Reborn I just want to concentrate on studying

Chapter 288 Mathematics: The core of competition thinking lies in running in both 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. After getting familiar with a certain thing or thing, the passion fades, and even becomes boring. This can be applied to many places, love, learning...

This matter should also be viewed dialectically. Human passion is unlimited but passion for one thing is limited. It is based on this that scientists can continue to explore new areas, and powerful conquerors can continuously expand their territory. A mature Only the Neptune can keep attacking new girls...

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

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

When I was in class, I was a little sleepy. I looked around, and I don't know when the vacant seats were still empty.

Naturally, as a summer cram school, the teacher does not have strict requirements on the attendance rate.

Although the teacher's class rhythm hasn't changed much, I can feel that the enthusiasm has receded a lot. Everyone lowers their heads. Occasionally, Liao Yifei asks a certain question before someone raises his head to respond. Compared with the beginning of the class, the atmosphere is obvious. A lot dull.

The first class of the morning is over.

Today is cloudy and the temperature is moderate. Although for many contestants, whether it is summer vacation has no special meaning, and even because the number competition league will start soon after the school starts, this summer vacation will become busier than 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, a jet plane dragged a long white line across the sky.

Then a pack of biscuits in a transparent food bag appeared in front of my eyes.

Yi Yang raised his head and said, "Chi Xiaohuan is really virtuous, I make this for you every day."

Luo Bing shrugged: "Everyone has it, and Deng Wenxiao has it too. How come it's for me?"

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

Luo Bing laughed loudly: "You mean me? Don't you yourself?"

Yi Yang was not polite, he opened the food bag, took the biscuits and ate them, and asked, "Are you with Chi Xiaohuan?"

Luo Bing shook his head: "No."

"But I'm quite surprised...you would admit that you have a crush on Chi Xiaohuan."

"Anyway, it won't affect my studies..." Luo Bing raised his head and thought for a while.

"So what are you going to do next?"

Luo Bing shook his head: "I don't know, let's take it one step at a time, after all, I don't have any experience in this field, so let's follow the feeling."

Yi Yang took a bite of the biscuit, which was a bit sour with raisins in it, and said, "I'm so envious of a winner in life like you, so go both ways."

Luo Bing smiled: "Your envy is hypocritical."

Yi Yang laughed, suddenly thought of something, paused, and said: "But when it comes to the word "going in both directions..." I do have some experience, and I don't know if it's right after I summed it up during this period of time. Please help me to see. "

Luo Bing said, "I'm not as good as you in this kind of thing..."

Yi Yang rolled his eyes at Luo Bing, sat down, took out a math competition, and said, "I didn't talk about falling in love...it's about mathematics."

"Mathematics? Two-way running?" Luo Bing was slightly taken aback.

Yi Yang nodded, pointed to the question, and said: "In the past, after learning the math competition, when doing the questions, I would naturally use some math competition skills to think about the college entrance examination questions, and it would be easier, but apart from those What is new knowledge learned only in math competitions?"

Luo Bing showed a thoughtful expression, and rubbed his chin, "Math competition thinking... so what conclusion did you think about?"

Yi Yang said: "Although the term mathematics competition thinking can be heard on many occasions, it seems that no one has explained in detail what is mathematics competition thinking and how is it different from traditional mathematical thinking."

"I've asked you, Deng Wenxiao, and Mr. Liao, you are more powerful contestants, and you are also observing your thinking patterns. How should I put it, compared to mine, your thinking patterns are more jumpy, such as , a combined number problem, ordinary mathematical thinking is to solve the problem step by step, and you seem to be very sensitive to the meaning of various combinations, always cut in from a certain point in the middle, and start solving the problem... But, this What is the nature of this thinking?"

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

Yi Yang snorted coldly: "So geniuses can't empathize with the mortal world."

Luo Bing smiled gently: "Ordinary people can't understand the thinking of a genius, but you seem to have analyzed the essence. I want to hear your conclusion."

Yi Yang thought, that is to say, am I the layer between a genius and a mortal?Because of this embarrassing position, even if I can't do what a genius can do, I can understand what a genius thinks, and at the same time understand what the crux of what ordinary people don't understand... But even so, I feel better Some.

Too much 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 for a while, his expression became serious, and he said, "The essence of this kind of thinking... Well, I think it's going in both directions."

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

Yi Yang pointed to the geometry problem in the workbook, and said, "Let's take these two geometry problems for example."

"This question is the penultimate question of last year's college entrance examination paper A. The traditional mathematical problem-solving thinking can do it. The first step is to interpret each known condition. Basically, when each known condition is almost translated, the answer to this question The idea came out, because a known condition basically corresponds to a theorem or a usable concept.”

"For example, point E is the midpoint of AC, and it is a right-angled triangle. When this condition is translated, it only corresponds to the theorem that the midline on the hypotenuse of the triangle is equal to half of the hypotenuse, that is, AE=BE=1/2AC... as long as the basic If the knowledge is solid enough, and other conditions are translated in the same way, basically there are only one or two theorem concepts corresponding to each known condition."

"When we translate all the known conditions in this way and compare them with each other, the idea of ​​​​solving this problem basically comes out."

Luo Bing nodded slightly.

Then Yi Yang said: "This is a question for the college entrance examination. Next, let's look at this competition geometry question... There are only four known conditions in total, but its graphics are very complicated. If one known condition needs to be translated, there are too many correspondences." Knowledgeable."

"For example, this line segment is not only the midline of the hypotenuse of this small triangle, but also the base of this triangle, and also the tangent line of this circle, and these four points also share 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 same is true for the other known conditions. After all translations, there may be more than a dozen directions in front of you, and you don’t know how to follow them. Thinking in that direction, it is likely that after thinking for a long time, I realized that this road does not work..."

"What's more... Many theorems in the math competition topics will make people dizzy if they change a little."

"Um……"

Yi Yang went on to say, "So when thinking about math competition questions, it is very difficult to use conventional mathematical thinking... This is also the difference between the thinking of contest students and ordinary college entrance examination students. Thinking, but... using a two-way thinking way to solve problems, reverse and positive thinking, to inspire inspiration."

Luo Bing remained silent.

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

"The relationship between this angle and other angles, there are four possibilities that can produce 90 degrees..."

Yi Yang began to write and draw on the draft paper, listed them out, and then said: "Follow these four possibilities, deduce forward, a certain path of reverse thinking will be in a certain path with more than a dozen translated positive thinking When a point converges, then filter and combine the possibilities translated by the known conditions to prove the point of intersection... so that we can see how to solve this problem."

"Simple positive thinking is not enough. Pure reverse thinking also has its limitations. Only by running in both directions can it be easy to inspire inspiration. Thinking animals like you basically take a look at this simple competition question and don't even realize it. Then, the reverse thinking was deduced to the penultimate step, and more than a dozen possibilities of positive thinking can be quickly reflected, and the approximate intersection position of them has also been reflected." After finishing speaking, Yi Yang raised his head and looked at Luo Bing, Say, "That's how I understand it."

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

Yi Yang finally concluded: "This is just a way of thinking that I can understand, but I suspect that when you think about math competitions, you don't even go in two 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 I had determined the direction of training my thinking mode. After I became proficient, even if I still couldn’t do some difficult math competition problems, this way of thinking didn’t have many directions after being translated into known conditions. Among the college entrance examination questions is the dimensionality reduction attack... This is why a good math competition student 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 would sigh depressingly when he mentioned this matter.

Now Yi Yang can calm down to study even in a noisy environment. Jiang Lili is watching TV while he sits on the side of the coffee table doing the questions.

It took nearly an hour to finally solve a problem. Yi Yang rubbed his temples in pain. Counting is really difficult.

At this time, a TV series that has nothing to do with love is playing on the TV. Jiang Lili is watching the TV with ecstasy, but suddenly asks a question: "Yi Yang, tell me, can two people with huge differences in family conditions really not be able to be together?" ?”

Yi Yang's eyes flicked, and he shook his head: "It shouldn't be..."

"But... don't you agree with my best friend's ex-boyfriend?"

Yi Yang said: "I'm just analyzing objectively, I have no tendency, and..." After a pause, he said seriously: "My sister has fallen into a misunderstanding."

"Ok?"

"What you are struggling with is rural origin and the identity of a rich girl, but your best friend and his boyfriend did not get together in the end because of different views."

"The two feel related, but are actually different."

"The formation of a person's three views is caused by various factors, even strange ones, except for childhood growth, the influence of parents, perhaps a certain sentence in a certain book, a choice made by the protagonist in a movie, It is possible to reshape a person's three views."

"A person who becomes a perverted killer may just be stepped on when he was a child."

"A person who loves life may just because he saw a flower withering with his own eyes when he was a child..."

"In short, it's not clear. The poor family conditions can make you try to guess that a person's consumption concept is austere and not generous, but is it accurate?"

Yi Yang looked at Jiang Lili.

"Are you sure?" Jiang Lili was stunned, still savoring Yi Yang's words just now, then shook his head and said with a smile: "Probably... not so accurate."

Yi Yang also laughed: "Yes."

"So, there is no need to get entangled in such things. Your best friend and his ex-boyfriend didn't get together in the end because her ex-boyfriend couldn't accept some of her living habits, but it doesn't mean that everyone like her People with the average family conditions of the ex-boyfriend couldn’t accept it.”

"There can't be two identical leaves in the world. Similarly, there can't be two people with the same three views in the world. We can only tolerate each other, and the focus is mutual, not tolerance."

After a pause, Yi Yang drew a circle on the notebook and said, "Look, a person's values, consumption, love, family, and all kinds of things make up a person's appearance. Many people think that it is It's a circle..."

Then I drew a big circle outside this circle to enclose it, saying: "This is how many people imagine two people get along, one side tolerates the other, but in fact..."

Then he drew a bumpy pattern next to it, saying: "But I think that a person cannot be a circle, and all aspects of him are concave and convex. When two people get along, some places are convex. You are concave, I tolerate you, in some places, you are concave, I am convex, you tolerate me..."

"For example, I don't like you leaving your shoes behind when you come in, but I won't be angry, I will just silently put them away for you, because I play games late at night, and you don't like it, but you will still act coquettishly with fruit I will go to rest, and I will definitely not yell... There is no absolute one party to tolerate the other party, it is all mutual."

After hearing Yi Yang's words, Jiang Lili felt a little shaken in his heart.

She couldn't help but recall that when Yi Yang came to her for the first time to make up lessons, he didn't even understand English in the first grade of junior high school, but now he calmly analyzed things about sex, life, and emotional communication...

His growth comes from learning, but this kind of things that can only be summed up after a lot of experience can no longer be obtained simply through reading, she thought, this is the case, the same environment can also breed various people of different shapes.

A few years ago, I met Yi Yang who might be very powerful in the future. He has the kind of traits that he can stick to if he believes in a correct thing. He is stubborn but not rigid. He knows how to listen, think, and is willing to stand in the position of others. Thinking about problems, all kinds of things, no matter which person or age group they are placed on, are enough to make people believe that his future is promising.

But witnessing Yi Yang's growth from ignorance to the person he is now, it still makes people feel an unreal dream...

Rich knowledge, strong physique like an athlete, understanding of music, calm personality, calm when encountering things, and radiate this emotion to the people around him, so that they can feel at ease, and at the same time it is very interesting... This also reflects In many ways, interesting hobbies, giving an interesting opinion on something... all kinds of things.

She couldn't help but glanced at Yi Yang's very comfortable face.

There really are such boys in this world.

And along the way, he was not only a witness... but also a participant, and now he was living under one roof, and the feeling of wonder became stronger and stronger.

Jiang Lili's eyes were in a trance, Yi Yang smiled: "What's wrong?"

"Ah?" Jiang Lili came back to his senses and said, "The summer vacation is coming to an end, are you okay tonight?"

"Not currently, but if there was, there wouldn't be any."

"Spoof." Jiang Lili laughed: "Accompany me to a concert."

(End of this chapter)