I just want to be a quiet scholar

Chapter 21 Thoughts Are Steady as Dogs

"Oh, I'm going, my train of thought is broken!"

Doing math problems is just like writing a novel. The idea is smooth and ten times a day, but if the thinking is broken, it is ten times a day.

At the critical moment when Shen Qi was about to solve the first geometry problem, he was interrupted by the vice president.

"This uncle is really annoying." Shen Qi had to reorganize his thoughts, which took him an extra 5 minutes.

The verification process filled the whole blank paper, and Shen Qi finally found the value of sinψ.

The answer surprised him, sinψ is actually 1/2, which is a 30-degree angle.

Take a ruler to measure, it seems to be 30 degrees.

Verified by Lobachevsky's drawing method, it is indeed 30 degrees.

"I'm stupid, I'm really stupid..." Shen Qi realized a low-level mistake, he was confused by the complex geometric pattern, and it took nearly an hour to deduce it forward.

If the Lobachevsky drawing method is used to directly calculate the degree of ψ, and then reversely verify that the angle of ψ is 30 degrees, at least half of the time can be saved.

Of course, Lobachevsky's drawing method certainly cannot be drawn on exam papers, and it is no problem to draw on scratch paper.

Having a conclusion to verify the conclusion is easier than deriving an unknown.

It's a game, a math game between the questioner and the answerer.

Fighting is the best training, and exams are the best review.

Despite the systematic assistance, Shen Qi also gained a new understanding of mathematics in the extremely difficult rematch.

There must be a deeper relationship between hypothesis and proof. Truth or fallacy is not as simple and contradictory as it seems on the surface, and fallacy may be an inversion of truth.

Shen Qi was distracted. He thought about it a lot, for several minutes, it seemed that his math level was still too low, and he couldn't understand many questions.

"There are still two hours for the test, please hurry up and answer the questions." An invigilator said to all the players.

"Two hours, there are two questions left." Shen Qi came back to his senses and entered the answer to the next question.

This semi-final exam paper is the one with the fewest questions he has done, with only three questions.

It was also the most difficult one, and the first question with the lowest score took Shen Qi an hour.

The second problem is an algebra problem, the topic is like this:
1
1-1
1-2-1
1-3-3-1
1-4-6-4-1
1-5-10-10-5-1
1. Please calculate the sum of all numbers on line 1024. (5 points)
2. And prove that any number in line 4201 is a fraction or a negative number. (15 points)
In fact, many high school students know this digital triangle. Who doesn't know Yang Hui's triangle? Middle school students who have participated in the Mathematical Union and Mathematical Olympiad know the regularity of Yang Hui's triangle.

Shen Qi certainly understands this digital triangle. This digital triangle is called Yang Hui's triangle in China and "Pascal's triangle" in the West, named after two Chinese and Western mathematicians.

The regularity of Yanghui's triangle is not difficult to observe, each number in the triangle is the sum of the two numbers immediately above it.

And so on, Shen Qi quickly calculated that the sum of all the numbers on line 1024 is xxxxx... This is an astronomical number, expressed in 2 to the 1023rd power.

The first sub-question of the second question is simply a sub-question, so the score is not high, only 5 points.

The most difficult part is the second sub-question, which is worth 15 points.

The forward derivation applies to any number in line 4201 that is a fraction or a negative number.

Shen Qi wanted to reverse, and the content of the second sub-question must be able to find a formula, theorem or inference as a basis.

"Bernoulli's permutation or probability theory? No, not like."

"Three special types of equation expansions for Veda? Neither."

"Playing this pure numbers game, Fermat is a top expert. Yes, it should be Fermat. He and Pascal are good friends. The two often exchange letters, and this question is based on Pascal's triangle."

"Fermat put forward hundreds of hypotheses in his life, 99% of which have been proved to be true by later generations. He is called the 'king of amateur mathematics', but I never believe that Fermat's mathematical level is the same as I'm an amateur like me."

"Big head, Fermat's 273 hypotheses, I have only studied at most 70, which one is it? Did it touch my blind spot in mathematical knowledge?"

Shen Qi put down the ballpoint pen, closed his eyes, and racked his brains to find a way.

The vice president swayed and swayed behind Shen Qi again, he showed a smug smile, and was very satisfied with Shen Qi's current state: "Young man, even if you can solve the first geometry problem and are familiar with the laws of Yang Hui's triangle, then you can How? The second sub-question I asked was more difficult than you imagined, right?"

At this moment, Shen Qi suddenly opened his eyes, his eyes were bright: "I thought about it, this is Fermat's (1+a) inference! He said that this inference must be established, and there is no need to prove it, but 100 years after his death, his French compatriots proved this inference."

Here comes the idea, here comes the idea!
Shen Qi's inspiration poured out like a spring, he picked up the ballpoint pen and prepared to solve the problem.

Just as he was about to start writing, Shen Qi felt a chill behind him, the same as before.

Shen Qi glanced back, very unhappy: "Damn, it's you again! Are you passing by again?"

The vice president pretended to be calm: "The exam room is so big, and as an invigilator, I occasionally pass by." After speaking, he left with his hands behind.

"Uncle, you're really annoying!" Shen Qi calmed himself down as quickly as possible, and entered the process of proving the second question and the second sub-question.

After 10 minutes, Shen Qi wrote the entire proof process of the second sub-problem, which was verified by the deduction of Feima (2+a). This proof is completely established, and the case where any number in line 1 is a fraction or a negative number is applicable .

"The first and second major questions have been solved, and 35 points have been obtained."

Shen Qi, who had broken two questions in a row, became confident, and he started to do the last question.

The vice-chairman is a restless person. After walking around for a while, he circled behind the other players to observe in secret.

"He Tao, this guy can't do it. Except for knowing Yang Hui's triangle, he can't write any other questions at all."

"Luo Ming, from Nangang Foreign Language School, is a student of a famous school after all, this guy is okay, he answered the first geometry problem correctly, but the second sub-question of the second question is obviously wrong, young man, you are in the opposite direction. Misdirection."

……

The vice president visually predicted that the player who answered the questions with the fastest progress and the highest accuracy rate was Shen Qi. He couldn't help it.

Shen Qi suddenly turned his head, he was about to collapse: "Don't do this, uncle, why do you insist on getting along with me?"

The vice president is still very innocent: "I wrote this test paper, I'll just look at it, is it okay to not speak?"

"Damn it, did you come up with this paper?" Shen Qi never expected that the master question maker in his mind was actually this wretched uncle.

(End of this chapter)