It's really hard to sum up in 50 words. I found a few words. You can try to sum them up yourself: 1. Su's story: Professor Su, a famous mathematician in China, went to France for an academic visit, and a mathematician accompanying him gave him several topics on the tram. French mathematician: Hello, Professor Su! May I ask you a question? Sue: Sure, go ahead! Fa: It's about the itinerary. Specifically, there is a distance of 50 kilometers between A and B .. A is in place A and B is in place B, and both of them set out at the same time and walked in opposite directions. A walks 3km per hour and B walks 2km per hour, so how many hours can they meet? Sue: There are two kinds of travel problems in life, meeting and catching up. You asked a typical chance encounter question. It can be solved well by listing one-dimensional linear equations. You see: suppose A and B meet in x hours, and according to the meaning of the question, it is obtained that 3x+2x = 505x = 50x =10a:10h can meet. Fa: It's really simple after listening to you. The French mathematician didn't expect the China people to answer his question so quickly. Then I asked another question. Method: A puppy runs 5 kilometers per hour. It starts from A, meets B, just visible and runs to A, meets A, just visible and runs to B. How many kilometers did the dog run when A and B met? Sue: Obviously, the puppy runs back and forth until A and B meet, so the time when the puppy runs is the time when A and B meet, and the problem is solved. According to the above questions, they met after 10 hour, so the dog ran 10 hour, and * * * ran 5× 10=50 (km). A: The puppy ran 50 km when A and B met. Professor Su, you are really something. China people are really smart. 2. Euler for the sheepfold: Euler is a famous mathematician in the history of mathematics. When he was a child, he was not liked by teachers at all, but he was a very clever boy. One day, when he got home and had nothing to do, he helped his father herd sheep. He read a book while herding sheep. 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. 3. Gauss's ingenious calculation: Gauss is a famous German scientist. His most famous story is that when he was 10, the primary school teacher gave an arithmetic problem: calculation 1+2+3+...+ 100 =? This stumbles the children who have just learned mathematics. They added up the figures one by one according to the requirements of the topic. But at this moment, there came Gauss's voice: "Teacher, I have calculated it!" " "The teacher was very surprised. Gauss explanation: because1+100 =10, 2+99 =10/kloc-0, 3+98 =10/kloc-. I hope I can help you, please adopt it in time if you are satisfied!