pjbooks Chapter 18: Damn it, can't you speak properly and stop acting so arrogant!
Chapter 18: Damn it, can't you speak properly and stop acting so arrogant!
Han Chuan, who was returning to the classroom with his math competition materials, had no idea that he had already been targeted by the physics teacher.
However, he was quite interested in participating in the National High School Mathematics League, as suggested by his math teacher, Cao Wen.
If it were before, seeing the words "National High School Mathematics League" two months ago would have seemed as absurd as winning 50 million in the lottery.
After all, back then, even a small math quiz in class would leave him frowning for ages, and he couldn't even pass. His monthly exam score of 67 was the score he achieved before his rebirth.
If someone were to take an exam after being reborn without any prior education, they might not even get a 7, let alone a 67.
Even if you do get it, it's highly likely you just guessed one of the multiple-choice questions correctly.
After all, he couldn't even understand the assembly language back then, and his junior high school foundation was a complete mess.
But it's different now.
What he holds in his hand now is not something unattainable.
Moreover, standing behind him now are Ge Jun, the "Mathematical Emperor," and Zhou Peiyuan, one of the founders of modern mechanics in China.
With these two big shots protecting him, coupled with his extraordinary learning speed after his rebirth—knowledge points that others take days to fully grasp, he can master in a day; problem-solving skills that others need to repeatedly practice to master, he can basically master in one go through concrete thinking skills.
If you can't even handle a 'small' CMO math competition, do you deserve the identity of a reborn person?!
Thinking about this filled Han Chuan with enthusiasm.
Having been a poor student for over a decade in his past life, he wants to experience what it's like to be a top student in this one!
He had already planned it out. He would talk to Mr. Ge Jun and Mr. Zhou Peiyuan about the competition later and ask these two big shots to "train" him!
.....
Just as I returned to my seat, Li Hao, who was frowning and doing his test paper, came over.
"Brother Chuan, you're finally back! Quickly help me figure out how to solve this problem. I just can't seem to get it right."
"Let me see."
Han Chuan placed the math competition materials on the corner of the table, turned to look at the math test paper that Li Hao pushed towards him, which was a big problem in solid geometry.
[As shown in the figure, in the quadrangular pyramid P−ABCD, the base is ABCD, PA⊥base ABCD, AB||CD, AD⊥CD, AB=1, PA=AD=CD=2.]
【(1) Prove that BE||plane PAD;】
【(2) If AE⊥plane PBC, find the sine of the dihedral angle B−EC−P.】
The solid geometry problem wasn't difficult; at least for Han Chuan, it was practically no challenge at all. He glanced at the answers to the two sub-questions and they were already in his mind.
However, for Li Hao, this question was still quite difficult.
When Han Chuan went to Cao Wen's office, Cao Wen had already written half a page of formulas on a draft paper. He crossed them out halfway through, then wrote them out again, and crossed them out again. The paper was crumpled from his repeated revisions.
"This question isn't difficult, it's very simple. I'll explain it to you and you'll understand."
Taking the pen from Li Hao, Han Chuan smiled and said, "This is a typical combination problem of 'proof of line-plane parallelism + calculation of dihedral angle'. The answer to question (1), proving that BE||plane PAD, can be seen directly."
"The simplest method is to find a plane parallel to plane PAD and prove that BE lies in this plane; or to construct a parallel relationship using proportional line segments."
As he spoke, he redrawn a new figure on the draft paper, following the diagram on the test paper, and then extended the auxiliary line through point B, parallel to CD.
Then, Han Chuan looked at Li Hao, pointed to the auxiliary lines, and asked, "Look at this, what has this ABED area become?"
Looking at the auxiliary extension lines on the manuscript paper, Li Hao tentatively replied, "A parallelogram?"
Han Chuan nodded and smiled, "Yes!"
"Because when the position of E satisfies DE=AB=1, quadrilateral ABED automatically becomes a parallelogram."
"But just looking isn't enough; you have to prove it."
"So, let's take a point here, E, as the midpoint of CD. Then we can get CE=DE=1, and from time to time, we can construct parallelogram ABED?"
In parallelogram ABED, is AD||BE?
"Furthermore, since AD ⊂ plane PAD, and BE is not within plane PAD, does that mean BE is plane || PAD?"
Is it simple or not?
With his pen, Han Chuan quickly wrote down the answer to the first sub-question on the draft paper, and then casually described the entire solution process.
Li Hao, who had listened to the whole story, gradually changed from being confused to having a bright look in his eyes.
"I see! The key is this auxiliary line! Right, Brother Chuan? Once we find this auxiliary line, we can construct a parallelogram!"
Han Chuan smiled and nodded, saying, "Yes!"
He paused for a moment, then continued, "However, there are other solutions to this question, which I will explain later."
Let me explain the second question to you.
"The second question is not difficult either. Its core is to find the plane angle of the dihedral angle and then use spatial vectors to calculate it."
"The plane angle of a dihedral angle can be determined by drawing auxiliary lines perpendicular to the edge in each of the two half-planes..."
"....."
"The answer is √2/2, that's it."
In just a few minutes, Han Chuan finished explaining the second question.
Unlike the enlightenment he gained from the first question, Li Hao's eyes began to gleam with confusion when faced with the more complex second question.
"Wait, wait, Brother Chuan, slow down."
"How come point F is the same as the point in the diagram? Where did this come from?"
Li Hao scratched his head anxiously, realizing he couldn't keep up with Han Chuan's explanation at all on the second question.
Although the approach to the first question was ingenious, it was essentially still based on the construction thinking of plane geometry, which he could barely keep up with.
But the vector method in the second question was a completely unfamiliar language system to him—establishing a coordinate system, coordinates, normal vectors, dot products—these things were like mush in his brain, impossible to stir up.
Before Han Chuan could answer, a voice interrupted from the side.
"Just look at the auxiliary parallel lines; Han Chuan has already drawn them for you."
Upon hearing the sound, Han Chuan and Li Hao looked over simultaneously. Chen Li, the math class representative of Class 09, was standing next to them, his face full of interest, staring intently at the steps and answers that Han Chuan had written on the paper.
Before Li Hao could answer, he shifted his gaze to Han Chuan and asked, "In the second question's algebraic calculation, you didn't use the generalization of the three perpendiculars theorem; you used the vector method instead?!"
Upon hearing this, Han Chuan nodded and asked, "What's wrong?"
Chen Li: "But Teacher Cao never covered this. This is a knowledge point that Teacher Gong, who teaches competition students, would explain. How do you know it?"
Han Chuan asked doubtfully, "The vector method is simpler than the three perpendiculars theorem, isn't that obvious at a glance?"
Chen Li: "..."
Watching this scene unfold, Li Hao's confusion had turned from muttering under his breath to a face full of question marks.
Chen Li took a deep breath and said, "This solution requires establishing a coordinate system. After establishing the coordinate system, we calculate the normal vectors of the two surfaces and then use the dot product to deduce the included angle."
"Moreover, if the coordinate system isn't established correctly, the subsequent computational workload will double, and establishing a coordinate system is much more difficult than the geometric method. How is it simple?"
"Uh... is it that difficult?"
Han Chuan hesitated for a moment, then said, "Isn't establishing a system basic knowledge?"
At least that's how Ge Jun taught him.
Chen Li: "..."
Damn it, can't you speak properly and stop acting so arrogant!
His lips twitched, and he looked at Han Chuan, pointing to the calculation paper on the table, and asked, "May I borrow your pen to copy your solution process?"
He had been standing to the side listening for quite a while, and he was very interested in Han Chuan's approach to building the department.
Last semester, he listened to Teacher Gong's lecture on vector methods in the competition training class, and it took him more than a dozen practice problems to barely master the vector method for solving solid geometry problems.
However, Han Chuan's method of establishing the department seems to be different from Professor Gong's.
He even had a vague feeling that Han Chuan's method of establishing the department was even simpler than Professor Gong's!
Thinking of this, Chen Li felt an absurd feeling of 'How is this possible?'
However, he did want to copy Han Chuan's solution approach and system construction steps, and then study them.
Especially the location of this department, even he had to admit that Han Chuan's choice of location was extremely clever.
Instead of using the "right angle of the base" method, he placed the origin in another corner, but through this point, the other key geometric points can be seen at a glance.
Just like the moon in the sky, it's so obvious that there's no need to search for it.
Last year when he participated in the competition, he didn't even pass the school's exams. This year, he's going to fight again and he'll definitely make it to the semi-finals!
Therefore, he was very interested in this geometric solution.
At the desk, Han Chuan nodded and said, "No problem."
As Chen Li reached for the pen and was trying to copy down Han Chuan's solution steps, he suddenly noticed the competition materials on the table.
"Are you also participating in the math competition, Han Chuan?"
After flipping through the math competition materials, Chen Li looked over with a look of astonishment.
Han Chuan: "Teacher Cao just gave this to me. Let me take a look and try it out."
"What? What?"
Upon hearing this, Li Hao immediately leaned over, his eyes wide, and snatched the competition materials from the table: "The National High School Mathematics League? The registration form?!"
"Holy crap, you're really going to participate in the math competition?!"
Li Hao has a loud voice, and this shout immediately attracted the attention of the other students.
Zhou Yu, sitting in the front row, was the first to turn around, his neck twisted like an owl's: "What? Who wants to participate in the math competition?"
"Han Chuan!"
Holding up the registration form, Li Hao's expression was even more excited than the person in question: "Teacher Cao gave it to him personally! It's the registration form for the National High School Mathematics League!"
These words were like a stone thrown into a calm lake. The previously noisy break time suddenly fell silent for a moment, and then erupted into chaos.
A few girls chatting in the front row turned around to look, and a few boys in the back row immediately surrounded them.
Zhou Yu leaned over from his seat, snatched the registration form from Li Hao's hand, glanced at the words on it, and his mouth formed an "O".
"Holy crap, really? Brother Chuan, you're going to participate in a math competition?"
The surrounding classmates also gathered around out of curiosity, and started discussing it animatedly.
"A math competition? I heard that only top students who score at least 130 or 140 can participate, right?"
"I remember Han Chuan only got 93 points in the last monthly exam, right? How can someone with 93 points even register?"
"I think only Chen Li, the math representative in our class, signed up once before, right?"
"....."
The discussions grew louder, and all sorts of gazes fell on Han Chuan—some were surprised, some admired, and a couple were filled with doubt and disapproval.
After all, participating in competitions is something that is too far removed from the lives of most students in regular classes.
Although everyone has heard of it, that's all they've heard of it.
For most students in Class 09, scoring above 140 in math was an unattainable dream.
Han Chuan felt a little uncomfortable under their gazes, so he took the registration form back from Li Hao's hand and explained, "I'm just trying it out."
"Want to give it a try?"
Standing to the side, Chen Li's expression was particularly complex: "The high school math competition is divided into two rounds. The first round is worth 120 points, and the second round is worth 180 points. There are three major questions to be chosen from algebra, geometry, number theory, and combinatorics, and each question is worth between 50 and 60 points."
As he spoke, his gaze fell on the stack of math competition materials on Han Chuan's desk, and he continued, "The first test examines basic skills, and the second test examines the depth of thinking."
"To advance to the semi-finals and win a medal, you need to consistently score above 100 points in the first round and above 150 points in the second round."
"Whether it's the first or second attempt, the difficulty is much greater than the college entrance examination."
Do you know how many points I scored when I took the exam last year?
Before anyone else could ask, Chen Li continued, with a hint of self-deprecation: "I scored 137 on the monthly exam, but when I took the first round last year, I only scored 89, and I didn't even qualify for the second round."
Upon hearing this, the other students sitting around the table erupted in uproar.
"Holy crap! Is it really that hard?"
"Li Ge only scored 89 points, and didn't even make it to the second round?"
"Hiss! That's terrifying!"
"Won't Han Chuan be in trouble then? He only got 94 points on the last monthly exam."
"..."
As far as his classmates were concerned, they knew what level Chen Li was at; he was a typical top student in the class.
Since the beginning of high school, my math score has never fallen out of the top 20 in the grade. My monthly test scores are consistently above 130, and I can occasionally reach an exceptionally high score of 145.
Even he only scored 89 points in the first test, so they couldn't even imagine how ridiculously difficult the math olympiad was.
After all, for most students in Class 09, an ordinary class, the college entrance examination questions were already very, very difficult.
Sitting in his seat, Han Chuan smiled and said, "I think I can make it to the second round."
Chen Li: "Then I'll wait."
After a pause, he added, "If you make it to the second round, maybe we can go to the provincial competition together."
Before Han Chuan could even reply, his best friend Li Hao immediately exclaimed, "Brother Chuan, Brother Chuan, if you really make it to the semi-finals, I'll buy you a banner! It'll say 'The God of Academic Excellence in Class 09!'"
"How is it!?"
Han Chuan rolled his eyes at him: "You're talking nonsense."
He paused, then continued, "I didn't tell you before, but tonight's problem has at least three other solutions besides the one I taught you."
"Your task for the next evening study session is to figure out at least one other different solution."
Upon hearing this, Li Hao immediately deflated, slumped onto the table, and yelled, "This is revenge! Revenge! I didn't even understand what you were explaining!"
.....