Teachers from all subjects in the second year of high school completed the review of the test papers and the total score statistics overnight. This is an efficient team of teachers.

On Thursday morning, in the classroom of Class 2 (2) of Grade 2, 48 students each had a transcript, which was also a ranking list.

This ranking table is printed after editing in Excel. The top row consists of seven cells: Chinese, mathematics, English, physics, chemistry, biology, and total score.

The leftmost column ranks in descending order to draw the rankings of 48 students in the class.

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

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

...

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

The full scores for Chinese, mathematics and English are 150, and the full score for physics, chemistry and biology are 100.

Shen Qi got full marks in mathematics again, and he was the only one in the class who got full marks in mathematics.

Relying on the contribution of mathematics, Shen Qi's total score ranking directly reached 20 in the class, which was 32 places higher than the last final exam.

"Analysis from the data, my math performance is normal. The average score of the whole class in this math exam was 109.5 points. Of course, I have to score higher than the math average. After all, the math index of level 3."

"Physics, chemistry and biology are also normal, with the average score of the whole class being 80.7 points."

"Chinese 88 and English 95 are all below the average, as expected."

The ranking table shows the scores of all subjects in all students in the class. Shen Qi silently conducted a simple mathematical analysis and ranked 15th in the class. You can get an explanation when you go home.

It is worth noting that Huang Zikun once again won the first place in the class in total, and led the second place Qian Huihui by more than 50 points.

"If Huang Zikun is defeated, he will not be as good as the full score in mathematics, physics, chemistry and biology. This guy has no weaknesses."

Once a person makes progress, his ambition will grow rapidly. Shen Qi glanced at Huang Zikun in the left front. If he wants to defeat this all-round player, it is necessary to invest in Chinese and English, and both physics, chemistry and biology must be upgraded to level 2, with a total investment budget of 5,200 points in five subjects.

The system suddenly prompted: "Congratulations to the host for obtaining new achievements: tied for the first place in the school in the mathematics exam! Reward 1,000 points of academic master points."

Shen Qi scored 150 in mathematics, and was the first in the whole class, and definitely the first in the whole grade. The first in the whole grade is equivalent to the first in the whole school, and it is tied for the first place. Some people in other classes also scored 150 in mathematics. After all, Nangang No. 2 Middle School is a key middle school, and there are more than Shen Qi, a master of mathematics.

What puzzled Shen Qi was: "I just got the first place in the class in the class for 150 in mathematics. The system rewards me 2,000 points of academic master points. This midterm exam is a big test, and I got the first place in the school. Why did you reward me 1,000 points of academic master points? I really need the best score!"

System: "If the host fights low-level monsters as a high-level player, a part of the top score must be deducted. 1,000 top scores can be understood as after-tax income."

"Damn, I can understand that the experience value of high-level players' low-level monsters is reduced, but your taxes are too heavy! Black shop!" Shen Qi corresponds to the ordinary high school mathematics exam as a level 3 math player. The points you get from the top student points need to be paid heavy tax. At level 2, you obviously don't pay tax, which means that level 3 is a critical point. In the future, you need to make some advanced copies in the field of mathematics to get more top student points.

Chen Xiaoting, a deskmate, has been paying attention to Shen Qi for a long time. Shen Qi never said a word after getting the transcript. He must be very happy, right?

"Shen Qi is so awesome, and she scored the full mark in mathematics again! And your total score ranking is surpassed by me, I am envious and jealous!" Chen Xiaoting said enviously that she scored 106 points in mathematics this time, with a total score of 549, and the class ranked 24th.

"Water?" Shen Qi came to his senses.

"I said, you! Good! Awesome!" Chen Xiaoting raised the volume.

"Oh, it's okay." Shen Qi was still happy to be able to get the 15th place in the class, after all, the small goal has been completed.

Chen Xiaoting asked carefully: "Shen Qi, I don't know whether I should speak or not?"

"You won't want to say MMP to me, right?" Shen Qi ate a whale. My total score ranking in this midterm exam surpasses you. Chen Xiaoting, are you holding a grudge? As expected, you will find that you have fewer and fewer friends and more loneliness!

However, Chen Xiaoting did not say a MMP, and she asked again: "Since recent times, Shen Qi, you have been running to Teacher Zhang's office every day...

"Is Teacher Zhang giving you a small hospital?" Chen Xiaoting showed deeper envy.

"So you want to say this." Shen Qi smiled. After thinking too much, Chen Xiaoting is still very skilled.

"It can't be considered a simple little training. Teacher Zhang and I mainly discuss and communicate." Shen Qi knew that the daily life between him and Zhang Wanbang could not be hidden from other classmates in the class. They were not fools and blind people. They were all classmates in the same classroom day and night, so who could hide it from anyone else.

"It seems that you are the key training target for Teacher Zhang, it's great." Chen Xiaoting's understanding of Shen Qi is changing subtly, and it is not easy to be favored by the class teacher.

"Xiaoting, you don't have to envy me. I have better math grades and my other subjects are average. The content of the communication between me and Teacher Zhang actually has nothing to do with high school mathematics, it is purely amateur interests."

"What a mysterious look. I want to take a look at your communication."

Shen Qi took out a piece of paper from his schoolbag, which was the "internal reference 10" between him and Zhang Wanbang.

"Here, this thing is actually nothing mysterious."

Chen Xiaoting took "Inner Reference 10" extremely sacredly, and the paper reads:

"The triangular formula of imaginary angles can be replaced by hyperbolic functions, and Euclidean geometry is no longer applicable here... Extended literature "A Discussion on Non-Euclidean Geometry" (J. Borjo Edition), "New Foundations of Geometry with Parallel Complete Theory" (Robachevsky Edition). "

"Infinite quadratic type is the treatment of quadratic type itself with infinite multiple variables. This is a purely algebraic problem. The higher generation is only general and not in-depth... Extended literature "Principles of General Theory of Linear Integral Equations" (Hilbert Edition)."

"When it comes to points, we have to mention Newton and Leibniz. We can first study Newton's lecture notes when he served in the Royal Academy of Sciences: "Popular Arithmetic."

...

Chen Xiaoting found that she knew all the words on the paper, but she couldn't understand them: "As a math scumbag, I can only read them... I only know Newton among so many foreign names, but I still know them through the physics class Newton's three laws."

"I said it has nothing to do with high school mathematics."

"Shen Qi, can you teach me about high school mathematics?"

"Teacher Zhang is very good. He is an excellent teacher in the city. Just listen to his lectures carefully." Shen Qi said sincerely. In his mind, Zhang Wanbang is indeed an excellent teacher, but he has a little bad temper.

"I have been listening to Teacher Zhang's math class carefully for almost two years. He has been scolded and cried several times, but he still has not made any progress." Chen Xiaoting sighed helplessly, feeling pitiful.

Shen Qi said cheerfully: "Okay, if you don't understand mathematics, please ask me."

"Thank you! How do you solve this problem?" Chen Xiaoting struck while the iron was hot and took out a math problem to ask Shen Qi for advice.

Shen Qi took the question and saw it very surprised: "Fibonacci sequence, is this question so simple and wrong? I don't understand, how did you deduce this 25?"

Chen Xiaoting covered her face in shame: "Why are you the same style as Teacher Zhang? I really can't do it..."

Shen Qi: "Sorry, Xiaoting, I'm a little bit harder. Come on, let me tell you a routine. After mastering this routine, you can follow the routine. Give me a draft piece of paper."

"Give it!" Chen Xiaoting handed his laptop to Shen Qi.

Shen Qi opened Chen Xiaoting's notebook and wrote the paper pages in a densely packed with elegant fonts.

It can be seen that Chen Xiaoting is studying mathematics very hard, and she recorded the knowledge points Zhang Wanbang talked about in her notebook without missing a miss.

However, the subject of mathematics is not enough to rely on hard work alone, and its talent is mediocre and not systematic. Even though Chen Xiaoting worked very hard, her math grades still couldn't improve.

"To use the Fibonacci sequence well, Xiaoting, you just need to remember that when n tends to infinity, the decimal part of the ratio of the latter term to the previous term infinitely approaches 0.618, so you can follow the routine by dividing it by 0.618." Shen Qi wrote a formula in Chen Xiaoting's notebook and explained.

The Fibonacci sequence summarizes the constant mathematical law from animal reproduction phenomena, and is recorded in the "Reading and Thinking" section of the high school mathematics textbook, and is described in smaller fonts.

When Shen Qi was studying high-end and numerical scores, he specialized in researching sequences. He thought that Fibonacci sequences were an interesting theory and had many practical applications in real life: "Xiaoting, have you seen Wong Kar-wai's "In the Mood for Flowers", Zhang Yimou's "Heroes", and Liu Weiqiang's "Infernal Affairs"?"

"I have watched it all classic blockbusters. I have watched "In the Mood for Love" nine times and I love Tony Leung very much." Chen Xiaoting, who likes art films, wondered. Didn't she teach me the routine of math problems? Why did she go to the movie?

"These three are all great directors. These three films have won many awards. If you take a closer look, the winners of "In Love", "Heroes" and "Infernal Affairs" all contain one award: Best Photography Award."

Chen Xiaoting: "So?"

Shen Qi smiled and said, "So I have to thank a photographer named Du Kefeng. He is a foreigner. He is the photographer of the three films "In the Mood for Love", "Hero" and "Infernal Affairs".

"When Du Kefeng filmed "In the Mood for Love", he divided by 0.618 in composition. When Du Kefeng filmed "Hero", he divided by 0.618 in composition. When Du Kefeng filmed "Infernal Affairs", he divided by 0.618 in composition."

"We can complain about the plot of "Hero", but we must admit that the style of "Hero" is very perfect, giving people a beautiful and harmonious visual enjoyment, because Du Kefeng understands mathematics, his landscape frame design and scene scheduling everywhere reflect the 0.618 Fibonacci sequence golden spiral line."

"So people who don't understand mathematics can't make blockbusters." Shen Qi made the final summary and asked again: "Xiaoting, can you do the question of the sequence just now?"

"I know, I understand!" Chen Xiaoting suddenly realized, and she realized the joy of learning: "Shen Qi, you are more interesting and vivid than Teacher Zhang's lectures. I didn't expect that the great photographer Du Kefeng is a math expert! Come on, I still have a dozen questions to ask you."

Shen Qi waved his hand quickly: "No, don't, you can completely digest and absorb today's content first. Xiaoting, don't be anxious and don't panic. Freezing is not a day's cold. Let's make an agreement between the two of us, limited to one question a day, learn endlessly, and the accumulation of small amounts will lead to qualitative changes." I am very busy, how can I have so much time to be your full-time mathematician tutor?

"Do you have two questions a day?" Chen Xiaoting's desire to learn is very urgent.

"No, I have a question a day." Shen Qi shook his head firmly.

"Since you like watching movies, I'll give you a movie ticket. Is it okay to ask two questions a day?" Chen Xiaoting secretly took out her phone and wanted to send a QR code to Shen Qi.

Shen Qi was unhappy: "Chen Xiaoting, can scientific knowledge be measured with money? Can mathematical skills be exchanged with movie tickets?"

"Yes... I'm sorry." Chen Xiaoting lowered her head in shame. Knowledge is priceless, science is sacred, and she is indeed shallow.

"Which cinema has tickets?" Shen Qi asked.

“Feiyang Cinema, 3D-MAX.”

"It's not interesting to watch it alone. If you are with me, you don't have to ask me to watch a movie. We both AA will buy their own tickets."

"But I don't have much time to watch movies with you. You know, we only have one day off a week in our second year of high school, and I still have to practice the piano..." Chen Xiaoting said hesitantly.

Shen Qi returned Chen Xiaoting's notebook to her: "Xiaoting, you really shouldn't be impatient to improve your math grades. Take your time, otherwise it will be counterproductive to pull out the seedlings and encourage growth."

"Then let me see which day I ask the violin teacher for half a day off... I only have half a day at most."

"I won't take an example. I have two questions a day. Let's talk about it. Which math problem does not understand?"
Chapter completed!