However, the great masters Euler and Lagrange finally only solved the restricted three-body problem.
Poincaré was the first to provide results for the three-body problem in ordinary situations.
It’s just that the three-body problem did not receive as much attention as the conventional sun, earth, and moon system, because at that time people did not believe that the three-body system would actually exist.
Poincaré's greatest contribution to this is actually a bit like Galois's solution to the root of the quintic equation mentioned above.
Galois used a set of complex and advanced group theory to actually prove one thing: the roots of the fifth-order equation cannot be found using conventional methods.
Poincaré also used a complex set of differential equation theory to prove one thing: the three-body problem has no solution.
Strictly expressed mathematically, there should be no definite analytical solution, but there can be specific solutions. This is a common feature of differential equations.
It seems that the result is a bit ridiculous. After working on it for a long time, two problems that have troubled mankind for hundreds of years came to nothing in the end!
In fact, this kind of thing is very common in the history of mathematics. The key is that in the process of proving that it has no solution, many incredible new mathematical theories were discovered.
The same principle applies to Fermat's last theorem. Although Fermat hated it and wrote the sentence "The space here is too small, I can't write down the proof process", but in the next three hundred years, many inventions were born to prove this theorem.
New mathematical methods.
Some people even say that after Fermat's last theorem was proved, a hen that could lay golden eggs died.
In short, the current call for submissions on the three-body problem is much simpler. Li Yu only needs to use Poincaré's differential equation to solve it.
This is very similar to the homework I did when I was in college.
He is very familiar with differential equations, and he is also very familiar with the three-body problem due to the subsequent popularity.
In fact, in the world he once lived in, Poincaré tried to calculate the solution to the three-body problem purely by hand calculation, but it was really difficult.
He also said: "These solutions are so confusing that I can't draw what they look like."
Indeed, calculation is a very labor-intensive matter. Generally, math masters only give ideas and do not actually do the calculations.
But since this is a question bounty, it would be best if we could come up with a few solutions.
Li Yu can do it!
Because although the calculation is complicated, he has a calculator!
Moreover, people in later generations have indeed calculated many specific solutions, and he also knows it.
But even so, writing this reply is not an easy task.
Solving differential equations is still very difficult. Maybe many people have no idea about "differential equations" because everyone who usually studies mathematics feels that solving equations is not difficult at all. Even equations are not an important difficulty in college entrance examination mathematics.
In fact, it’s because real differential equations are too difficult!
Let’s put it this way, two of the seven major mathematical problems of the millennium are partial differential equations.
Wei Shen Wei Dongyi, he studies the Navier-Stokes equation in differential equations, which is about fluid mechanics. If you have the ability, you can go and have a look. I can't understand a word.
Anyway, you only need to know two points about partial differential equations. The first is that it is difficult, and the second is that there is no general solution and can only be solved violently.
It's just that Poincaré's era is difficult to solve violently because hand calculations are too non-violent.
Li Yu could use the limiting conditions and then use a calculator to calculate several solutions, which actually perfectly answered the bounty question.
But it's really not sensational at all.
Fortunately, after the question about the bounty offered by the King of Sweden and Norway, he mentioned the sun-earth-moon system. It was supposed to be just an additional question, but the result of this question was very terrifying.
Because he knows the answer: the solar system will definitely be in chaos in the future!
After all, the result of the three-body problem itself will be very, very messy.
Ahem! Don’t worry, everyone!
It’s hard to say how long this chaos will last. It ranges from hundreds of millions to billions of years, or the sun may explode without any chaos. You don’t have to worry about the money in your bank card not being spent when the earth dies.
Li Yu could also do a general calculation after given the initial conditions. It would not be too accurate, but the conclusion that the solar system would be in chaos was enough to shock the world.
But it will take him a long time to write something later.
After all, all of the above involve a relatively large and well-known mathematical theory: chaos.
It was Poincaré who knocked on the door of chaos theory, but Poincaré was really unwilling to calculate too many solutions, so although he had glimpsed a corner of chaos, it was a pity that he did not take a step forward.
Fortunately, Li Yu's calculator has a certain degree of violence, and at least it can save a lot of time.
Chaos theory is a great thing. Li Yu suddenly felt that he had done something during this period, but he still needed to get a few special solutions to the three-body problem first, and then consider other things. It was impossible to achieve much results in a short time.
Li Yu returned to the house and planned to buy more manuscript paper tomorrow. It would be better if he could buy pencils and pens.
The next day, Li Yu visited all the Wenfangsibao stores in Liulichang, but could not find any selling Western stationery. He only bought some white paper from Rongbaozhai.
It seems that I have to give some advice to Ding Haoliang in the future. In any case, he should ask the Capital University to buy more stationery!
When did I ever worry about stationery in the past? It’s really intoxicating to think about it.
He had no choice but to find Puland again.
Pulande has returned to Beijing, and he also wants to meet Li Yu, who has made a lot of big news in Europe.
"I'm talking about Mr. Li! You are so amazing, I don't even know how to describe it in words! Did you read the Times report I wrote?"
Li Yu smiled and said: "It turns out you wrote it."
Puland immediately shook his head and said: "It's not all me. The editor of "Shenbao" pays special attention to your news. He has many reports and writes more manuscripts. I refer to some of his press releases."
Uh! It’s really hard not to read the newspaper.
Li Yu said: "I should order a few newspapers in the future."
"Of course, no problem. I can directly order you a free copy of the Beijing-Tianjin Times and Zilin West News for the whole year!" Puland said, "As long as you can write a manuscript for us."
Li Yu asked: "Manuscript? What manuscript?"
Puland said: "Our newspaper wants to ask you for a manuscript. As for the content and theme of the manuscript, there are no big restrictions. You can write whatever you want. It is best to write about the trip to Europe. I have already thought of a name, 'Pilgrimage to the Scientific Journey'."
What do you think?"
Li Yu didn't like the title of the article, so he said, "I can write it, but I will also draw up the title myself."
"No problem! As long as you can submit the manuscript. And the fee we will pay you will be very high. As long as you can write it by yourself, we can give you a fee of at least 100 yuan for one article." Puland added to the fire.
"Really just write casually?" Li Yu asked.
Puland nodded, "Of course, readers are the general public after all. We are not asking you to write some scientific research masterpiece, otherwise everyone will not understand it."
"That'll be easy!"
Li Yu is now a big celebrity. Anyone who has read the newspaper will definitely remember his name now. He is a famous celebrity with great traffic.
Maybe you can still accept advertisements in the future! Although in the era when Li Yu lived, it seemed difficult for a scientific researcher to have enough traffic to accept advertisements, but Li Yu seems to be slowly doing it now, which is quite amazing!
"One more thing," Li Yu asked, "do you have any way to buy pencils or pens? I'd like to buy some."
"Pencils and pens?" Puland was stunned, "Of course there are. I'll get you some from the embassy directly. Just wait for me."
Puland left the office and came back within a few minutes. He put down a dozen pencils and two pens on the table: "The pencils were brought from the UK. There is a big box. I got you a dozen pencils, enough for you."
Used it.”
Then he picked up the pen again: "This is the newly arrived Parker pen. It uses a lucky curve technology called Lucky Curve, which is the most advanced at present."
Li Yu picked up the Parker pen and looked at it. Pens are not cheap now.
This Parker pen can be regarded as a representative work of the pen-making industry in the early 20th century. Parker was able to compete in the pen market, which later became very competitive, largely relying on this patent.
Don't underestimate pens and pencils. At that time, the Qing Dynasty did not even have the ability to manufacture them. It took 20 or 30 years later during the Republic of China to produce them independently. Moreover, the process of starting from scratch was indeed very difficult.
Moreover, the ordinary production process of pencils and pens is not as easy as imagined, let alone advanced technology.
Take this Parker pen as an example. The ordinary fountain pen tongues at that time did not have the ability to buffer ink, or could not absorb and hold excess ink, so it was difficult to ensure that water was discharged evenly when writing. Either the ink would break or a large drop would suddenly drip out.
Parker's Lucky Curve patent not only solves this problem, but also solves the problem of ink overflowing when the pen cap is closed and put into the pocket.
When an ordinary pen is taken out for use again, the air in the pen will expand, causing the ink to squeeze out and drip, staining the paper or the user's hands.
Parker's improvement is very clever. The pen feed is designed to be deep into the pen barrel, and then the rear end of the pen feed is bent and contacts the inner wall of the pen barrel or the wall of the ink bag, which creates a capillary effect and allows the excess ink on the pen feed to flow back into the pen.
Although this technology was very old-fashioned in later generations, it was indeed the most advanced fountain pen in the late Qing Dynasty.
Li Yu was very satisfied with this Parker pen, and then asked greedily: "Is there any more ink?"
Puland immediately took out two bottles from the drawer and said, "Take it and use it!"
"Thank you, Mr. Reporter. You will deduct this money from the subsequent royalties."
"It depends on what you said! It's all for you!" Puland said, "As long as the manuscript can be delivered quickly."
Li Yu said: "That's too bad. There is an old saying in China that you can take advantage of others with short hands."
Puland smiled and said: "I know, the worst case scenario is that I will increase your manuscript fee, and after deducting the fees, it will always be no less than 100 silver dollars."
There was no need for Li Yu to refuse, so he said, "Okay, I'll write it when I get back."