Chapter 31 The story of the competition and the college entrance examination (I have something to do tonight, so I will post in advance)
"This question is really not easy."
After getting the test paper, Xu Chuan stared at the first geometry question for five minutes before sighing.
A plane geometry question almost applies all five axioms and five postulates of Euclidean geometry. It can be said that the geometric characteristics of flat space are brought into full play.
The most important thing is that this question almost blocks the geometry knowledge learned in most college mathematics. It is difficult to apply the new geometry theory of Gaussian Prince or the absolute geometry and non-Euclidean geometry of Porgy to this question. superior.
The professor who asked this question must have a high level of achievement in geometry.
There are only a handful of domestic mathematicians who have achieved high achievements in geometry. Xu Chuan thought about it, and the most famous among them are Mr. Qiu and Mr. Chen.
But the probability of these two big guys coming up with the question is almost zero.
Although Qiu Lao has high attainments in geometry and is now in China, his geometric achievements are mainly in differential geometry, and his attainments in plane geometry are not top-notch.
Moreover, this boss is older, so he may not remember the geometry knowledge clearly in high school and college.
As for Mr. Chen, he passed away ten years ago, so it is even more impossible for him to come up with the question.
But this reminded Xu Chuan of another person in the country, Academician Zhang, ‘Zhang Weiping’, a close disciple of Mr. Chen.
This big guy won the honor of being an academician of the Academy of Sciences in 2008, and is now in his prime. In addition, he is a close disciple of Mr. Chen. It is logical that he will continue on the mathematical path of geometry. It can be said that he has made great achievements in plane geometry. His attainments are quite high.
If he had come up with the question, he would indeed be able to do this.
In fact, Xu Chuan's guess was indeed correct. The two geometry questions in this year's IMO, yesterday's and today's, were written by Academician Zhang Weiping.
This big shot happened to serve as a director of the 10th Council of the Mathematical Society last year.
The CMO’s test teachers are basically selected from the directors of the Mathematics Society. In 2014, this year, this boss personally compiled two geometry questions and entered them into the 2014 National Mathematics Competition.
As a result, all CMO candidates in 2014 were wiped out, and not one of the more than 400 people got a perfect score.
At the same time, the boss also screened other test questions, resulting in this year's CMO results being miserable, with scores of more than 100 points being less than one slap in the face.
This also caused the admission score of this year's training team to drop from the average of more than 85 points in previous years to 65 points, which directly reduced the admission score by nearly 20 points.
Up to this point, the story of this boss has not stopped yet.
Later, he participated in the CMO questions in 2015 and 2016, and the results of these two times were equally dismal.
In 2015, he assassinated all the candidates that year with a single three-dimensional geometry.
For the 21-point question, among hundreds of candidates across the country, only a handful of students got 7 points for the first question, while the other students all turned in blanks.
In 2016, it was the same 21-point question, but there was no perfect score.
Full marks? In the hands of this big boss, that's out of the question.
Miserable is just one word, how can it be so big?
Later, the Mathematical Society did not let this big boss take action, for fear of damaging the confidence of the reference students.
However, after three attacks, his reputation in the math industry was as good as that of Ge Junge, the boss who specializes in dealing with college entrance examination candidates.
Students who have participated in these three CMOs tremble when they hear the name of this big man.
"Crouching Tiger, Hidden Dragon, this year's CMO, the question maker actually has such a super boss involved."
Although Xu Chuan was not sure whether this geometric figure was created by Academician Zhang Weiping, the teacher who asked this question was definitely at the same level as him.
This geometry question extremely tests students' derivation and graphic observation abilities. It requires at least three auxiliary lines to accurately derive the required angle.
These three auxiliary lines are quite secretive, and one of them is sandwiched between the two circles. It is quite difficult to find this auxiliary line.
With a sigh, Xu Chuan picked up the protractor and drew on the geometric diagram. After confirming that the angle he guessed was correct, he began to draw auxiliary lines on the test questions. The geometric figures of this question were too complex, and he was too lazy to copy them onto scratch paper.
In fact, in geometry problems, there is a fairly simple method to determine the required values and angles.
That is to go back to basics and use a protractor to measure directly, but it is only useful for plane geometry.
This method can solve more than 90% of geometry problems.
Of course, it can only give you an answer, and you still need to write the derivation and proof process yourself.
After the auxiliary lines were drawn, the rest of the proof was just ordinary to Xu Chuan. Although the proof process was more complicated, after climbing Mount Everest, are you still worried about not being able to climb Mount Tai?
Solution: According to Pascal's theorem, the three points P, Q, and R are collinear, because ∠DTF=AC+DF/2=AB+DF/2=
Therefore, if QK is extended and handed over to BC, SK/KT=BN/NC
In the same way, we can know that △CQN∽△APC, and CN=QN·AB/PB, so we know that BN/NC=
Rotate △ABP around point A to △ACL
It can be proved that the angle of ∠KIP is thirty-five.
Certification completed!
The black pen in his hand continued to list rows of calculations on the answer sheet, almost filling the entire A4-sized answer sheet, and the geometry question was finally answered.
In the process of solving the problem, almost all twenty-six letters are used, and characters like A and A are also used to represent auxiliary lines, which shows the difficulty of this problem.
After solving the first question, Xu Chuan breathed a sigh of relief and looked up at the alarm clock on the blackboard of the podium, which read nine thirty-five.
This was the longest time he had spent on a question since he participated in the math competition, taking more than half an hour.
It is worthy of being asked by a figure as famous as the mathematician Ge Jun. Even if it is so difficult for him, it is probably even harder for other students.
Thinking about it, Xu Chuan turned his head and looked at the classroom.
What didn't happen yesterday happened today.
A row of students were either looking up at the sky or looking down at the ground.
These students who were in high spirits in the first half of yesterday and felt that CMO this year was not that difficult, today were completely confused.
There are no multiple-choice questions or fill-in-the-blank questions in the National Number Competition. They can't do it even if they want to throw dice or guess the answers with paper balls.
At most, write a ‘solution’.
The rest is a blank.
This is probably, ‘Is it okay if I fuck you? ’
A geometry problem has stumped hundreds of students, and the smarter ones have already bypassed it and solved the next problem.
But in the second half of the national finals, there is no easy problem.
Especially since this year's questions have all been read by Mr. Zhang, even if the difficulty is slightly inferior to Geometry, it won't be much different.
It took Xu Chuan an hour and a half to complete three major questions in an orderly manner.
After carefully checking it twice to confirm that there was no problem, he handed in the paper in advance and left the examination room.
This move can be regarded as completely irritating the other students in the same examination room. Some gritted their teeth, some bowed their heads in silence, and some cruelly followed suit and left early.
After all, with such a difficult question, it’s normal to hand in a blank paper along with it, right?
Anyway, I’m not the only one with a blank paper.
I beg for monthly votes, recommendation votes, follow-up reading, and I am begging for everything.
ps: If you have a book list, please add it, thank you
(End of chapter)