present a golden crown to God. He found a jeweler and gave him some gold to make a crown. This crown is beautifully made and weighs as much as the gold given by the king. But the king still suspected that the jeweler had stolen some gold and mixed the same amount of silver in Wang Guanzhong. He asked Archimedes to identify whether the crown was pure gold, but he was not allowed to open it. Archimedes thought hard for several days, but he still didn't get to the point. One day, he stepped into a bathtub full of water to take a bath. When he saw the water overflowing, he suddenly realized and shouted excitedly, "I found a way to test the crown." Archimedes discovered the buoyancy theorem, thus solving the problem of crown measurement. In ancient China, there was also a story about "Cao Chong as an elephant" by using the principle of buoyancy. Cao Chong, the son of Cao Cao, was very clever when he was a child. One day, someone gave Cao Cao an elephant. Cao Cao is very happy and wants to know how heavy this monster is. But where can we find such a large scale? Wei's advisers and warriors racked their brains and couldn't think of a way. Little Cao Chong came up with a wonderful method: he taught people to lead the elephant to a big wooden boat and carve out the draft of the wooden boat; Then take the elephant off the boat, put some stones on the boat, and stop loading stones when the draft of the wooden boat is consistent with the original scale. According to the principle of buoyancy, the weight of the elephant is equal to the weight of the stones on board, and the scattered stones can be weighed by ordinary scales. "Cao Chong as an elephant" has become an eternal beauty talk. The idea of "Cao Chong's image representation" not only uses the buoyancy principle in physics, but also uses a very common idea in mathematics: the idea of transformation. That is to say, the problem to be solved is transformed into a problem that has been solved or the solution of which has been known through appropriate methods. In a sense, every step of mathematical proof or mathematical calculation is a transformation, and the idea of transformation is the most basic and important idea in mathematics. It is no exaggeration to say. The level of transformation ability is one of the important signs to measure a person's mathematical level. The Hungarian mathematician Rosa once made an interesting analogy: If you have a gas stove, kettle, faucet and matches in front of you and want to boil a pot of boiling water now, what should you do? The answer is simple. Everyone knows what to do. Fill the kettle with water; Light the gas; Put the kettle on the gas stove. Then Rosa asked this question: Now all the conditions are the same as before, but the kettle is full of water. What should you do now? The usual answer to this question is: light the gas and put the kettle on the gas stove. But Rosa pointed out that this is not the best answer, because only physicists will do this, and mathematicians will empty the water in the pot, because he has turned the latter problem into the former one, and the former one has been solved. Rosa's metaphor may be exaggerated, but it does show a characteristic of mathematical thinking method. She is good at using transformation method.