Traffic safety blackboard information 1:

Take off the Pearl in the Crown of Mathematics-Chen Jingrun

German mathematician Goldbach, born in 1690, was elected as an academician of Russian Academy of Sciences from 1725. In Petersburg, Goldbach met the great mathematician Euler, and they corresponded for more than 30 years. He has a famous conjecture, which was put forward in his correspondence with Euler. This has become a popular story in the history of mathematics.

On one occasion, when Goldbach studied a number theory problem, he wrote:

3+3=6,3+5=8,

3+7= 10,5+7= 12,

3+ 1 1= 14,3+ 13= 16,

5+ 13= 18,3+ 17=20,

5+ 17=22,……

Looking at these equations, Goldbach suddenly found that the left side of the equation is the sum of two prime numbers and the right side is an even number. So he guessed that the sum of any two odd prime numbers is even, which is of course correct, but it is just an ordinary proposition.

For ordinary people, things may stop here. But Goldbach is different. He is especially good at association and looking at problems from another angle. He used reverse thinking to write the equation in reverse:

6=3+3,8=3+5,

10=3+7, 12=5+7,

14=3+ 1 1, 16=3+ 13,

18=5= 13,20=3+ 17,

22=5+ 17,……

What does this mean? Goldbach asked himself and answered himself: from left to right, there are even numbers from 6 to 22, and each number can be "split" into the sum of two odd prime numbers. Under normal circumstances, right He began to continue the experiment:

24=5+ 19,26=3+23,

28=5+23,30=7+23,

32=3+29,34=3+3 1,

36=5+3 1,38=7+3 1,

……

All the way to 100 is correct. Some numbers have more than one split form, such as

24=5+ 19=7+ 17= 1 1+ 13,

26=3+23=7+ 19= 13+ 13

34=3+3 1=5+29= 1 1+23= 17+ 17

100=3+97= 1 1+89= 17+83

=29+7 1=4 1+59=47+53.

So many examples show that even numbers can be decomposed into the sum of two odd prime numbers in at least one way. Under normal circumstances, right He wants to say: Yes! So he tried to find a proof, and after several efforts, he failed; He wanted to find another counterexample, which showed that it was wrong. He thought hard and failed.

So, 1742 on June 7, Goldbach wrote a letter to Euler, describing his conjecture:

* * *1* * Every even number is the sum of two prime numbers;

***2*** Every odd number is either a prime number or the sum of three prime numbers.

* * * Note that since Goldbach regarded "1" as a prime number and thought that 2= 1+ 1 and 4= 1+3 also met the requirements, Euler corrected his statement in his defense. ***

On June 30th of the same year, Euler replied: "Any even number greater than * * * or equal to ***6 is the sum of two odd prime numbers. Although I can't prove it yet, I am sure that this is a completely correct theorem. "

Euler was a great number theorist. This proposition, which even he can't prove, shows its great difficulty and naturally attracts the attention of mathematicians all over the world.

People call this conjecture Goldbach conjecture. For example, if mathematics is the queen of science, Goldbach conjecture is the jewel in the crown. For more than 200 years, thousands of mathematicians have worked hard to get this dazzling pearl.

1920, the Norwegian mathematician Brown created a new "screening method", which proved that every even number large enough can be expressed as the sum of two numbers, and these two numbers can be expressed as the products of no more than 9 prime factors respectively. We might as well call this proposition "9+9" for short.

This is a turning point. Following the path pioneered by Brown, mathematicians proved "6+6" in 932. 1957, China mathematician Wang Yuan proved "2+3", which is the best result obtained by Brown method.

The disadvantage of Brown method is that neither number can be determined as prime number, so mathematicians have come up with a new method to prove "1+C". 1962, China mathematician Pan Chengdong and another Soviet mathematician independently proved "1+5", which made the problem a big step forward.

From 1966 to 1973, Chen Jingrun finally proved "1+2": every even number large enough must be expressed as the sum of the products of one prime number and no more than two prime numbers. Even number = prime number+prime number × prime number.

You see, this result of Chen Jingrun is only one step away from the final solution of Goldbach's conjecture! People praised "Chen Theorem" as a "brilliant theorem" and a "glorious culmination" in the application of "screening method".

Design of traffic safety blackboard

Traffic safety blackboard information II:

Han Xin ordered the soldiers.

Han Xin was a famous general of Han Dynasty in China. He once commanded thousands of troops and knew his soldiers like the back of his hand. He had a unique method of counting soldiers, which was later called "Han Xin Point Soldiers". His method is like this. After the troops were together, he asked the soldiers to report 1, 2, 3- 1, 2, 3, 4, 5- 1, 2, 3, 4, 5, 6, 7 three times, and then reported the rest to him every time. His calculation methods are also called "ghost valley calculation", "partition calculation" and "pipe cutting" in history, while foreigners call it "Chinese remainder theorem". Someone summed up the solution to this problem with a poem: Seventy-three people walked together, five trees and twenty-one branches, and seven children got together in the middle of the month, only after 105 did they know. This means that the first remainder is multiplied by 70, the second by 2 1 and the third by 15. Add up the results of these three operations and divide by 105, and the inexhaustible remainder is the number * * * that is, the total number * *. For example, if three 3-site reports are 1, five 5-site reports are 2, and seven 7-site reports are 3, the total is 52. The formula is as follows:

1×70+2×2 1+3× 15= 157

157÷ 105= 1……52

Here is a question for the students. Please use the "Han Xin's Point Troop Method" to calculate.

Xiaohong helped Aunt Zhang release ducks in the summer vacation, but she always couldn't count how many. She counted three first, and there were three left. She counted five more, leaving only four. She counted seven more, leaving only six. She still can't figure out how many ducks are in a * * *. Please help Xiaohong calculate how many ducks did Aunt Zhang feed?