I just want to be a quiet scholar

Chapter 22 Complete the answer sheet
Shen Qi knows that the people who produce the exam papers of the National Mathematical Union are well-known mathematicians in China, and the people who produce the exam papers of the IMO International Competition are internationally renowned mathematicians.

Last year's national test paper was jointly set by the deputy director of the Institute of Mathematics, Chinese Academy of Sciences, Tsinghua mathematics professor, and Fudan mathematics professor. Last year's IMO final exam paper was jointly set by Princeton mathematics professor, Cambridge Trinity College mathematics professor, and Tokyo University mathematics professor.

The author of this provincial semi-final exam paper must be an expert in the province's mathematics community.

The vice president of the Provincial Mathematics Association is about 1.6 meters tall, with a few strands of thin dry hair hanging on his forehead, thin lips, and a mouthful of smoked yellow teeth when he opens his mouth. He is obviously an old smoker.

Said he was the uncle who bargained at the vegetable market, Shen Qixin.Shen Qi felt sad when he said he was an expert in mathematics in the province.Could it be that people who engage in mathematics will become like this in the later stages of their careers. The higher the academic level, the lower the image?

"This expert, since you produced the paper, then you can read it." Shen Qi compromised, you like to see it, this is your territory, what can I do?
The vice president smiled and said nothing, took two steps back, and kept a certain safe distance.

Shen Qi stabilized his emotions and continued to do the last geometry problem.

This question is difficult and interesting.

The question asks the respondents to draw a schematic diagram of the motion of the planets in the solar system. The graphics used can only contain ellipses, straight lines and points.

At first glance, this is a physics or astronomy question.

But if you don't understand math, it's hard for the answerer to draw the correct diagram.

If you only know mathematics, you don't know anything about the most basic physics or astronomy, and you can't give a correct diagram.

"It's interesting, quite interesting." After Shen Qi drew the first ellipse, he thought about his next plan.

To give the correct answer, at least three basic knowledge of physics or astronomy are required: the solar system has eight planets, they all revolve around the sun while they are rotating, and Kepler's first law.

It is common sense that the solar system has eight planets. In 2006, the International Astronomical Union defined Pluto as an asteroid and removed it from the nine planets in the solar system, so the solar system has eight planets.

Metal, wood, water, fire, earth, earth, Neptune, and Uranus all revolve around the sun. Of course, this is also common sense, and elementary school students know it.

The explanation of Kepler's first law is: "The orbit of each planet is not the result of a combination of moving circles but an ellipse with the sun at one of its focal points." This law is recorded in high school physics textbooks.

In fact, many high school students have a large amount of knowledge and information stored in various disciplines. This information is scattered in their brains and stored in a fragmented manner.If they can't effectively connect them according to a reasonable logic, they will be distressed to find that I have read a lot of books, but I still can't do the questions, and that kind of comprehensive problems can't be written at all.

This reflects the importance of mathematics. Mathematics is a universal and powerful tool that serves various natural sciences. It provides concise and effective mathematical descriptions and concatenated and focused thinking logic.

Even Newton could not perfectly explain astronomical, mechanical and optical phenomena in purely physical language, so he invented the integral, he explained physical phenomena and the motion of celestial bodies in mathematical language.Einstein did the same, as did Kepler.

The text description of Kepler's first law has only one sentence. Kepler used a lot of mathematical theory to deduce this sentence. He is an all-around scholar with extremely high attainments in astronomy, mathematics and optics.

In addition to mathematics, Shen Qi's other subject indicators are level 1, including physics.

Level 1 physical indicators are just enough. What Shen Qi wants to do is to use geometric drawing to explain Kepler's first law. He takes S point to represent the sun, A, B, C, D, E, F, G, The eight points of H represent the eight planets of the solar system.

Explaining the motion of the planets in the solar system by geometric construction also involves some algebraic calculations. For example, taking the revolution period of the Earth and its semi-major axis to the sun as the unit of time and distance, which actually constitutes a system of equations.It took Kepler seven years to solve this system of equations with complicated algebraic methods.On the day of Kepler's death, Newton and Leibniz had not yet been born, so Kepler did not know the existence of integrals.

Shen Qi was not born on the day Newton and Leibniz died, so Shen Qi knew how to use the points technically.

Through the combination of geometric drawing method and integral calculation, Shen Qi has obtained the laws of motion of the planets in the solar system and described them in his mathematical way.

Of course, two-dimensional drawing is only simple quantitative and qualitative, what can be explained by Two-dimensional is a schematic diagram, and the precise explanation of a higher dimension is impossible even with Shen Qi's current level of mathematics.

Seeing that Shen Qi was about to solve the last question, the vice president was in a complicated mood: "This young man named Shen Qi from Nangang No. [-] Middle School is a talent! I remember that eight years ago, their No. [-] middle school had a math genius, and the feng shui took turns. The No. [-] Middle School, which has been silent for many years, finally broke out."

It took a total of 2 hours and 35 minutes for Shen Qi to answer all three questions in the rematch examination paper. After checking it, he handed in the paper and left the examination room.

Five minutes later, the vice president announced: "The three-hour time for answering questions has come. All students, please submit your papers."

"Disaster!"

"too difficult!"

"I did a 3-point sub-question in 5 hours, and spent the rest of the time in a daze!"

"Despair!"

The remaining 11 players complained that the test paper for the rematch was too difficult, and no one was sure to get a full score.

The 12 contestants, including Shen Qi, stayed at the headquarters building of the Provincial Mathematical Society and had lunch.

At the same time, the grading work is in full swing.

Including the vice president, 12 judges reviewed 12 test papers for the semi-finals at the same time, one for each.

The marking progress was very fast, and the preliminary results were available in 10 minutes.

"He Tao, Zhudao No. 5 Middle School, [-] points."

"Luo Ming, Nangang Foreign Language School, 35 points."

"Qian Shengyi, Qingjiao Experimental Middle School, 20 points."

"Tang Zhengwei, Zhanyang Middle School, 20 points."

……

"Shen Qi, Nangang No. 60 Middle School, [-] points." The vice president personally reviewed Shen Qi's test paper for the rematch.

"Shen Qi, is it him again?"

"He actually got full marks again?"

"This classmate Shen Qi is really so amazing?"

"The difficulty of the test paper for the rematch is several times that of the first test."

The rest of the judges expressed their surprise. Among the 12 contestants, only Shen Qi got a perfect score of 60, while the second place was 35 points. A total of 3 people got 35 points and tied for second place.

The vice president nodded and said: "The result of the preliminary review is indeed the case. Only Shen Qi got a perfect score and was 2 points ahead of No.25. Next, the review will start. Please exchange the test papers in hand."

"Give me Shen Qi's test paper, and I'll review him."

"Give it to me, give me Shen Qi's paper!"

"Old Qin, I remember that Shen Qi's first test paper was approved by you. It should be someone else's turn for the rematch test paper, right?"

"Old Qu, this pack of cigarettes is for you, He Tian Tian, ​​the store sells more than 100 packs. I will review Shen Qi's semi-final exam paper."

"Hetian is amazing? Lao Qin, you think I'm very poor and can't afford good cigarettes, don't you?"

"Lao Qu, why do you always hate me? I think you should change your name to Lao Ran."

"What's wrong with you, I'll kill you!"

The judges quarreled in order to compete for Shen Qi's right to review the re-examination papers.

The vice president was furious: "What qualities, what qualities! You are all high-level intellectuals, what a quarrel! Ah Ping, take Shen Qi's paper and make 11 copies, one for each judge, and review at the same time. "

(End of this chapter)