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Some mathematical phenomena and problems
If a tire rotates, it is rotating.

Euler is a famous mathematician in the history of mathematics. He has made outstanding achievements in several branches of mathematics, such as number theory, geometry, astronomical mathematics and calculus. However, this great mathematician was not liked by teachers at all when he was a child. He is a student expelled from school.

Things are caused by stars. At that time, little Euler was studying in a missionary school. Once, he asked the teacher how many stars there were in the sky. The teacher is a believer in theology. He doesn't know how many stars there are in the sky, and the Bible doesn't answer. In fact, there are countless stars in the sky, which are infinite. There are thousands of stars visible to the naked eye. Without pretending to understand, the teacher replied to Euler, "It doesn't matter how many stars there are in the sky, as long as you know that the stars in the sky are inlaid by God."

Euler felt very strange: "The sky is so big and so high, and there is no escalator on the ground. How did God embed the stars on the screen one by one? " God himself put them in the sky one by one. Why did he forget the number of stars? Could God be too careless?

He asked the teacher a question in his heart, and the teacher was confused again, blushed and didn't know how to answer. A sudden anger rose in the teacher's heart, not only because a child who just went to school asked the teacher such a question, so that the teacher could not step down, but more importantly, the teacher regarded God above everything else. Little Euler blames God for not remembering the number of stars. The implication is that he doubts almighty god. In the teacher's view, this is a serious problem.

In Euler's time, there was absolutely no doubt about God. People can only be slaves of ideas, and they are absolutely not allowed to think freely. Little Euler didn't "keep in line" with the church and God, so the teacher told him to leave school and go home. However, in little Euler's mind, the sacred aura of God disappeared. God is a loser, he thought. Why can't he even remember the stars in the sky? He thought, God is a dictator, and even asking questions has become a crime. He thinks that God may be a guy made up by others and does not exist at all.

After returning home, he helped his father herd sheep and became a shepherd boy. He read a book while herding sheep. Among the books he read, there are many math books.

Dad's flock increased gradually, reaching 100. The original sheepfold was a little small, so my father decided to build a new sheepfold. He measured a rectangular piece of land with a ruler, 40 meters long and 15 meters wide. He calculated that the area is exactly 600 square meters, with an average of 6 square meters per sheep. When he was ready to start construction, he found that his materials were only enough for the fence of 100 meters, which was not enough at all. If you want to enclose a sheepfold with a length of 40m and a width of 15m, its circumference is110m (15+15+40+40 =1/kloc-0). If we want to build it according to the original plan, my father feels very embarrassed. If the area is reduced, the area of each sheep is less than 6 square meters.

Little Euler told his father that there was no need to shrink the sheepfold and not to worry that the territory of each sheep would be smaller than originally planned. He has an idea. Father didn't believe that little Euler would have a way, so he ignored him. Little Euler was in a hurry and said loudly, only moving a little stake in the sheepfold.

Father shook his head and thought, "How can there be such a cheap thing in the world?" However, little Euler insisted that he would be able to kill two birds with one stone. The father finally agreed to let his son try.

Little Euler saw his father agree, stood up and ran to the sheepfold to get ready to start work. He shortened the original side length of 40 meters to 25 meters centered on the stake. The father was anxious and said, "How can that be done? Then how to do it? This sheepfold is too small, too small. " Little Euler didn't answer, so he ran to the other side and extended the original side length of15m, and increased it by10m to 25m. In this way, the original planned sheepfold has become a square with a side length of 25 meters. Then, little Euler confidently said to his father, "Now, the fence is enough and the area is enough."

Father built a fence according to the sheepfold designed by little Euler. 100 meter fence is really enough, no more, no less, all used up. The area is enough, a little bigger. Father felt very happy. Children are smarter than themselves, they really use their brains, and they will definitely have a bright future.

Father thinks it's a pity to let such a clever child herd sheep. Later, he tried to let little Euler know the great mathematician Bernoulli. On the recommendation of mathematicians, little Euler became a college student in university of basel on 1720. This year, little Euler 13 was the youngest student in this university.

/kloc-At the age of 0/7, Galileo was admitted to the University of Pisa as a medical major. He likes asking questions and won't stop until he gets to the bottom of it.

Once in class, Professor Biro gave a lecture on embryology. He said: "Whether a mother gives birth to a boy or a girl is determined by her father's strength. When the father is strong, the mother gives birth to a boy; If the father is weak, the mother will have a daughter. "

As soon as Professor Biro's voice dropped, Galileo raised his hand and said, "Teacher, I have a question."

Professor Biro said unhappily, "You ask too many questions! You are a student. Listen carefully to the teacher in class, take more notes, don't think about it, it's easy to ask questions, which will affect students' study! " "This is not thinking, and it is not easy to ask questions. My neighbor, the man is very strong, but his wife has given birth to five daughters in a row. This is just the opposite of what the teacher said. How do you explain this? "Galileo was not intimidated by Professor Biro and continued to ask questions.

"I said it according to Aristotle, a famous ancient Greek scholar, and it can't be wrong!" Professor Biro moved out the theoretical basis and tried to convince him.

Galileo went on to say, "Is it necessary for Aristotle to insist that what he said is true? Science must conform to the facts, otherwise it is not real science. " Professor Biro was stumped by this question and could not step down.

Later Galileo was criticized by the school, but his spirit of persistence, curiosity and pursuit of truth has not changed at all. Because of this, he finally became a generation of science masters.

Hua used to be a naughty boy, but he was very talented in mathematics. Once, the math teacher worked out a famous math problem in ancient China-there was one thing, I don't know how many. Three places and three places, with a surplus of 2; 5 digits, 5 numbers, and the remaining 3; Seven numbers of seven, leaving two. How much is this thing? After the topic came out, the students talked about it, and no one could tell. The teacher was about to speak when Hua raised his hand and said, "I have worked it out." It is 23. " Not only did he get the numbers right, but the algorithm was also very special. This surprised the teacher greatly.

However, the clever boy dropped out of school after finishing middle school because his family was poor. He returned home and did business in his small grocery store, selling cigarettes, needle and thread, etc., and shouldered the burden of bringing home the bacon for his father. However, Hua still loves mathematics. If you can't go to school, try to learn by yourself. On one occasion, he borrowed some math books from his teacher, and became fascinated when he saw them. From then on, he studied mathematics while doing business and accounting. Sometimes he is so absorbed in reading that he forgets to say hello when people buy things. In the evening, after the shop closed, he wandered around the kingdom of mathematics wholeheartedly. For a whole year, I spent more than ten hours studying the borrowed math books almost every day. Sometimes when I sleep until midnight and think of a solution to a difficult math problem, he will definitely turn over, light a small oil lamp and write down the solution.

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