The unparalleled talent of the country started from Harbin Institute of Technology

Chapter 78, Is this question easy? How is it easy? A special type of compact four-dimensional manifold without holes

Wang Shuting is the daughter of her sixth brother. She is in the second grade of junior high school this year and school is about to start. Her parents keep saying one thing every day: Look at your ninth uncle, he got 496 points in the college entrance examination, and he is only four points away from the full score.

With a score of 496, Wang Duoyu became famous overnight, especially the "graduation banquet" some time ago, which was so grand. Although the notification time was a bit tight, all the relatives who were supposed to come came.

Even many of my illiterate relatives who don’t know much about the college entrance examination understand the value of 496 points.

Because she was often nagged, Wang Shuting had no choice but to bite the bullet and ask her uncle for advice. In fact, she herself did not like studying, and asking her uncle for advice made her feel ashamed.

"Math problems. Come on, sit down first and let me take a look." Wang Duoyu took the homework book with a smile. When he saw the crooked words and symbols on it clearly, his smile became even wider.

The other little kids were watching obediently at this moment, not daring to speak loudly, and even gradually quieted down.

"Xiaoting, math problems are actually very simple. You just need to remember a universal formula. Whenever you encounter these problems, just apply this formula."

After just scanning the questions, many solutions flashed through Wang Duoyu's mind, but there were not many solutions suitable for junior high school students.

But it doesn’t matter, he can just tell you the universal formula for solving math problems in junior high and high school.

Xue Yuqing, Wang Shuting, Xu Xiangdong and other children all widened their eyes, especially Wang Shuting, who urged urgently to tell them what the universal formula was. At this moment, she did not feel any shame, but only had a strong desire for knowledge.

Wang Duoyu smiled and said softly in the children's expectant eyes:

"It's very simple. The universal formula is to locate the knowledge, break down the problem, translate and transform it, deduce the problem, and review and organize it."

“你看你这道题目，已知:3x-6y-5-0，则2x-4y+6=？题目十分简单对不对？”

Hearing this, Wang Shuting's eyes were filled with clear stupidity and confusion, and her face was full of confusion: "Uncle Jiu, this question is very simple? How is it simple?"

Several other children of the same age or older have already returned their junior high school math knowledge to the teacher, so how could they still remember it?

As for the younger Xue Yuqing and the others, there is no need to mention them at all.

Seeing his niece's expression, Wang Duoyu almost sighed. This child is really difficult to teach.

"Based on the universal formula, should we first identify the key knowledge points of this question? What knowledge does it test us, the candidates? Is it algebra?"

"Okay, now that we've determined the key points, let's break down the problem. For this type of problem, we usually use the global substitution method, which means first simplifying the conditions, then converting the required algebraic expression into a form that can be substituted directly."

In the next few minutes, Wang Duoyu explained the problem to his niece at a relatively slow pace, in a way and tone that he tried his best to make sure she could understand.

“.所以很快求得2x-4y+6=2(x-2y)+6=2*(5/3)+6=28/3，你看结果是不是出来了？”

"Besides the whole-substitution method, there's also a special value method that's also very suitable for you in junior high. Take y = 0, and since 3x - 6y - 5 = 0, we get x = 5/3. Substituting the values ​​of x and y into 2x - 4y + 6, we get the answer 28/3. Isn't that simple?"

"Next, we will review and sort it out. You will be able to solve similar problems easily in the future."

However, Wang Shuting was still confused at this moment, because she had already returned all her knowledge to the teacher during the past summer vacation. Even though her uncle Jiu's explanation was very thorough, she still couldn't absorb so much knowledge all at once. Seeing this, Wang Duoyu could only sigh. One still has to rely on oneself.

If you don't want to make progress yourself and are unwilling to put in the effort, then wanting to achieve certain results is undoubtedly wishful thinking.

For the next half hour, he broke it down in detail and slowly explained it to his niece. After the fifth explanation, she finally understood.

After making sure that she really understood, Wang Duoyu gave her ten similar questions and asked her to do them next to him. She could try to do the questions herself first, and if she really couldn't solve them, they could talk about it later.

Anyway, Wang Duoyu taught her two methods of solving problems, one is the global substitution method, and the other is the special value method. As long as she is proficient in using these two methods, it will not be difficult to solve similar problems.

However, the next half hour surprised Wang Duoyu a little, because Wang Shuting seemed to have her Ren and Du meridians opened up, and she solved all ten questions in just half an hour.

Moreover, all the answers are correct and the problem-solving process is perfect!

So Wang Duoyu praised the child highly, which made the child very happy.

"After you go back, think about it carefully and remember the universal formula I gave you. You can read the book first. Before school starts, use our previous textbook to prepare for the exam."

"You have to spend time on this, otherwise if you just play around, you'll easily forget about it."

After encouraging his niece, Wang Duoyu was about to do his own thing, but she took the opportunity to make a request: could she do the questions next to him?
"No problem, this is your home, you can do the homework wherever you want. And I think you will be disturbed and easily distracted if you do the homework at home, so just stay here with me."

He agreed without thinking twice, and even asked his sister Wang Meili to help keep an eye on things and maintain discipline here.

Then the next day, his house instantly turned into a school, and all the children including Xue Yuqing came.

Each of them was forced here by their parents. Looking at the sad faces of those little ones, it really makes people laugh.

Wang Shuting seemed to have come to her senses. She no longer ran around like before, but stayed quietly at her uncle's house, reading and doing exercises. Her serious study stunned her friends.

In the next few days, Wang Duoyu was busy continuing to improve his paper. In five dimensions and higher dimensions, the geometric representation of shapes no longer seriously restricts their topological possibilities.

Now he needs to derive the basic theory of four-dimensional manifolds, that is, a complete classification of special types of compact four-dimensional manifolds without holes. Once it can be derived, then this result will inevitably prove that the Poincare conjecture holds in four dimensions.

However, this is a relatively long process and requires careful improvement of the paper.

Hua Luogeng hoped that he could make an impact on prime number problems such as the Riemann hypothesis and the Goldbach conjecture, but he did not agree. On the contrary, he thought that he might be able to achieve success on the Poincaré conjecture.

In the 1960s, Smale, a mathematics professor at the University of California, Berkeley, successfully proved the Poincaré conjecture in five-dimensional space and above.

Therefore, this speculation has become more popular, and Wang Duoyu certainly wants to join in the fun.

(End of this chapter)