Making Progress

The teachers of the second year of high school completed the grading of the exam papers and the statistical tally of total scores overnight. This was an efficient team of teachers.

On Thursday morning, in the classroom of Class 2(2), 48 students each held a report card, which also served as a ranking table.

After this ranking table was edited in Excel, it was printed out. The top row consisted of seven cells: Chinese, Mathematics, English, Physics, Chemistry, Biology, and Total Score.

The leftmost column listed the ranks of all 48 students in descending order.

1, Huang Zikun, Chinese 126, Math 145, English 138, Physics 97, Chemistry 90, Biology 99, Total 695

2, Qian Huihui, Chinese 139, Math 122, English 148, Physics 72, Chemistry 81, Biology 80, Total 642

15, Shen Qi, Chinese 88, Math 150, English 95, Physics 86, Chemistry 80, Biology 82, Total 581

The maximum score for Chinese, Math, and English was 150, while the maximum for Physics, Chemistry, and Biology was 100.

Shen Qi's Math score was a perfect 150 again. He was the only one in the entire class to achieve a perfect score in Math.

Thanks to his Math score, Shen Qi's total score ranking directly broke into the top 20 of the class, an improvement of 32 places from the previous final exam.

"Analyzing the data, my Math performance was normal. The class average for this Math exam was 109.5. Of course, I should score higher than the Math average, especially with a Level 3 Math indicator."

"Physics, Chemistry, and Biology also showed normal performance. The class average for these subjects was 80.7."

"Chinese 88 and English 95 are both below the average line, which was expected."

The ranking table showed the scores for all subjects for all students in the class. Shen Qi silently performed a simple mathematical analysis. A 15th-place ranking in the class meant he could give a satisfactory explanation at home.

It was worth noting that Huang Zikun once again secured the first place in the total score for the entire class, leading the second-place student, Qian Huihui, by over 50 points.

"If I want to unseat Huang Zikun, even getting perfect scores in Math, Physics, Chemistry, and Biology won't be enough. This guy has no weak points."

Once a person makes progress, ambition grows rapidly. Shen Qi glanced at Huang Zikun in front of him. To defeat this all-around prodigy, it was necessary to invest in Chinese and English, and also raise Physics, Chemistry, and Biology to Level 2. The investment budget for five subjects was 5200 scholar points.

The system suddenly prompted: "Congratulations to the host for obtaining a new achievement: Tied for first place in the school for Math! Reward: 1000 scholar points."

Shen Qi's Math score was a perfect 150, which was first in the class and definitely first in the entire grade. First place in the grade was equivalent to first place in the school. Tying for first place meant that other classes also had students who scored 150 in Math. Nangang Second High School was, after all, a key high school, and Shen Qi was not the only math prodigy.

What Shen Qi couldn't understand was: "Last time, it was just a regular class test, and I got 150 in Math to be first in the class, and the system rewarded me with 2000 scholar points. This midterm exam is a major test, and I tied for first place in the entire school, why are you only rewarding me with 1000 scholar points? I really need scholar points!"

System: "The host is playing as an advanced player against low-level monsters. A portion of scholar points must be deducted. You can consider the 1000 scholar points as after-tax income."

"Damn it, I can understand that an advanced player fighting low-level monsters gets reduced experience points, but your tax rate is too damn high! What a shady establishment!" Shen Qi felt that as a Level 3 Math player facing ordinary high school math exams, the scholar points he earned were heavily taxed. At Level 2, there was no tax. This indicated that Level 3 was a critical point. In the future, he would need to tackle some high-level instances in the field of mathematics to earn more scholar points.

His deskmate, Chen Xiaoting, had been watching Shen Qi for a long time. Shen Qi hadn't said a word since receiving his report card. He must have been overjoyed, right?

"Shen Qi, you're amazing! You got a perfect score in Math again! And your total score ranking has surpassed mine. I'm so envious!" Chen Xiaoting said enviously. She scored 106 in Math this time, with a total score of 549, ranking 24th in the class.

"What?" Shen Qi snapped back to reality.

"I said, you! Are! Amazing!" Chen Xiaoting raised her voice.

"Oh, oh, it's alright." Shen Qi was happy to have achieved 15th place in the class; after all, his small goal was accomplished.

Chen Xiaoting asked cautiously, "Shen Qi, there's something I don't know if I should say or not?"

"You're not going to tell me to 'MMP', are you?" Shen Qi was taken aback. I surpassed you in total score this midterm exam, Chen Xiaoting, are you holding a grudge? It seems that being a scholar for a long time leads to fewer friends and more loneliness!

However, Chen Xiaoting did not say "MMP." She asked again, "Lately, Shen Qi, you've been going to Teacher Zhang's office every day..."

"Is Teacher Zhang giving you special tutoring?" Chen Xiaoting showed even deeper envy.

"So that's what you wanted to say." Shen Qi smiled. She's overthinking it, overthinking it. Chen Xiaoting is quite well-behaved after all.

"It can't be called simple special tutoring. What Teacher Zhang and I have is mainly discussion and exchange." Shen Qi knew that his daily interactions with Zhang Wanbang couldn't be hidden from the other classmates. They weren't fools or blind; they were in the same classroom, studying together day in and day out. Who could hide anything from whom?

"It seems you're Teacher Zhang's key protégé. That's great." Chen Xiaoting's perception of Shen Qi was subtly changing. To be favored by the homeroom teacher, that's not simple.

"Xiaoting, you don't need to envy me. I'm only good at Math; my other subjects are very average. The content of my exchanges with Teacher Zhang actually has nothing to do with high school Math. It's purely a hobby."

"It sounds so mysterious. I really want to see what you guys discuss."

Shen Qi casually pulled a piece of paper from his backpack. It was "Internal Reference 10" between him and Zhang Wanbang.

"Here, it's this thing. It's not really that mysterious."

Chen Xiaoting reverently took "Internal Reference 10." The paper read:

"The imaginary angle trigonometric formula can be replaced by hyperbolic functions. Euclidean geometry is no longer applicable here... Extended references: 'Discourse on Non-Euclidean Geometry' (J. Bolyai edition), 'New Principles of Geometry with a Complete Theory of Parallels' (N. Lobachevsky edition)."

"Infinite quadratic form refers to the handling of quadratic forms with an infinite number of variables. This is a purely algebraic problem. Advanced Algebra only discusses it generally and not in depth... Extended references: 'Principles of the General Theory of Linear Integral Equations' (D. Hilbert edition)."

"Speaking of integrals, one cannot fail to mention Newton and Leibniz. One can first study Newton's lecture notes during his tenure at the Royal Academy of Sciences: 'A Treatise of Arithmetick'."

Chen Xiaoting found that she recognized all the words on the paper, but she couldn't understand them. "As a math failure, I can only look at it... Among so many foreign names, I only recognize Newton, and that's through learning about Newton's laws of motion in physics class."

"I told you, this has nothing to do with high school Math."

"Shen Qi, then can you tutor me in high school Math?"

"Teacher Zhang explains things very well. He's an outstanding teacher in the city. You just need to listen carefully to his lectures," Shen Qi said sincerely. In his mind, Teacher Zhang was indeed an excellent teacher, just a bit short-tempered.

"I've been listening to Teacher Zhang's Math lectures carefully for almost two years. I've been scolded to tears several times, but I still haven't made any progress," Chen Xiaoting sighed helplessly, looking pitiful.

Shen Qi readily agreed, "Alright. If you don't understand anything in Math, you can ask me."

"Thank you! How do I solve this problem?" Chen Xiaoting seized the opportunity and presented a math problem to Shen Qi.

Shen Qi took the problem and was surprised. "The Fibonacci sequence? You got this problem wrong? I don't understand how you got 25."

Chen Xiaoting covered her face in shame. "Why are you just like Teacher Zhang? I really don't know how to do it..."

Shen Qi said, "Sorry, Xiaoting, I was a bit harsh. Here, I'll tell you a method. Once you master this method, you can solve this type of problem easily. Give me some scratch paper."

"Here!" Chen Xiaoting handed her notebook to Shen Qi.

Shen Qi opened Chen Xiaoting's notebook, revealing densely packed, elegant handwriting filling the pages.

It was clear that Chen Xiaoting studied math diligently. She had meticulously recorded all the concepts Teacher Zhang had taught.

However, math isn't just about diligence and effort. With average talent and no system to help, her math scores wouldn't improve no matter how hard she studied.

"To use the Fibonacci sequence effectively, Xiaoting, you just need to remember that as n approaches infinity, the ratio of the next term to the previous term approaches 0.618. So, you can divide by 0.618 and follow the pattern." Shen Qi wrote an equation in Chen Xiaoting's notebook as he explained.

The Fibonacci sequence, derived from animal reproduction phenomena, is a constant mathematical rule recorded in the "Reading and Thinking" section of high school math textbooks in small print.

Shen Qi had studied sequences extensively when he was self-studying Advanced Algebra and Calculus. He found the Fibonacci sequence to be a very interesting theory with many practical applications in real life. "Xiaoting, have you seen Wong Kar-wai's In the Mood for Love, Zhang Yimou's Hero, or Andrew Lau's Infernal Affairs?"

"Yes, I have. They're all classic films. I've watched In the Mood for Love nine times. I absolutely love Tony Leung." Chen Xiaoting, who enjoyed art films, was puzzled. Wasn't he supposed to be teaching her math problem-solving methods? Why had they veered off into movies?

"These are all directed by great directors, and these films have won many awards. If you observe closely, the list of awards for In the Mood for Love, Hero, and Infernal Affairs all include one specific award: the Best Cinematography Award."

Chen Xiaoting: "So?"

Shen Qi smiled. "So, we have Christopher Doyle to thank. He's a foreigner, and he was the cinematographer for all three films: In the Mood for Love, Hero, and Infernal Affairs."

"When Christopher Doyle shot In the Mood for Love, he used 0.618 in his composition. When he shot Hero, he used 0.618 in his composition. When he shot Infernal Affairs, he used 0.618 in his composition."

"We can criticize the plot of Hero, but we must admit that its visuals are stunning, providing a beautiful and harmonious visual experience. This is because Christopher Doyle understands mathematics. His framing and staging constantly embody the 0.618 Fibonacci sequence's golden spiral."

"Therefore, people who don't understand math can't make blockbusters," Shen Qi concluded. He then asked, "Xiaoting, about that sequence problem just now, can you do it now?"

"Yes, I get it now!" Chen Xiaoting suddenly understood, experiencing the joy of learning. "Shen Qi, you're more interesting and engaging than Teacher Zhang. I never expected the great cinematographer Christopher Doyle to be a math whiz! Come on, I have a dozen more problems I need your help with."

Shen Qi quickly waved his hands. "Whoa, whoa, hold on. Let's make sure you fully digest and absorb today's content first. Xiaoting, don't rush or panic. Rome wasn't built in a day. Let's make a deal: one problem a day. Learning has no end; accumulating knowledge leads to qualitative change. I'm busy, I don't have that much time to be your full-time math tutor."

"How about two problems a day?" Chen Xiaoting's thirst for knowledge was urgent.

"No, one problem a day," Shen Qi firmly shook his head.

"Since you like watching movies, I'll treat you to a movie ticket. How about two problems a day?" Chen Xiaoting subtly took out her phone, intending to send Shen Qi a QR code.

Shen Qi was displeased. "Chen Xiaoting, can scientific knowledge be measured by money? Can mathematical skills be exchanged for movie tickets?"

"I... I'm sorry." Chen Xiaoting lowered her head in shame. Knowledge is priceless, and science is sacred. She realized how superficial her thinking was.

"Which cinema is the ticket for?" Shen Qi asked.

"Feiyang Cinema, 3D-MAX."

"It's no fun watching alone. You come with me. You don't have to treat me; we'll split the cost, buy our own tickets."

"But I don't have much time to watch movies with you. You know, we second-year students only get one day off a week, and I still have to practice my violin..." Chen Xiaoting said hesitantly.

Shen Qi returned Chen Xiaoting's notebook to her. "Classmate Xiaoting, improving your math scores really can't be rushed. Take it slow, otherwise, pulling up seedlings to help them grow will be counterproductive."

"Then I'll see which day I can ask for half a day off from my violin teacher... I can only spare half a day at most."

"Don't let this happen again, okay? Two problems a day. Now, tell me, what other math problem don't you understand?"