Great Country Academician

"It's not easy to come up with this topic."

After getting the test paper, Xu Chuan stared at the first geometry problem for a full five minutes before sighing.

A plane geometry problem almost applied the five axioms and five postulates in Euclidean geometry. It can be said that the geometric characteristics of flat spaces are brought into full play.

The most important thing is that this question almost blocks the geometry knowledge learned by most college mathematics students. Whether it is the new geometry theory of the little prince of Gauss, or the absolute geometry and non-Euclidean geometry of Bolejo, it is difficult to apply to this question. superior.

The professor who came up with this topic will definitely not be low in geometry.

There are only a handful of domestic mathematicians with high achievements in geometry. Xu Chuan thought about it, and the most famous ones are Qiu Lao and Chen Laoshen.

However, the probability of these two bigwigs asking 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, and I am afraid that he does not remember the geometry knowledge so 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 write a question.

But this made Xu Chuan think of another person in the country, Mr. Chen's closed disciple 'Zhang Weiping' Academician Zhang.

This big guy won the honor of academician of the Academy of Sciences in 2008, and he is now in his prime, plus he is the closed disciple of Mr. Chen, so it is logical to go down the mathematical path of geometry. It can be said that in plane geometry The academic attainments are quite high.

If it was him who came up with the question, he could indeed achieve this step.

In fact, Xu Chuan's speculation is indeed correct. The two geometry problems of this year's IMO, yesterday's and today's, were all given by Academician Zhang Weiping.

This big guy just served as a director of the 10th Council of the Mathematical Society last year.

The CMO's question-making teachers are basically selected from the directors of the Mathematics Society. In 2014, this year, this boss personally edited two geometry questions and put them in the 2014 National Mathematics Competition.

As a result, all CMO candidates in 2014 were annihilated, and none of the more than 400 people got full marks.

At the same time, the boss also screened other exam questions, resulting in a miserable CMO score this year, with no score above 100 being slapped in the face.

This also caused the entry score of this year's training team to drop directly from the average of more than 85 points in previous years to 65 points, which directly dragged the admission score by nearly 20 points.

So far, the story of this big guy has not stopped.

Later, he participated in the 2015 and 2016 CMO questions, which led to the same dismal results.

In 15 years, he assassinated all the examinees that year with a single solid geometry.

For the 21-point question, among the hundreds of examinees across the country, only less than a handful of students got 7 points for the first question, and all other students gave blanks.

In 2016, it was also a question with 21 points, but there was also no perfect score.

Full marks? Don't even think about it in the hands of this big guy.

Miserable is just one word, what's the matter?

Afterwards, the Mathematics Association did not let the big guy make a move, for fear of damaging the confidence of the reference students.

However, after three shots, his reputation in the digital competition industry was comparable to that of Ge Junge, who specializes in dealing with college entrance examination candidates.

Students who have participated in these three CMOs trembled when they heard the name of this big guy.

"Crouching Tiger, Hidden Dragon, this year's CMO, the questioner actually has such a super boss participate in it."

Although Xu Chuan was not sure whether this geometric figure was made by Academician Zhang Weiping, the teacher who came up with this question was definitely at the same level as him.

This geometry question is an extreme test of students' derivation ability and graphic observation ability. It requires at least three auxiliary lines to accurately deduce the desired angle.

And these three auxiliary lines are quite hidden, and one of them is sandwiched between two circles tangent to each other. It is quite difficult to find this auxiliary line.

Sighing, Xu Chuan picked up the protractor and made gestures on the geometric diagram. After confirming that the angle he guessed was correct, he began to draw auxiliary lines on the test questions.

This time the geometry of the topic was too complicated, so he didn't bother to copy it to the scratch paper.

In fact, in geometry problems, there is a fairly simple method to determine the required value and angle.

That is to return to the basics and measure directly with a protractor, 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 the derivation and proof process still needs to be written by yourself.

After the auxiliary line is drawn, the rest of the proof is normal for Xu Chuan. Although the proof process is more complicated, are you worried that you will not be able to climb Mount Tai after you have turned over Mount Everest?

Solution: According to Pascal's theorem, the three points P, Q, and R are collinear, because ∠DTF=AC+DF/2=AB+DF/2=

So extend QK and pay to BC to get SK/KT=BN/NC

Similarly, we 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 35.

Proof!

The black signature pen in my hand continuously listed line after line of calculation formulas on the answer sheet, almost filling the entire page of the A4 answer sheet, and this geometry problem was completed.

In the process of solving the problem, almost all the twenty-six letters are used, and characters such as A and A are used to represent the auxiliary line, which shows the difficulty of this problem.

After solving the first question, Xu Chuan breathed a sigh of relief, looked up at the alarm clock on the blackboard on the podium, it was nine thirty-five.

This is the longest time he has spent on a problem since he participated in the math competition, and it took more than half an hour.

As expected of a person who is as famous as Mathematics Emperor Ge Jun, he did such a difficult problem, and other students probably had a harder time.

Thinking about it, Xu Chuan turned his head and glanced 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.

Those students who were still in high spirits in the first half of yesterday and felt that CMO is not that difficult this year, were completely dumbfounded today.

There are no multiple-choice questions and fill-in-the-blank questions in the Shujing Guojue. They can't do it even if they want to throw dice or balls of paper.

Write a 'solution' at most.

The rest is blank.

This is probably 'I can do it too? '

A geometry problem has baffled hundreds of students, and those who are smarter have already bypassed it to do the next one.

But in the second half of the national finals, there is no easy problem.

Especially this year's topic has been read by that boss Zhang, even if the difficulty is slightly inferior and geometric, it will not be much worse.

After spending an hour and a half, Xu Chuan methodically completed the three major questions.

After carefully checking twice to confirm that there was no problem, he handed in the papers ahead of time and left the examination room.

This move can be considered to have thoroughly stimulated the other students in the same examination room, some gritted their teeth, some bowed their heads in silence, and some cruelly followed the early submission of papers and left.

After all, with such a difficult topic, it is normal to hand in blank papers together, right?

Anyway, I'm not the only one with a blank paper.

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