I just want to be a quiet scholar

Chapter 27 A variant of Euler's Seven Bridges?
On the morning of July 7, the second teaching building of Shuimu University.

Erjiao is an old building, built before 1949.

It is rumored that there are often supernatural events in the Second Religion, commonly known as haunted.

The second teaching is never open at night, and the school says it is to save water and electricity.

The highest scientific research and academic institution like Shuimu University naturally advocates science. In the face of powerful scientific forces, bulls, ghosts, snakes and gods have only the fate of being crushed.

This season, more than half of the college students have completed the final exam, and the second teacher is free. This is the venue for this year's high school mathematics league national preliminaries and national finals.

At 9:[-] a.m. today, there will be a national preliminaries.

还有半个小时开赛，来自32个省市的共192位选手全部在201和202待命，他们中的十支队伍共60人将拿到国决资格。

"Actually, I'm very satisfied to be able to participate in the national competition, really," said Qi Jianhong, the youngest member of the Southern Guangdong Provincial Team.

Shen Qi scolded: "Qi Jianhong, you know nothing, you can't make it to the national finals, let's come to Shuimu University for nothing. You think you are a member of the five hegemons of Hubei, Hunan, Zhejiang, Beijing, and Shanghai, and you can be selected for the provincial team. Got the contract from Shuimu University and Yenching University?"

Qi Jianhong was not convinced: "I don't rely on the guarantee, can I get Shuimu and Yan Daxing in the college entrance examination?"

Shen Qi asked, "You got good grades in other subjects?"

Qi Jianhong said triumphantly: "That is, in our high school, my total score was the first in the whole grade for a long time, and if I couldn't beat No. 250 or more, I would lose. Mathematics is just my hobby. I dominate the whole grade by relying on Invincible comprehensive strength."

"You little Zhengtai is quite good, but I don't care how good you are in your high school, this time you must give me your highest level in the National Preliminary Exam, otherwise I will beat you." Shen Qi said resolutely. arrive.

"You, you... so barbaric!" Qi Jianhong is only 1.5 meters tall, and he has no strength to restrain a chicken. He must not be able to beat Shen Qi who is 1.7 meters tall.

"Actually, what can I do if I beat you? From the beginning of the training camp, I repeatedly emphasized that we are a team, from the same place, and have the same dream. I can't beat the five of you alone, but I have a champion. Heart. And you are all hot chickens." After Shen Qi finished speaking, he took his stationery set and left classroom 202 without looking back.

"Shen Qi, you... You actually said we were spicy chickens!" Qi Jianhong was ashamed and annoyed, he said to the other four teammates, "Shen Qi said we were spicy chickens, so disgusting!"

"Hmph, Shen Qi is such a coercive thing."

"We are not spicy chickens, we are strong!"

"Shen Qi, Soul Dan, I must defeat you!"

"I must be higher than you in the National Preliminary Exam!"

"+1!"

Qi Jianhong and other five people share the same hatred, and the atmosphere of unprecedented unity appeared in this team for the first time.

Shen Qi, Qi Jianhong and other six people were arranged in six different classrooms. It was five minutes before 9:5. The invigilators began to read out the rules of the competition: "The rules are very simple, you have three hours to complete the national pre-examination paper, and you must not look around during the answering process. , please raise your hand if you have anything. After the competition rules have been read out, the test papers and scratch paper will be distributed."

Shen Qi took the exam in classroom 101. He got the national pre-examination paper, and quickly browsed through the three exam questions, each question was seven points, and the score on the paper was 21 points.

From the provincial preliminaries to the provincial semi-finals, and then to the national preliminaries, the scores of the rolls are getting lower and lower, but the difficulty is getting higher and higher.

For the first question, a pattern was drawn on the scroll.

There are two small islands floating in a river, the islands are connected by bridges, and the islands and the river banks are connected by bridges.

A total of one river, two islands and eight bridges.

Q: How can a walker walk all eight bridges without repetition or omission, and finally return to the starting point?

"Hey, who came up with this question, does Euler allow you to do this?"

Shen Qi saw through everything at a glance. This question is a variant of "Euler's Seven Bridges", Shuimu Baqiao?

Euler, the god-level master in the history of mathematics, was energetic when he was young. He liked mathematics and also liked girls.

When Euler was in her twenties, she fell in love with a girl, a beautiful and gentle art teacher.He frantically pursued this art teacher and finally succeeded. The two got married and had 13 children... It can be seen that Euler is not only academically top-notch, but also has a great body.

On a bright spring day in 1736, Euler was in a park in Konigsberg waiting for his art teacher girlfriend to arrive.

Being late is a woman's innate attribute, waiting left and right, an hour has passed, and the girl who teaches art has not yet made her appointment.

Euler was bored, so he began to study mathematics. He found that two small islands were suspended in a river in Königsberg Park. There were seven bridges connecting the islands and the river bank. Travel between the two islands.

Euler suddenly came to inspiration, he proposed an idea, whether there is a path, starting from any point, can pass through the seven bridges without omission and repetition, and finally return to the starting point.

Later, Euler wrote this idea into a paper and submitted it to the St. Petersburg Academy of Sciences. The paper was called "The Seven Bridges of Konigsberg".It is also known as the "Eulerian Seven Bridges Problem".

Later, Euler himself overturned this assumption, proving that such a path could not exist.

In order to slap himself in the face, Euler invented a new method of proof, and he created a new branch of mathematics - geometric topology.

This is the pattern of top mathematicians, I am invincible, I have no opponent, my only opponent is myself, in order to defeat myself, I create a new branch of mathematics.

Two or three hundred years have passed, and Shen Qi is facing a new problem, the Eight Bridges problem.

The original version of Euler's Seven Bridges cannot get the answer. As for whether there is such a path for the Eight Bridges, it is necessary to calculate.

Shen Qi counted up and down, left and right, half an hour later, he couldn't figure it out!

Whether the Eighth Bridge is the same as the Seventh Bridge, there is no so-called path at all, and it can pass through each bridge without omission and repetition, and finally return to the starting point.

"The national competition is a national competition after all. Topology is a very difficult thing to do. I have no way to find this path, nor can I prove that it does not exist."

Shen Qi put down his pen ruler and pressed hard on his temples.

As time passed by, Shen Qi was unable to write, he was a bit obsessive-compulsive and had to solve the first question and then solve the next two questions.

"Euler, seven bridges, eight bridges... By the way, why do I have to use Euler's theory to solve variant problems based on Euler's seven bridges, this is a trap, an infinite loop!"

Shen Qi suddenly realized, I thought, I thought, Poincaré's network theory!
If the two disconnects are exactly the same as before, then this is an allowable topology operation.

Otherwise, it is not allowed!
That's right, the singularity of this eight-bridge diagram is at both ends, so there is no such connection at all, and each bridge can be passed without omission and repetition.

The answer to this question is: No!live!exist!
Shen Qi hurriedly wrote down the proof process. He completed the proof in only 3 minutes, and the thinking process took up to 1 hour.

"Huh... 7 points, next question." Shen Qi took a deep breath, burning a lot of brain cells, so tired.But the battle has just begun, he can't relax, he must complete all the answers within the stipulated time, and ensure that it is absolutely correct.

Even so, Shen Qi didn't know whether his goal could be finally achieved.I hope the five pig teammates can give me a chance!
(End of this chapter)