A genius? I just love studying.

Chapter 1 Chen Hui

Chapter 1 Chen Hui
February 17th, the second day of school.

China, Sichuan Province, Chengdu.

Even in Chengdu, known as the Land of Abundance, it is still freezing in February.

Chengdu No. 2 Middle School.

A bright red banner has been hung on the senior high school teaching building opposite, reading "Building the dream of the college entrance examination, pursuing the dream of youth", "If you don't fight, your senior year is in vain", "Strive for a year, spring, summer, autumn and winter, and fight for a lifetime without regrets"...

Class 7, Grade 1

The classroom was bustling with activity, a lively and bustling scene.

The solemnity of the senior high school teaching building opposite had nothing to do with them. They had just returned from the Chinese New Year and had so many new experiences they wanted to share.

Chen Hui did not join in the reunion carnival. In front of him was an exercise book, which he bought for himself with his New Year's money for extra practice.

His classmates can squander their youth, but he doesn't have the capital to do so.

As shown in the figure, the base of the tetrahedron P-ABCD is a rectangle, PD is perpendicular to the base ABCD, PD=DC=1, M is the midpoint of BC, and PB is perpendicular to AM.

(1) Find BC
(2) Find the sine of the dihedral angle A-PM-B

Looking at the questions in the exercise book, Chen Hui frowned slightly. After reading the questions once, nothing remained in his mind. He felt like a sieve full of holes, and the water of knowledge flowed through without leaving any trace.

He was not discouraged and turned back to read the question again.

He had experienced this kind of thing countless times, and he knew that he was different from other students.

After reading the question three times in a row and looking at the figure given under the question, Chen Hui finally had some understanding of the problem.

I understand the question, but can I ask for BC?

Chen Hui frowned again, his mind went blank, without any idea.

He had no idea what the known conditions had to do with BC. He felt like a stranger suddenly ran up to him and told him, "The weather is really nice today," and then asked, "Do you know how old I am this year?"

Chen Hui suppressed the irritable thoughts in his mind and opened the math textbook at hand.

Turn to the table of contents, Chapter 1, Space Vectors and Solid Geometry.

1. Space vectors and their operations
2. The Fundamental Theorem of Space Vectors...

Distant memories began to slowly surface in my mind, and each piece of knowledge emerged extremely slowly like squeezing toothpaste. It was like watching a video with extremely high network latency, and a rotating loading daisy icon kept appearing in my brain.

And this was the result of him memorizing the textbook ten times. He knew that he was different from other students, so he dared not waste a minute or a second.

Fortunately, my efforts were not in vain. Although memorizing textbooks is stupid, it is useful.

He has found a solution to the problem!
There must be an antidote within seven steps of a poisonous snake. This exercise book is a set of exercises that comes with the textbook, and the solutions are naturally in the textbook.

This problem requires space vectors. The first step in solving space vectors is to establish a system. First, find a few perpendicular relationships, establish a space coordinate system, and then write down the coordinates of a few points...

There was no sudden sense of clarity. Chen Hui felt that his brain was like a rusty machine, with difficulty running, but fortunately it was still working.

Use the perpendicular relationship to build the system, and then set BC = 2t, so the coordinates of B are (2t, 1, 0)...

Write down the coordinates of several points, and then based on the fact that PB is perpendicular to AM and the product of the perpendicular vectors is equal to 0, calculate t and get the length of BC!
All this seemed simple, but it took Chen Hui nearly half an hour. When he calculated the length of BC, his forehead was already covered with sweat.

Perhaps because of the fire when he was a child, Chen Hui felt that his brain was countless times slower than that of his classmates. So even though he put in several times the effort of other students, he couldn't even achieve the same results as them.

Chen Hui let out a sigh, wiped the sweat from his forehead, and looked at the second question of the problem.

At this time, a burly middle-aged man with a strong build came slowly down the corridor holding a stack of test papers.

As soon as half of his figure appeared at the door, the classroom, which was originally as quiet as a vegetable market, suddenly became so quiet that you could hear a pin drop. The students all returned to their seats consciously, with their backs straight and their eyes not looking around. One student even took out a book to cover his face, pretending to be studying seriously. Unfortunately, he was so flustered that he didn't notice that he held the book upside down.

The middle-aged man stood at the door, his face stern, and he glanced around the classroom with an air of authority. Wherever his gaze fell, the students lowered their heads. Finally, his gaze fell on the young man in the middle of the classroom.

The boy has a handsome face, a straight head, a straight body and a straight spine. He stands out among a group of high school boys.

At this time, the boy was concentrating on doing his homework and did not notice his arrival, nor did he notice the abnormality in the sudden silence of the classroom.

After sighing, the middle-aged man continued walking towards the podium.

He understood Chen Hui's family conditions and saw Chen Hui's efforts, but he still didn't understand why Chen Hui, who worked so hard, could only achieve the current results.

Perhaps acquired efforts really cannot overcome innate deficiencies!
He knew that there were some things that people didn't have at birth and would never have in their lifetime. This was the way the world was, and even mathematics was like this!
All the doubts and regrets turned into this sigh.

"How many times have I told you?"

The middle-aged man threw the test paper on the podium. The sigh in his eyes disappeared instantly. His eyes widened like an angry lion. "When you encounter solid geometry questions, build the system first, build the system, build the system!"

"How many times do I have to say this?"

The middle-aged man slammed the table, and the chalk box on the table jumped up and down nervously. "If you don't practice for three days, your hands will become rusty. If you don't recite for three days, your mouth will become rusty. I think you haven't read a single day at home during the winter vacation!"

"I'm already in my first year of high school. It'll be my second year, and then my third year. If I don't work hard now, will I work hard when I take the college entrance exam? Or when I start screwing screws in a factory?"

"You are the worst class I've ever taught. Don't ever tell anyone that I taught you. I can't afford to lose face!"

Find the sine of the dihedral angle.

The teacher's anger did not affect Chen Hui. In this state, he only had this question in mind.

After reading the chapter on spatial vectors in his textbook three times, Chen Hui finally found the key to solving the problem.

The dihedral angle is equal to or complementary to the angle between the two face normal vectors. Regardless of whether they are equal or complementary, their sine values are equal, so we only need to find the sine value of the angle between the two face normal vectors.

To find the normal vector, use the formula for perpendicularity between a line and a plane.

The ideas are gradually becoming clear, but there is still a lot of work to be done.

If you are good at geometry, you can use geometric knowledge to solve solid geometry problems quickly and effectively.

Although the method of using space vectors is simple and brainless, it requires a lot of calculations. If the coordinate system is not well constructed, it will be even more difficult.

Calculation is also not Chen Hui's forte.

"137?"

"The boss is awesome!"

At this time, the test papers had already been distributed, and a commotion was heard in front of Chen Hui's right.

Even the middle-aged man on the podium looked over.

This set of questions is not easy to perform. If you can get a score of 137, you can join the competition team. No wonder your classmates are amazed.

Naturally, this little commotion had no effect on Chen Hui.

Five-fourteenths below the square root!

He finally figured out the answer!

Suddenly, a message that only Chen Hui could see popped up in front of him.

[Your math level has increased from level 1 59% to level 1 60%]

Mengxin's new book is asking for collection and reading, thank you