Chapter 288 Mathematics: The core of competition thinking lies in rushing to the two directions!

In a blink of an eye, the summer vacation is coming to an end.

No matter what you do, people are always full of passion at the beginning. When they gradually become familiar with something or thing, their passion fades and even begins to become bored. This can be applied to many places, love, learning...

This matter must also be viewed dialectically. People have infinite passion but limited passion for something. It is based on this that scientists can constantly explore fresh fields, and powerful conquers can continuously expand their territory and become mature.

Aquaman can continue to guide new girls...

Of course, this characteristic of human nature is not a good thing to put in the current scene.

Even though most of the people in this training class had excellent grades, Yi Yang still felt the fatigue of many people at the end of the cram school.

During class, I was a little sleepy and looked around. I didn’t know when the vacant positions started to begin.

Of course, as a summer cram school, teachers do not have strict requirements on attendance.

Although the teacher's class rhythm has not changed much, I can feel that the passion has retreated a lot. Everyone lowered their heads. Occasionally, Liao Yifei asked a question, and someone raised his head to respond. Compared to the beginning of the class, the atmosphere was obvious.

Much more boring.

The first class in the morning is over.

Today is cloudy and the temperature is moderate. Although it does not mean particularly for many contestants whether it is summer vacation or not. Even because the competition league will start soon, this summer vacation will become more busy than in school, but at this time

The temperature is still reminding everyone... the summer vacation is really coming to an end.

Yi Yang looked at the high sky outside the window, and a long white line was dragging across the sky from behind a jet plane.

Then a pack of biscuits in transparent food bags appeared in front of me.

Yi Yang looked up and said, "Chi Xiaohuan is really virtuous. I will make this for you every day."

Luo Bing shrugged: "Everyone has it, Deng Wenxiao has it too, why did it be for me?"

Yi Yang sneered: "Just pretend to be stupid, you damn winner in life."

Luo Bing laughed: "You said I? You are not yourself?"

Yi Yang was not polite, so he opened the food bag to pick up the biscuits and started eating it, asking, "Are you with Chi Xiaohuan?"

Luo Bing shook his head: "No."

"But I was quite surprised... You actually admit that you have a good impression of Chi Xiaohuan."

"Anyway, it won't affect your studies..." Luo Bing raised his head and thought.

"So what are you going to do next?"

Luo Bing shook his head: "I don't know, just take one step at a time. After all, I don't have any experience in this area, so let's follow my feelings."

Yi Yang took a bite of the biscuit and added raisins. It was a little sour and said, "I envy you for a life winner like you. Go in both directions."

Luo Bing smiled: "Your envy is hypocritical."

Yi Yang laughed, suddenly thought of something, paused, and said, "But when it comes to the word "two-way"... I have some experience. I don't know if it's right after summarizing it during this period. Please help me see.

”

Luo Bing said: "I am not as good as you in this kind of thing..."

Yi Yang gave Luo Bing a white look, sat down, took out a counting question, and said, "I didn't say that I was in love... it was about mathematics."

"Mathematics? Go in both directions?" Luo Bing was slightly stunned.

Yi Yang nodded, pointed to the question, and said, "In the past, after learning mathematics competitions, when doing the questions, he would naturally use some math competition skills to think about college entrance examination questions. It would feel easier, but except for those

New knowledge that can only be learned in mathematics competitions. What exactly is mathematical competition thinking?”

Luo Bing showed a thoughtful expression and touched his chin, "Mathematics competition thinking...so what conclusion did you come up with?"

Yi Yang said: "Although the term mathematical competition thinking can be heard on many occasions, no one seems to have explained in detail what mathematical competition thinking is and what is the difference between traditional mathematical thinking."

"I have asked you, Deng Wenxiao, and Teacher Liao, you are a more powerful competition student, and you are also observing your thinking patterns. How to say, compared to me, your thinking style is more jumpy, for example,

, A combination number problem, ordinary mathematical thinking is to solve problems step by step, and you seem to be very sensitive to the meaning of various combinations, always entering from a certain point in the middle, and then starting to solve problems... But,

What is the essence of thinking?”

Luo Bing's eyes also became a little curious, and he nodded slightly: "Well... that's the case. I haven't thought about the principle of my own thinking."

Yi Yang snorted coldly: "So geniuses have no way to empathize with the world of mortals."

Luo Bing smiled gently: "Mortals cannot understand the thinking of geniuses, but you seem to have analyzed the essence. I want to hear your conclusion."

Yi Yang thought to himself, that is, am I between a genius and a mortal? Because I am in such an awkward position, even if I can't do what a genius can do, I can understand what a genius thinks.

At the same time, we can understand the crux of what mortals don’t understand... But despite this, we still feel better.

Being too genius is not a good thing. He still wants to be a vulgar mortal and empathize with the happiness that most people can empathize with.

Yi Yang thought about it, his expression became serious, and said, "The essence of this kind of thinking...well, I think it's just rushing in both directions."

Luo Bing's eyes moved, "Running in both directions."

Yi Yang pointed to the geometry question in the exercise book and said, "Take these two geometry questions as examples."

"This question is the penultimate question of the A-term paper of the college entrance examination last year. The traditional mathematical problem-solving thinking can be done. The step is to interpret each known condition first. Basically, when each known condition is translated almost completely, this question

The idea comes out, because a known condition basically corresponds to a theorem or available concept."

"For example, point E is the midpoint of AC and is a right-angle triangle. When translated, it only corresponds to the theorem that the center line on the oblique side of the triangle is equal to half of the oblique side, that is, AE=BE=1/2AC... as long as the basic

If you have a solid knowledge, and translate other conditions in this way, basically there are only one or two theorem concepts corresponding to each known condition."

"When we translate all known conditions in this way and compare them with each other, the problem-solving ideas for this problem will basically come out."

Luo Bing nodded slightly.

Then Yi Yang said: "This is a college entrance examination question. Let's look at this competition geometry question... There are only four known conditions in total, but its graphics are very complex. If a known condition is to be translated, it will correspond to too many.

Knowledge points."

"For example, this line segment is both the oblique midline of this small triangle, the base edge of this triangle, and the tangent of this circle, and these four points are still a circle... so this line is equal to this line,

If you translate this known condition, there are five or six theorems involved, and the other several known conditions are the same. If you translate them all, you may have more than a dozen directions in front of you and don’t know how to follow them.

Thinking about that direction, it is very likely that after thinking for a long time, I realized that this road is not working..."

"What's more, many theorems of math competition questions are dizzy when they change slightly."

"Um……"

Yi Yang continued, "So it is difficult to think about math competition questions, using conventional mathematical thinking... This is also the difference between competing students and ordinary college entrance examination students. When mathematics competition students think about such questions, their thinking is not done step by step.

What you think is...the way you solve the problem with a two-way thinking method, reverse plus positive thinking, and inspire inspiration."

Luo Bing remained silent.

Yi Yang pointed to this question: "Continue to take this question as an example. Since we are asking us to prove that the angle ADF=90 degrees, so here is the starting point to think about it, and the direction will be much less."

"The relationship between this angle and other angles can produce 90 degrees of four possibilities..."

Yi Yang began to write and draw on the draft paper, list it, and then said: "Follow these four possibilities, deduce forward, a certain path of reverse thinking will be followed by more than a dozen translated positive ideas.

When a point meets, then filter and combine these possibilities translated by known conditions to prove this intersection point... In this way, you can see how this problem is solved."

"Simple positive thinking cannot do, simple reverse thinking also has its limitations. Only by rushing in both directions can it be easy to inspire inspiration. For a simple competition question like you, you basically have no awareness of it if you look at it at a glance.

When it comes, it deduces the reverse thinking to the third to last step, and more than a dozen possibilities of positive thinking can be quickly reacted, and their roughly converged position also reacted." After saying that, Yi Yang looked up at Luo Bing,

Say: "That's how I understand."

Luo Bing was silent for a long time before laughing: "Awesome."

Yi Yang finally concluded: "This is just a way of thinking that I can understand, but I suspect that when you think about counting competition questions, you don't even go in both directions, but come from all directions at the same time..."

"Ha...not that exaggerated."

"You are very proud."

"No."

"You are very proud."

"Hey……"

...

When I went back today, Yi Yang was in a good mood. At least he had determined the direction of his thinking mode. After he was proficient, even if he still couldn't do some difficult math competition questions, this way of thinking was not much after the translation was translated by known conditions.

The college entrance examination questions are dimensionality reduction strikes... This is also why the powerful mathematics students can see how to solve some college entrance examination questions at a glance.

It has been a month since Jiang Lili’s best friend failed to get back together, but occasionally Jiang Lili will sigh a little depressed when she mentioned this.

Now Yi Yang can calm down and study in a noisy environment. Jiang Lili was watching TV, and he sat on the edge of the coffee table to do the exam.

It took nearly an hour to finally solve a question. Yi Yang rubbed his temples in pain. It was really difficult to count the competition.

At this time, a TV series that you don’t want to do with love is playing on TV. Jiang Lili watched the TV in a daze, but suddenly asked a question: "Yi Yang, you said, two people with huge differences in family conditions really can’t be together.

?”

Yi Yang's eyes moved and he shook his head: "It shouldn't be... it shouldn't be."
To be continued...