Chapter 273: Rural Absurd Past Events Chapter 273: Discovering the Beauty of Mathematics

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Protagonist:

Li Xiulan

After the Homeroom Teacher confirmed the list of students attending the National Mathematics Competition, she quickly arranged for the math teacher to give special training to the students participating in the Mathematics Competition.

Xiao Hua still remembers the first class of special training vividly to this day.

"Students, you are the elite among elites of our school, but looking across the country, you are like a grain of millet in the vast sea, as tiny as can be, so you must not be complacent, nor think that just because you got good grades now, you don't need to keep working hard. How does that saying go? Learning is like sailing against the current—if you don't advance, you retreat. Actually, it's not just students; our entire lives are like sailing against the current. After you go out into society, you must also keep striving."

The Special Training Teacher spoke from the heart to the students below, then continued:

"In this next class, I will lecture on one problem. I'll let you think about it for half an hour first, and only start explaining in the last fifteen minutes. This problem can be solved using the knowledge points we learned in high school, but it requires very clever thinking. Only students with extremely flexible thinking and very sensitive mathematical intuition can quickly find the way to solve it. Among the students I've specially trained in previous years, no one has been able to think of the answer to this problem within half an hour. This year, I hope such a person will appear."

After saying this, the Special Training Teacher picked up chalk and wrote a math problem on the blackboard.

This math problem was very concise; the problem statement was short, but it incorporated many knowledge points.

Vectors, differentiation, calculus, and so on—all of them.

If solved using the methods of Advanced Mathematics from university, one would quickly get a clue, but high school knowledge is limited, and many problems can only be solved by taking a roundabout way. This requires mental agility and leaps.

The students below the podium began thinking about how to solve this math problem given by the Special Training Teacher.

Everyone thought seriously, but the more they thought, the more worried they looked.

Puzzled expressions appeared on the students' faces, and some even frowned.

Even Xiao Hua was momentarily at a loss.

Seeing that more than a dozen students attending the Mathematics Competition special training all showed such expressions, the Special Training Teacher couldn't help but sigh.

"This is one of the easiest problems from the National Mathematics Competition a few years ago. If you can't find the solution approach relying solely on intuition and thinking, then even if you've learned competition techniques, when you encounter harder problems, you probably won't have any approach either."

Soon, half an hour passed.

The Special Training Teacher said to those below the podium:

"Has anyone solved the answer to this problem? Raise your hand and let me see."

The students looked at each other, and for a long time no one raised their hand.

The Special Training Teacher looked at Xiao Hua:

"Xiao Hua, you didn't find the answer either?"

Xiao Hua's face was full of guilt. He stood up and answered:

"Teacher, I just thought of a solution approach, but I didn't have time to solve it, and I'm not too sure if my approach is correct."

The Special Training Teacher said:

"Then come to the blackboard and write down your approach."

Xiao Hua immediately went up to the stage and began writing his approach.

"First like this, like this, then like this, then like this. I don't know if it's right or not. The amount of calculation needed in between is quite large..."

Xiao Hua was originally not good with words, so when he wrote his solution approach on the blackboard, his mouth couldn't keep up with what was written on the blackboard. He could only say "like this, like this."

Looking at the solution approach Xiao Hua gave, the Special Training Teacher couldn't help but nod slowly.

"This approach is a bit roundabout, but it cannot be denied that it is indeed a method of solving the problem. It's just that it requires a large amount of calculation in between."

Hearing the Special Training Teacher say this, a joyful smile appeared on Xiao Hua's face.

He thought his solution approach had a problem. Since there was no problem, he just needed to do the calculations well, and he should be able to get the correct answer.

However, at this moment, the Special Training Teacher changed his tone:

"But using this approach to solve problems, in the National Mathematics Competition exam, you'd probably be able to solve at most two problems, while for the other problems you could only write the character 'solve.' Students, remember this: the beauty of mathematics lies in its ability to simplify the complex. Take Euler's Formula, for example: e to the i pi power plus 1 equals 0. How concise! Yet it contains the truth of mathematics. So when we solve problems, we must have a mindset of simplifying the complex. If it's a multiple-choice or fill-in-the-blank question, and your solution approach requires a large amount of calculation, then obviously your approach is wrong. You've been led astray by the problem setter. This is a trap. Doing a large amount of calculation in multiple-choice and fill-in-the-blank questions—whether in competitions or the college entrance exam—is extremely fatal. Even if you eventually get the correct answer, it's not worth it, because you waste a huge amount of time and won't have enough time for the later problems. So remember: the mindset of simplifying the complex is very important!"

As he spoke, the Special Training Teacher began writing the solution approach on the blackboard.

The solution approach he wrote consisted of only three formulas.

Three seemingly unrelated formulas were finally cleverly linked together!

Then the correct answer was easily obtained!

And no large amount of calculation was needed.

The students below, seeing this solution approach, were all surprised, even filled with admiration.

Xiao Hua was also dumbfounded.

He never expected that this problem could be solved this way.

This deeply shocked him, and he deeply felt the wonder and beauty of mathematics.

He was not discouraged because he hadn't thought of this clever solution approach; on the contrary, he was full of motivation and wanted to explore this breathtaking beauty of mathematics.

This math special training class ended quickly. For the entire class, the Special Training Teacher only lectured on this one problem.

And when class ended, he also gave the students a homework problem:

"This problem has an even more concise solution approach. Students, go back and think about it. When we have the competition class next time, I hope someone can give me the answer I want."

More than a dozen students attending the competition special training walked out of the classroom and began discussing that problem animatedly.

"Does that problem really have a more concise solution approach?"

"Maybe, but it might require knowledge points we haven't learned yet."

"If I'd known the competition was this hard, I wouldn't have come. It feels like listening to heavenly scriptures!"

"If it weren't hard, would it be called a competition? This is normal!"

The students attending the competition special training returned to their normal classes one by one.

Xiao Hua also returned to his seat.

All the way back, he had been thinking about that problem given by the Special Training Teacher.

"Is there really a more concise approach to solving this problem?"

Wang Xiaohua racked his brains, thinking that the next class was physics.

When the physics teacher came in to lecture, Wang Xiaohua still couldn't help thinking about that problem.

Fortunately, the physics teacher mainly went over last semester's final exam papers that period; Wang Xiaohua had long since recorded and reviewed his mistakes from last semester's final exam, so he could skip this class if he wanted.

So he started privately pondering that mathematics competition problem.

The physics teacher at the podium saw Wang Xiaohua buried in his math problems but didn't say anything.

After all, on last semester's final physics exam, Wang Xiaohua had scored ninety-five, missing only one small question, and even got the hardest physics question right.

Students studying science all know that the two biggest difficulties in science are the hardest math questions and the hardest physics questions; as for biology and chemistry, they're much simpler.

Wang Xiaohua's grades were so excellent that the teachers' tolerance for him was higher; ordinary teachers would allow excellent students to learn at their own pace and wouldn't deliberately disrupt their rhythm.

Because teachers all know that excellent students are never taught into excellence, but learn it themselves.

Even if they changed teachers, he would still be just as excellent.

But if the teachers changed classes, they might not be able to produce such excellent students.