Help me read the answers to the questions in the dream!

How many dreams are there?
He would always have such dreams. He knew that there would be an exam, but he couldn't find his classroom after walking up and down the building. Otherwise, when he entered the classroom and the teacher came, he found that he had never attended such a class before. He didn't have a textbook either. He sat in his seat and felt anxious and afraid.
The most common dream was to take out a book, only to find that he couldn't understand a single word on it, while the others were very certain. The teacher called me up. I was tongue-tied and unable to speak. All the students turned their heads and looked at me with cold and disdainful eyes, making me tremble in my dreams. After waking up, in the dark night, he would laugh happily in bed, glad that he had finally grown up.
He had finally grown up and escaped from the sea of suffering. I finally didn't have to go back to that era of suffering and nightmares where I had to study mathematics and physics.
After I entered Bei Er, I didn't understand anything the math teacher taught me. It was a very uncomfortable feeling. The teacher was talking non-stop on the stage, and the students were listening with great interest. Only I sat alone in a daze, with a heavenly book in front of me. I tried my best to watch and listen, but I couldn't enter their world. The only thing I can do is to use a pen to draw on the Tomes of Arcane. In one semester, he drew a book full of geometry or algebra, which amazed my tutor at home. He even took one back to show his classmates. After reading it, the boys who were studying in the Institute of Science and Technology appreciated it. I haven't forgotten that after almost twenty years, there are still people who can remember my name and come to tell me that they once admired my mathematics textbook.
At that time, only students with good grades in math and science could become good students envied by their classmates. No matter how good a person was in humanities, if they were bad at math, it would not be easy for them to raise their heads in class. I remember that once, I got first place in the Chinese reading test in the third year of junior high school. When my name was announced, the physics teacher came to class and said in a very regretful tone,
"What a pity! He was so good at Chinese, but why was he so bad at physics? What a pity!" He smiled and shook his head.
My classmates also turned around and smiled at me while shaking their heads. Probably because I had just won an award, the class was still filled with a warm and friendly atmosphere. At that time, she hated her teacher and herself. For my sake, there are endless tutors at home. However, at that time, no one knew that I was born "blind to numbers." If there was such a disease in the world, I would be such a person. Unlike " illiterates ", who could be cured as long as they received education, number blindness was incurable.
She stumbled into the second semester of the third year of junior high school, and she had to take a make-up exam in mathematics before she could take the graduation exam. On the first night of the make-up exam, he knew that the situation was serious. He did not dare to sleep that night and memorized a geometry book from beginning to end. However, he knew that it was useless. He was just doing his best.
The next morning, in the middle of the math class, the teacher suddenly stopped and said that he needed to revise. He wrote four questions on the blackboard for the class to calculate. As usual, I fiddled with the numbers in my math book, but I was thinking about the make-up test in the afternoon.
After class, the teacher left, but the students in the class started to make a fuss. They thought that the four questions had nothing to do with the paragraph being taught. The teacher must have had an ulterior motive for the four simple questions to be on the blackboard.
The make-up exam was scheduled for the first class in the afternoon in another classroom. The seven people in our class who had to take the make-up exam suddenly became the most loved ones in the class. The thirty or so outstanding students were divided into seven groups, and each group was responsible for teaching one student. After teaching for half a day, there was no effect, so he simply wrote out the standard answers to the four questions and taught us to memorize them. Among the four questions, I memorized three questions and got 75 points on the afternoon make-up test paper. I was finally able to participate in the graduation examination and finally graduated.
So many years have passed, but the scene of that day still remains in my heart. If the two years of middle school mathematics were a nightmare, then the last class was a warm and beautiful memory. I still remember how my classmates laughed and sighed as they taught us. The classroom was filled with tolerance and reluctance before parting. That sincere friendship warmed my heart and made me, who never cried, cry hard at the graduation ceremony. The math teacher and the Chinese teacher sitting on the podium were smiling at me. Their eyes were equally concerned and loving, sending me away from my junior high school days.
1. In the second paragraph, the teacher " smiled and shook his head ", and the students also " smiled and shook their heads at me ". Was the laughter here mocking? Why?
2. The sixth paragraph says," Teacher must have ulterior motives." Do you know what Teacher's ulterior motives are?
3. Do you think the math teacher in the article is right or wrong? Please explain it in context.
4. The last paragraph said," If the two years of middle school mathematics were a nightmare, then the last class was a warm and beautiful memory." Why did the author say that the last lesson was a warm and beautiful memory? And?

Answer 1

" Geometry-Shocking Dreams " was a well-known online novel by Tian Can Tu Dou. The following is a summary of the plot and content of the novel:

The novel tells the story of a young mathematician named Zhang Qiling who explored the world of geometry in a mysterious dream. In the dream, he met a mathematician named Mo Fan, who introduced him to the basic concepts of geometry and mathematical theorem. Zhang Qiling began a wonderful mathematical journey. In his dreams, he encountered all kinds of strange geometric figures and mathematical problems and solved them through his own efforts.

At the end of the novel, Zhang Qi Ling wakes up and finds himself back in the real world, but his exploration of the geometric world still bothers him.

If you want to understand the storyline and mathematical content of the novel, you can refer to the following answers:

The plot of the novel mainly involved several important concepts in the field of mathematics, such as functions, equations, geometric figures, and calculus. Qiling's mathematics journey in the dream mainly involved some basic geometry problems such as triangle, quadrilateral, pentagon, and circle. By solving these geometry problems, he gradually mastered some basic concepts and theories of geometry and achieved some mathematical achievements in his dreams.

In the novel, Mo Fan had introduced some important mathematical theories to Zhang Qiling, such as the Gauss Elimination Method, the Eulerian theorem, and Fermat's theorem. Zhang Qiling successfully solved some geometry problems through these theories.

There were also some mysterious elements in the novel, such as dreams, souls, and supernatural phenomena. These elements had an important impact on the development of the story.

I hope these answers will help you better understand the storyline and mathematical content of the novel.