"Draw a closed curve arbitrarily, connecting end to end and not crossing itself. On this curve, prove that four points can be found so that they can be connected to form a square..."

"Creating a square within a closed curve, I think you've heard of it?"

Wang Hao thought a little doubtfully. He felt like he had seen this problem before, but he couldn't remember it.

Mainly because his initial research direction was partial differential equations, and now he is also studying analytic number theory, which does not involve too many geometric issues.

He just felt like he had seen it before and thought it was a classic question in some course.

"Is this a problem..."

"this……"

Wang Hao thought about it carefully and found that he was stumped.

There are really too many sub-disciplines of mathematics. The knowledge involved in different subjects is basically repetitive to a certain extent, but there will definitely be differences in advanced content.

Geometry has a lot to do with function theory, and it also has a certain connection with differential equations, but for proof questions like this in pure geometry, the connection is relatively small.

Wang Hao thought carefully for a few minutes, but could not think of a breakthrough in the proof. He knew that he did not have in-depth research in related fields, and there might even be some basic problems. If he wanted to solve this problem in a short time, it would be almost impossible to just rely on thinking.

impossible.

In this case...

Wang Hao put down the booklet in his hand and asked, "Ding Zhiqiang, are you stuck on which step of this proof, or are there some problems that you can't solve?"

He seems to be checking students' problem-solving progress normally.

Ding Zhiqiang secretly exclaimed, "Sure enough," because he knew that Wang Hao would definitely ask this question. When he found that the problem could not be solved, he might suspect that the student was deliberately making things difficult for him.

That's why he worked hard all night to study related content.

Now comes the use.

"Then I'll tell you."

Ding Zhiqiang said confidently, "To address this problem, I have studied the proof that closed curves have built-in rectangles and equilateral triangles."

"It's the method of using hypothetical line segments. Let me talk about the rectangle first. First, draw a rectangle..."

Ding Zhiqiang began to explain while drawing.

He spent one night carefully studying two proof papers. The proof process was not complicated, but involved some advanced knowledge.

It takes him more time to look up this knowledge and understand it.

Now it is just a matter of explaining what he understands in sequence, and there is no difficulty at all. As for the formulas and theorems involved, he just says them directly and then makes transformations, and there is no need to explain them in too much detail.

This little trick doesn't work in front of Wang Hao.

The same goes for Luo Dayong.

When he discovered that Ding Zhiqiang was explaining to Wang Hao, Luo Dayong came over curiously to see what the specific topic was, and then he discovered that it was the proof of a square within a closed curve.

Luo Dayong knows this problem and knows that no mathematician has been able to prove it so far.

Seeing Wang Hao's confident look, he did not ask directly, but patiently listened to Ding Zhiqiang's explanation.

Later, Luo Dayong was a little surprised, "This student is amazing. He knows so much advanced knowledge even before he is a graduate student."…

"Although I just stated the formulas and theorems, my understanding is probably not very deep. But it is still very impressive."

Wang Hao also feels the same way.

He didn't know yet that no mathematician had solved the problem Ding Zhiqiang asked, but when he discovered that Ding Zhiqiang said something profound, he suddenly felt that he had a really good vision.

This Ding Zhiqiang may be a genius!

Ding Zhiqiang is only a junior in the Department of Physics and a student of Xihai University. Of course, he is not looking down on students from Xihai University, but the admission score of Xihai University is low. The admissions scores of other provinces are just above the key points, and the admission scores are comparable to those of Shuimu University.

, the first time I went to college was a hundred points difference, and on average in mathematics, I was even a difference of 20 or 30 points.

And some students who are talented in mathematics, even if they just memorize formulas and do problems at will, without studying hard or solving problems, they will basically have no problem if they get close to full marks in mathematics.

Of course.

The college entrance examination alone cannot directly evaluate a student. Some students who did not study well in high school can still stand out by working hard in college.

Ding Zhiqiang seems to be this kind of student.

At this time, Ding Zhiqiang seemed to be in a state of excitement. The more he talked, the more excited he became. What made him excited was that he realized that he was giving a lecture to Wang Hao.

Although in name, Wang Hao was inspecting his progress in solving the problem, but in any case, he was also explaining the problem to Wang Hao!

Who can do this?

Who else in the world would be better than me!

Ding Zhiqiang felt a surge of domineering power in his heart, but soon felt a little nervous because many people came to listen to his explanation.

This incident spread in the corridor.

The female teacher surnamed Deng in the office next door is a more gossipy person than Zhu Ping. She saw a student giving a lecture to Wang Hao at the door of the office, and it seemed that the lecture was very exciting, so she kept standing at the door and watched.

Invite others to watch together.

When he found that there were several teachers watching behind him, Ding Zhiqiang felt very nervous. Fortunately, he had reached the final stage of his lecture.

After completing the last step of explanation, Ding Zhiqiang stopped and looked at Wang Hao with some tentative eyes. He didn't know how Wang Hao would react, but what was certain was that Wang Hao definitely didn't know the proof of forming a square within a curve.

He studied it carefully and found that this was a problem that mathematicians had not yet solved.

Wang Hao was silent for a moment and asked, "In other words, you have already studied the methods of proving rectangles and equilateral triangles, and you want to use this to study how to prove squares yourself, right?"

This is Wang Hao's understanding.

He didn't know that a square built into a closed curve was a problem that mathematicians had not yet solved, but by listening to Ding Zhiqiang's explanation, he knew that Ding Zhiqiang understood it based on the answer instead of proving it himself.

So he thought about it carefully and thought that Ding Zhiqiang wanted to study the square proof method himself after seeing the two proof methods.

This is a great way to learn.

I read some proofs of the same type and then tried to complete a proof myself.

Wang Hao suddenly admired Ding Zhiqiang even more, but he still didn't know how to solve the square problem...

Square, because of the particularity of the figure, is obviously more difficult to prove than rectangles and regular triangles.

Wang Hao felt that it was okay to just say that he couldn't think of it for a while, and it was a bit embarrassing. But this was the first time for Ding Zhiqiang to ask himself a question. For such a good student, if he couldn't answer the question for the first time, it might make the student very disappointed.

?

Don't let the students down!

Wang Hao was very concerned about his image in the minds of his students. He simply took a look at the task system and then created a task.

【Task 2】

[Research project name: Proof of a square built into a closed curve (Difficulty: D).]

[Inspiration value: 0.]

"D level difficulty?" Wang Hao glanced at the difficulty level of the task and suddenly realized the problem.

He originally thought it might be an F-level difficulty question. The lowest level of difficulty in research and development is F-level, which is the kind of question that is more difficult in textbooks. He can deduce it after thinking about it carefully.

If it is a D-level difficulty, it means that research and development issues are already involved.

In other words, no one has been able to prove this problem before. It is a pioneering question, and it can reach D level even if it is not difficult.

Many very small problems and conjectures in mathematics are at this level.

The reason why those mathematical problems and conjectures have not been proved is not because of how difficult it is, but because there are too many of them. Those who are capable don't bother to study them, and those who are incompetent naturally needless to say.

The problem of a square built into a closed curve is one of them.

Top mathematicians will not spend a lot of time on this small proof, because even if it is proved, it is of little significance, and it is not easy for inferior mathematicians to prove it.

Wang Hao did not think that Ding Zhiqiang was deliberately making things difficult for him. He felt that the other party might be really researching and wanted to rely on his own ability to solve a problem that no one else had solved.

This spirit is worthy of recognition.

Wang Hao asked, "The proof of a square is much more difficult than that of a triangle and a rectangle. No one has proved it before, right?" He said and looked at Luo Dayong.

Luo Dayong nodded.

Ding Zhiqiang showed a surprised expression. In fact, he was so panicked that he couldn't say a word and didn't know how to react.

Wang Haodao, "However, just because no one has proven it, it doesn't mean that we can't prove it. The research we do is all about cutting-edge exploration."

"In this case, let's analyze it together."

"First, let's take a look at the proofs of rectangles and triangles. This is of great reference value for the proof of squares."

"Let's review it together..."

After Wang Hao finished speaking, he began to repeat Ding Zhiqiang's explanation. Because of his in-depth understanding of basic knowledge, his explanation was much more detailed. Even Luo Dayong also listened along.

After listening to it for the second time, he found that Wang Hao's explanation could make people understand it more deeply.

Soon others came over.

Teacher Deng, who was standing at the door just now, had slowly approached, as if he wanted to know what they were talking about, but Zhang Zhiqiang simply walked over.
To be continued...