I am reborn and just want to concentrate on my studies

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

No matter what they do, people are always full of passion at the beginning. When they become familiar with a certain thing or object, the passion fades and even begins to become boring. This can be applied to many places, love, learning...

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

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

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 fatigue of many people.

During class, I felt a little sleepy and looked around. I don’t know when the few seats that became vacant were still empty.

Naturally, 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 enthusiasm has faded a lot. Everyone has their heads lowered. Occasionally, when Liao Yifei asks a question, someone will raise their head to respond. Compared with the beginning of the class, the atmosphere is obviously different. A lot duller.

The first class in the morning is over.

It is cloudy today and the temperature is moderate. Although for many competitive students, whether it is summer vacation does not have any special meaning. Even because the math competition league will start soon after school starts, this summer vacation will become busier 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 out the window at the high sky. A jet plane dragged a long white line across the sky from behind.

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

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

Luo Bing shrugged: "Everyone has one, including Deng Wenxiao. Why is it just for me?"

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

Luo Bing laughed loudly: "Are you talking about me? Are you not?"

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

Luo Bing shook his head: "No."

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

"It won't affect study anyway..." 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 step by step. After all, I have no experience in this area. Just go with your feelings."

Yi Yang took a bite of the biscuit, which was a little sour with raisins added, and said, "I'm so envious of a winner in life like you, running 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 rush"... I have some experience. I have summarized it during this period. I don't know if it is correct. Please help me take a look. "

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

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

"Mathematics? Going in both directions?" Luo Bing was slightly startled.

Yi Yang nodded, pointed at the question, and said: "In the past, after studying mathematics competitions, when doing questions, I would naturally use some mathematics competition skills to think about college entrance examination questions. It would be easier, but apart from those New knowledge can only be learned through mathematics competitions. What exactly is mathematics competition thinking?”

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

Yi Yang said: "Although the term mathematical competition thinking can be heard on many occasions, no one seems to explain specifically what mathematical competition thinking is and how it is different from traditional mathematical thinking."

"I've asked you, Deng Wenxiao, and Teacher Liao, you, the more powerful competitors, and I've also been observing your thinking patterns. How should I put it, compared to me, your thinking patterns are more jumpy, such as , a combined number problem, ordinary mathematical thinking is to solve the problem step by step, but you seem to be very sensitive to the meaning of various combinations, always cutting in from a certain point in the middle, and starting to solve the problem... But, this What is the nature of this kind of thinking?”

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

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

Luo Bing smiled gently: "Mortals can't 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 to say, am I the one between genius and mortal? Because of being in this awkward position, even if I can't do what a genius can do, I can understand what a genius thinks, and at the same time I can understand what the crux is that ordinary people don't understand... But despite this, I still feel better. Some.

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 for a while, his expression became serious, and he said: "The essence of this kind of thinking... Well, I think it goes in both directions."

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

Yi Yang pointed to the geometry problem in the exercise book and said, "Take these two geometry problems for example."

"This question is the penultimate question in Paper A of last year's college entrance examination. It can be solved by traditional mathematical problem-solving thinking. The step is to first interpret each known condition. Basically, when each known condition is almost translated, the answer to this question The idea comes 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 triangle. Translated, this condition only corresponds to the theorem that the midline on the hypotenuse of a triangle is equal to half of the hypotenuse, that is, AE=BE=1/2AC... As long as the basics If you have a solid grasp of knowledge and translate other conditions in the same way, basically there will only be 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 solution to 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... Only four known conditions are given in total, but its graphics are very complicated. If one known condition needs to be translated, it will correspond to too many More knowledge.”

"For example, this line segment is not only the center line of the hypotenuse of this small triangle, but also the base of this triangle. It is also the tangent line of this circle, and these four points are also cocircular...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 several other known conditions. If you translate them all, you may have more than a dozen directions in front of you to think about, and you don’t know which direction to follow. If you think about that direction, you may have to think about it for a long time before you realize that this path doesn't work..."

"What's more...many of the theorems in mathematics competition questions will make people dizzy if they change slightly."

"Um……"

Yi Yang continued, "So when thinking about mathematics competition questions, it is very difficult to use conventional mathematical thinking... This is also the difference between the thinking of competition students and ordinary college entrance examination students. When mathematics competition students think about this kind of question, their thinking is not step-by-step. Thinking, but... using a two-way thinking method to solve problems, adding reverse thinking and forward thinking to stimulate inspiration."

Luo Bing remained silent.

Yi Yang pointed to this question: "Continuing to take this question as an example, since we are asked to prove that the angle ADF = 90 degrees, so if we think about it here as a starting point, there will be a lot less direction."

"There are four possibilities for the relationship between this angle and other angles to produce 90 degrees..."

Yi Yang began to write and draw on the draft paper, listed it out, and then said: "Following these four possibilities, deducing forward, a certain path of reverse thinking will be followed by more than a dozen translated forward ideas in a certain way. A point intersects, and then we screen and combine the possibilities translated from the known conditions to prove this intersection... In this way, we can see how to solve this problem."

"Simple forward thinking is not enough. Pure reverse thinking also has its limitations. Only by running in both directions can inspiration be easily inspired. But thinking beasts like you can basically take a look at such a simple competition question without even realizing it. By then, the reverse thinking has been deduced to the third to last step, and the dozen possibilities of forward thinking can be quickly reflected, and the approximate intersection position of them has also been reflected." After saying that, 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: "It's awesome."

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

"Ha...it's not that exaggerated."

"You're very proud of yourself."

"No."

"You're very proud of yourself."

"Hey……"

…

When I went back today, Yi Yang was in a good mood. At least he had determined the direction of training his thinking mode. After he became proficient, even if he still couldn't do some difficult mathematics competition questions, this way of thinking would not have much direction after the translation of known conditions. Among the college entrance examination questions is dimensionality reduction... This is why powerful math 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 would sigh a little depressedly when she mentioned this matter.

Now Yi Yang can concentrate on studying in a noisy environment. Jiang Lili is watching TV while he sits on the edge of the coffee table doing questions.

It took nearly an hour to finally figure out a question. Yi Yang rubbed his temples in pain. The math competition was really difficult.

At this time, a TV series that had nothing to do with love was being played on the TV. Jiang Lili was watching the TV in rapt attention, but suddenly asked a question: "Yi Yang, do you think two people with hugely different family conditions really can't be together? ?”

Yi Yang's eyes flickered and he shook his head: "Probably...not so."

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

Yi Yang said: "I just analyzed it objectively, without any tendency, and..." After a pause, he said seriously: "Sister has fallen into a misunderstanding."

"Um?"

"What you struggle with is your background in a rural area and your status as a rich girl. And the reason your best friend and her boyfriend didn't get together in the end was because they had different views."

"The two feel connected, but in fact they are essentially different."

"A person's outlook on life is formed by various factors, which can even be said to be bizarre. In addition to childhood growth, the influence of parents, perhaps a certain sentence in a certain book, or a choice made by the protagonist in a movie, It is possible to reshape a person’s outlook on life.”

"A person may become a perverted murderer just because he was stepped on when he was a child."

"A person may love life just because he saw a flower wither with his own eyes when he was a child..."

"In short, if you can't tell clearly and have poor family conditions, you can try to guess that a person's consumption outlook is tight and not generous, but is it accurate?"

Yi Yang looked at Jiang Lili.

"Is it accurate?" Jiang Lili was stunned for a moment, still savoring what Yi Yang had just said. Then she shook her head and said with a smile: "Probably... not very accurate."

Yi Yang also laughed: "Yeah."

"So, there is no need to get entangled in such things. Your best friend and his ex-boyfriend did not get together in the end because her ex-boyfriend could not accept some of her living habits, but that does not mean that everyone like her No one with an ordinary family background would be able to accept his ex-boyfriend."

"There are no two identical leaves in the world. Similarly, there are no two people in the world who have exactly the same three views. They can only tolerate each other, and the key point is mutuality, not tolerance."

After a pause, Yi Yang drew a circle on the notebook and said, "Look, a person's values, consumption outlook, love outlook, family affection outlook, all these make up a person's appearance. Many people think that it It’s a circle…”

Then he drew a big circle outside the circle to wrap it, and said: "This is how many people imagine two people getting along, with one party tolerating the other, but in fact..."

Then he drew a rugged pattern next to it and said: "But I feel that a person cannot be a circle. All aspects of him are concave and convex. When two people get along, I am convex in some places. If you are concave, I tolerate you. In some places, you are concave, and I am convex, and you tolerate me..."

"For example, I don't like you leaving your shoes neatly when you come in, but I won't be angry. I will just help you put them away silently, because I play games late at night, and you don't like it either, but you will still act coquettishly while holding the fruit. I will take a rest and I will never yell out loud... There is no absolute way for one party to tolerate the other, it is all mutual."

Jiang Lili felt a little shocked in her heart after hearing Yi Yang's words.

She couldn't help but recall the first time Yi Yang came to her place to make up lessons. He didn't even understand English in the first year of junior high school, but now he was calmly analyzing things about gender, life, and emotional communication...

His growth comes from learning, but this kind of thing 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 give birth to different kinds of things. different shapes of people.

A few years ago, I met Yi Yang, who may be very powerful in the future. He has the kind of characteristics that he can stick to if he believes in the right thing. He is stubborn but not rigid, knows how to listen, can think, and is willing to stand in other people's positions. Thinking about all kinds of problems, no matter which person or age group, it is enough to make people believe that his future is promising.

But witnessing Yi Yang's step-by-step growth from knowing nothing to the person he is today still gives people an extremely unreal dreamlike feeling...

Rich knowledge, a strong body like an athlete, understands music, has a calm personality, is calm when things happen, and radiates this emotion to the people around him, making them feel at ease, and at the same time very interesting... This is also reflected in In many ways, interesting hobbies, having an interesting perspective on something... all kinds of things.

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

There are actually such boys in this world.

And along the way, he was not only a witness... but also a participant. Now that he was living under the same roof, the wonderful feeling became even more intense.

Jiang Lili's eyes were in a daze as she thought about it, and Yi Yang smiled: "What's wrong?"

"Ah?" Jiang Lili came back to her senses and said, "Summer vacation is about to end. Are you okay tonight?"

“Not at the moment, but if there was, it’s gone.”

"Poor talker." Jiang Lili laughed and said, "Come with me to a concert."