A genius? I just love studying.

Chapter 27 Euler Integrals
During evening study, An Chengzhang walked up to the podium, holding the math team's materials. He looked at the dozen or so team members waiting for their turn and said, "I've distributed the analytic geometry materials to everyone. If you have any questions, you can ask me now."

There was silence in the classroom.

Analytical geometry is not too difficult in high school. It is more about the use of techniques and calculations, and there is not much that people do not understand.

So no one asked any questions.

Seeing this, An Chengzhang smiled inwardly and calmly continued his lecture, "Let me review the standard equation of a circle... the general equation of a circle..."

At the same time, he wrote down the formulas on the blackboard.

Of course, mathematics does not require rote memorization, but if you can remember these formulas, you can save a lot of time in derivation.

Chen Hui stared at Teacher An who was explaining on the podium. Even though he already knew all the knowledge, he still listened to Teacher An's explanation attentively.

According to the experiment in the afternoon, listening carefully can increase the speed of proficiency improvement.

"The formula for chord length is the square root of 1 plus K squared times..."

The class passed quickly. Teacher An had already sat down and was drinking water from his thermos. The students also stood up to stretch or go to the toilet.

Chen Hui still stared at the blackboard, frowning slightly.

After listening carefully to a math class, he did not feel that he had learned much and his proficiency had improved rapidly as he had before when listening to geography and English.

This feeling is hard to describe. It's like spring has arrived. Even if you can't see the seeds under the soil, you can vaguely feel that the sprouts are trying hard to break through the restrictions of the soil and are about to break out of the ground. This feeling is so strong.

The feeling of the tender shoots hitting the mud is real!

But in the math class just now, Chen Hui didn't feel that way.

"Is it because I already know all this knowledge by heart, so even if Teacher An explains it again, it's hard to gain anything new from it?"

Chen Hui quickly came up with a guess. Since listening to the lectures did not bring any additional improvement, he stopped wasting time and turned his attention back to the textbook.

Soon, the class bell rang. An Chengzhang stood up and waited calmly for the bell to end before speaking.
"Last class, I reviewed analytic geometry. Since everyone has no problems, it means you've mastered the key points in the material. Now, let me give you a high-level overview."

As he spoke, he turned around and wrote a question on the blackboard.

Given that the left and right foci of the hyperbola x^2/3-y^2=1 are F1 and F2 respectively, draw two perpendicular lines L1 and L2 through F2 that intersect the right branch of E at points A, C and points B, D respectively. Find the minimum area of ​​quadrilateral ABCD.

An Chengzhang was even thoughtful enough to draw a diagram for his classmates on the blackboard.

"???"

Seeing this question, many students were stunned.

They can calculate the area of ​​a quadrilateral, but this question doesn’t provide anything except drawing a quadrilateral!
However, those who can enter the mathematics competition team all have some ability. After thinking for a while, everyone started to write and draw on the draft paper. Analytic geometry is nothing more than setting up analytical expressions and equations.

Some smart ones also opened the learning materials that Teacher An distributed yesterday. Since the purpose was to assess their learning outcomes, the methods to solve the problems were naturally in the materials distributed yesterday.

When Tan Junjie saw the question, he already had an idea in his mind. There are many formulas for the area of ​​a quadrilateral, but since the diagonals are perpendicular, then S=1/2 (the product of the diagonals) is naturally the answer.

The length of the diagonal is not given in the question, but by assuming the equations of the two diagonal lines and applying Vieta's theorem together, we can deduce the length of the chord, and the area of ​​the quadrilateral will naturally come out.

As for the minimum value, we can easily get it by finding two constraints from the graph and substituting them into the calculated area.

The rest is all calculation.

Looking at his classmates who were frowning, Tan Junjie finally regained some confidence. He was sure that he could solve the problem within ten minutes.

Subconsciously, he looked at the newcomer sitting in the last row of the classroom.

"?" He found that Chen Hui was actually reading other books!

mad! So crazy!
Tan Junjie didn't know how to describe his feelings at the moment.

Of course, he didn't think that Chen Hui couldn't solve this problem, but he didn't expect that Chen Hui was too lazy to even do it.

Is it disdain?

An Chengzhang also noticed Chen Hui's actions.

It was okay before. The content taught in normal classes was naturally too simple for Chen Hui. It was okay for him to read books and learn his own things.

But what he talked about in the math competition team was at least something that top math students needed to think carefully about before they could come up with it.

Especially the question on the blackboard, which is more difficult than the last question in the college entrance examination mathematics.

Chen Hui was fine in the last class, why did he suddenly stop paying attention in this class? What was he doing?
An Chengzhang took a step forward and walked towards Chen Hui in the last row.

Chen Hui was completely immersed in his studies and naturally did not notice An Chengzhang's unusual movements. Liang Peixuan, who was sitting next to Chen Hui, looked up, then glanced at Chen Hui, but did not remind him in the end.

He knows Chen Hui.

No reminder necessary.

Seeing that Chen Hui was oblivious to the surroundings, An Chengzhang did not warn him. Instead, he quietly walked behind Chen Hui, looked over his shoulder at the book on his desk.

1. Gamma function (Γ function)
Expression: Γ(s)=∫x^(s1)e^(x)dx, where s>0.

Properties: Γ(s) is continuous and differentiable in the domain s>0.

Recursive formula: Γ(s+1)=sΓ(s). From this, we can deduce that for any positive integer n, Γ(n+1)=n!.

The Γ function has the property of extension on the image, and meaningful function values ​​can be obtained when s<0 through Γ(s)=sΓ(s+1).

Covariate formula: For s∈(0,1), Γ(s)Γ(1s)=sin(πs)π
"Euler integral."

"Yo, mathematical analysis!"

An Chengzhang sighed inwardly. This textbook was so familiar to him. It was compiled by East China Normal University and published by Higher Education Press. This was also the textbook he studied when he was in college.

"This kid is actually teaching himself advanced mathematics!"

The course of mathematical analysis is not difficult, but it is still a bit challenging for a high school student. In addition, mathematical analysis is the basis for subsequent courses such as complex analysis, functional analysis, and real analysis. After learning these, you can study Fourier analysis and harmonic analysis.

Of course, these are still too far away for Chen Hui now, but at least it shows that Chen Hui is on the right track.

Back then, An Chengzhang was also a graduate student in mathematics, but later he gave up being a scholar and became a mathematics teacher.

Wow!

Chen Hui didn't notice An Chengzhang behind him. He flipped the pages of the book and woke up the distracted An Chengzhang.

"We've learned Euler integrals!"

An Chengzhang was very familiar with this edition of the mathematical analysis textbook, and he had already read most of it, which meant that Chen Hui was almost done with it.

He looked at the watch on his wrist and found that more than ten minutes had passed. Without interrupting Chen Hui, An Chengzhang walked back to the podium and said, "Okay, now I will tell you about the solution to this problem..."

(End of this chapter)