Louis? Posa is a famous young mathematician in Hungary. It is said that when he 14 years old, he can publish a quite in-depth mathematical paper. He got the title of doctor of science before he graduated from university.
Is this about Louis? Posa's mother is a mathematician, so he has been influenced by her since childhood and loves to think. Mother saw that he was interested in mathematics and encouraged him to develop in this field. She gave him some math games or toys to inspire him to think independently. Under the guidance of his mother, he taught himself high school math books when he was in primary school. However, it was the famous Hungarian mathematician Erdos who really trained him as a mathematician.
According to historical records, Erdos was a famous mathematician in Hungary. In-depth research in mathematical branches such as number theory and graph theory. It can be said that he devoted his life to mathematics, never thought about getting married, and only accompanied his mother. Moreover, he often leaves his motherland to do research and give lectures abroad. In eastern European countries, there are not many mathematicians who leave their country at will and enter and leave the western world like Erdos. He is a friend of mathematics everywhere. His prolificacy in mathematics and ingenious methods of solving problems have made him enjoy a high reputation in the world of mathematics. For his motherland, his important contribution is not only in the study of mathematics. After returning to his own country, he devoted himself to training the younger generation of mathematicians, telling them the problems that foreign mathematicians are concerned about at present and expanding their horizons. Here, I mainly tell you how he found Louis. The story of Posa.
On one occasion, Ordos just came back from abroad. He heard from a friend that there is a clever little thing that can solve many math problems in primary schools. So, he personally visited the child's family. Is this child Louis? Posa.
Posa's family is very happy with the arrival of Ordos. So they invited Professor Erdos to dinner. While drinking soup, Erdos wanted to test the ability of the 12-year-old child sitting next to him. So he asked Posa this question: "If you have n+ 1 integers and these integers are less than or equal to 2n, then you must have a pair of numbers that are coprime. Do you know why? " However, Posa answered this question in less than half a minute's thinking. And his answer was so clever that Professor Erdos was deeply impressed. Such a rare "talent" must be well cultivated.
Since then, Posa has systematically studied mathematics under Erdos. In less than two years, Posa became "small mathematics" and some profound theorems of graph theory were discovered. One of the theorems is mathematically called "Dove Cage Theorem".
Don't underestimate this pigeon coop principle, it has a wide range of applications in real life. Give some questions related to daily life here, and you will know its application in mathematics.
First, it's dark and windy, so wear socks.
If one night, the light in your room suddenly breaks down, you can't see your fingers, you want to go out, so you touch the socks under the bed. You have three pairs of red, white and blue socks, but you usually do things casually and throw them away as soon as you take them off. You can't know which pair is the same color in the dark. You want to take out the minimum number of socks and borrow the street lamp outside to make a pair of the same color. What should be the minimum quantity? If you know the pigeon coop principle, you will know that you only need to take out four socks. Why? In fact, the reason is very simple. If we have three boxes painted red, white and blue, and socks of different colors are put in each box, as long as four socks are drawn out, one box must be empty. Then the socks taken out of this empty box can be used to wear. So, isn't such a problem easy to solve?
Second, fingerprints and hair.
No two people in the world have the same fingerprints. Therefore, the police attach great importance to the observation of fingerprints when dealing with criminal problems, hoping to solve the case or identify the prisoner through fingerprints. But did you know that in China's population of 654.38+0.2 billion, at least two people have the same amount of hair? There is a simple reason. The number of human hair will not exceed 65.438+0.2 billion. Suppose a person has at most n hairs. Now let's imagine a house numbered 1, 2, 3, 4 ... until N. Whoever has the same amount of hair enters the house. Therefore, if someone has three hairs, they will enter the house 3. Now suppose that there is one person in each room, and there are still "900 million MINUS N" people left, which will not be equal to zero. Then, now just pick any one and put it in a house with the same amount of hair as him, and he will meet someone with the same amount of hair in it.
Third, the birthday of the theater audience.
There is a theater that can accommodate 1500 seats, which proves that if the theater is full, at least three spectators must be born on the same day of the same year. Now suppose there are 365 days in a year. Just like having a big pigeon coop, each coop has signs numbered from 1 month 1 day, 1 month 2 to1February 3 1 day. If four people are crammed into each section now, 4×365= 1460 people will enter the pigeon coop. Then, there are 1500- 1460=40 people left. As long as one of these 40 people enters dovecote, five people have the same birthday.