In the blink of an eye, the summer vacation has come to an end.

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

This matter should also be viewed dialectically, people's passion is infinite but the passion for one thing is limited, it is based on this that scientists can continue to explore new fields, powerful conquerors can continue to expand their territory, and a mature sea king can continue to conquer new girls......

Of course, this quality 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 exhaustion of many people.

During class, I was a little sleepy, and I looked around, but there was still no one in the few places that began to vacate at some point.

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

Although the teacher's class rhythm has not changed, but I can feel that the passion has retreated a lot, everyone lowered their heads, occasionally Liao Yifei asked a certain question, and someone raised his head to respond, compared to the beginning of the class, the atmosphere was obviously a lot duller.

The first class in the morning is over.

Today is cloudy and the temperature is moderate, although for many competition students, whether it is summer vacation is not particularly meaningful, and even because the competition will start soon after the start of the school year, this summer vacation will become busier than in school, but the temperature at this time is still a reminder to everyone...... Summer vacation is really coming to an end.

Yi Yang looked out the window at the sky, a long white line trailing across the sky behind the butt of a jet plane.

Then a packet of biscuits in a transparent grocery bag appeared in front of me.

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

Luo Bing shrugged: "Everyone has it, Deng Wenxiao also has it, why did it become for me?" ”

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

Luo Bing laughed: "You said me? Aren't you yourself? ”

Yi Yang was also polite, opened the food bag and took the biscuits to eat, and asked, "Are you with Chi Xiaohuan?" ”

Luo Bing shook his head: "No." ”

"But I was surprised...... You would even admit that you have a crush on Chi Xiaohuan. ”

"Anyway, it won't affect your 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 one step at a time, after all, I don't have any experience in this area, just follow the feeling." ”

Yi Yang took a bite of the biscuit, added raisins to it, a little sour, and said, "I envy a winner in life like you, go both ways." ”

Luo Bing smiled: "Your envy is fake." ”

Yi Yang laughed, suddenly thought of something, paused, and said, "But when it comes to the word two-way running...... I have a little experience, which has been summarized during this time, and I don't know if it's right, you can help me take a look. ”

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

Yi Yang glanced at Luo Bing, sat down, took out a number competition, and said, "I didn't say that I was in love...... It's about math. ”

"Mathematics? Going both ways? Luo Bing was slightly stunned.

Yi Yang nodded, pointed to the question, and said: "In the past, after learning mathematics competitions, I would naturally use some mathematics competition skills to think about college entrance examination questions when doing questions, which would feel easier, but in addition to those new knowledge that will only be learned in mathematics competitions, what is mathematics competition thinking?" ”

Luo Bing showed a thoughtful expression and touched his chin, "Math competition thinking...... So what conclusions did you come up with? ”

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

"I have consulted you, Deng Wenxiao, and Teacher Liao, you are a more powerful competition student, and then you are also observing your thinking mode, how to say, compared to me, your way of thinking is more jumpy, for example, a combination of number problems, 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 start from a certain point in the middle, and start to solve the problem...... But what is the essence of this thinking? ”

Luo Bing's eyes also became a little curious, and he nodded slightly: "Hmm...... Well, I didn't think about the principle of my own thinking. ”

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

Luo Bing smiled gently: "There is no way for mortals to understand the thinking of geniuses, but you seem to have analyzed the essence, I want to hear your conclusions." ”

Yi Yang thought to himself, that is, am I the layer between a genius and a mortal? It is precisely because of being in such an awkward position that even if you can't do what a genius can do, you can understand what a genius thinks, and at the same time, you can understand what the crux of a mortal can't understand...... But despite this, the mood is a little better.

It's not a good thing to be too genius, he still wants to be a vulgar mortal, empathizing with the happiness that most people can empathize with.

Yi Yang thought for a while, his expression became serious, and said, "The essence of this kind of thinking ...... Well, I think it's a two-way street. ”

Luo Bing's eyes moved, "Go both ways." ”

Yi Yang pointed to the geometry problem in the workbook and said, "Take these two geometry problems as an example." ”

"This question is the penultimate question in last year's college entrance examination A paper, the traditional mathematical problem-solving thinking can be done, the step is to first interpret every known condition, basically when every known condition is almost translated, the idea of this question will come out, because a known condition, basically corresponds to a theorem or usable concept."

For example, if point e is the midpoint of AC and is a right-angled triangle, this condition is translated so that it only corresponds to the theorem that the middle line on the hypotenuse of the triangle is equal to half of the hypotenuse, that is, ae=be=1/2ac...... As long as the basic knowledge is solid enough, and the other conditions are translated in the same way, there are basically 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 the problem is basically out."

Luo Bing nodded slightly.

Then Yi Yang said: "This is the college entrance examination question, let's look at this competition geometry question...... In total, only four known conditions are given, but its graph is very complex, and one known condition corresponds to too many knowledge points if it is to be translated. ”

For example, this line segment is both the hypotenuse center line of this small triangle, the bottom edge of this triangle, and the tangent of this circle, and these four points are still round...... So this line is equal to this line, this known condition, if you translate it, there are five or six theorems involved, and the same is true of several other known conditions, all translated, there may be more than a dozen directions in front of you, you don't know how to think down that direction, it is likely that you think for a long time, only to find that this road does not work......"

"What's more...... Many of the theorems in math contest questions can be dizzying at the slightest change. ”

"Hmmm......"

Yi Yang continued, "So it is very difficult to think about math competition topics with conventional mathematical thinking...... This is also the difference between the thinking of competition students and ordinary college entrance examination candidates, when mathematics competition students think about this kind of topic, the idea is not to think step by step, but to ...... Use a two-way way of thinking to solve the problem, reverse plus positive thinking, and stimulate inspiration. ”

Luo Bing was silent.

Yi Yang pointed to this question: "Continue to take this question as an example, since we are going to prove that the angle adf = 90 degrees, so if we think about it here as a starting point, the direction will be much less." ”

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

Yi Yang began to write and draw on scratch paper, listed them, and then said: "Following these four possibilities, deduce forward, a certain path of reverse thinking will intersect with more than a dozen translated positive ideas at a certain point, and then filter and combine these possibilities translated by known conditions to prove this intersection point...... In this way, you can see how to solve this problem. ”

"Pure positive thinking is not good, pure reverse thinking also has its limitations, only two-way running, it is easy to inspire, and thinking animals like you, this kind of simple competition problem basically glances, they don't realize it, they deduce the reverse thinking to the penultimate step, and more than a dozen possibilities of positive thinking can also be quickly reacted, and the position of their approximate intersection has also been reflected." After speaking, Yi Yang looked up at Luo Bing and said, "That's how I understand it." ”

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

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

"Hah...... It's not that exaggerated. ”

"You're proud."

"Nope."

"You're proud."

"Hey ......"

……

When I went back today, Yi Yang was in a good mood, at least he determined the direction of the exercise of the thinking mode, and after becoming proficient, even if he still couldn't do some difficult math competition questions, but this way of thinking was put in the college entrance examination questions with few directions after the translation of known conditions...... This is also the reason why powerful math students can see at a glance how to solve some college entrance examination questions.

It's been a month since Jiang Lili's best friend failed to reunite, but occasionally Jiang Lili mentions this matter, and he still sighs a little depressedly.

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

It took nearly an hour to finally make a question, Yi Yang rubbed his temples a little painfully, it was really difficult to compete in numbers.

At this time, a TV series that didn't want to do anything with love was playing on TV, Jiang Lili watched the TV attentively, 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 should be ...... Not really. ”

"But...... Don't you say that you agree with my best friend's ex-boyfriend? ”

Yi Yang said: "I just analyzed objectively, and I have no inclination, and I ......" paused, and said seriously: "My sister has fallen into a misunderstanding of thinking. ”

"Huh?"

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

"The two feel connected, but they are fundamentally different."

In addition to the growth of childhood, the influence of parents, perhaps a sentence in a book, or a choice of the protagonist in a movie, it is possible to reshape a person's three views."

"A person who becomes a psychopathic murderer may only be trampled on as a child."

"A person who loves life may only be because he saw the withering of a flower when he was a child......"

】

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

Yi Yang looked at Jiang Lili.

"Accurately?" Jiang Lili was stunned, still savoring Yi Yang's words just now, and then shook his head and said with a smile: "Probably...... Not exactly. ”

Yi Yang also laughed: "Yes." ”

"So, there's no need to get entangled in such a thing, 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 with a family like her ex-boyfriend can't accept it."

"There are no two identical leaves in the world, and in the same way, there will be no two people in the world who have exactly the same three views, they can only tolerate each other, and the focus is on each other, not tolerance."

After a pause, Yi Yang drew a circle on his notebook and said: "You see, a person's values, consumption outlook, love outlook, family outlook, all kinds of things constitute a person's appearance, many people think that it is a circle ......"

Then he drew a large circle on the outside of the circle and wrapped it, saying, "This is what many people imagine two people to get along with, one side accommodates the other, but in fact, ......"

Then he drew a rough and uneven picture next to it, and said: "But I think that a person cannot be a circle, his various aspects are concave and convex, when two people get along, some places I convex, you concave, I tolerate you, some places, you concave, I convex, you tolerate me......"

"For example, I don't like you to put your shoes in order when you enter the door, but I won't be angry, I will just silently help you put them away, because I play games late at night, and you don't like it either, but you will still take me to rest with fruit, and I will definitely not scold...... There is no absolute one side to accommodate the other, it is all mutual. ”

Jiang Lili listened to Yi Yang's words, and his heart was slightly shaken.

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

His growth comes from learning, but this kind of thing that seems to be summed up with a lot of experience is no longer something that can be obtained simply by reading, she thought, it is like this, the same environment can also give birth to all kinds of different shapes of people.

A few years ago, I have met Yi Yang in the future, he may be very powerful, the kind of trait in him, he can stick to a correct thing, stubborn but not rigid, know how to listen, can think, willing to think from the perspective of others, all kinds of things, no matter which person, which age group, is enough to make people believe that his future can be expected.

But witnessing Yi Yang grow from not knowing anything to being like this person step by step, it still makes people feel a very unreal dream......

Rich knowledge, athlete generally strong physique, understand music, have a calm personality, encounter things calmly, and radiate this emotion to the people around them, so that they can also feel at ease, and at the same time it is fun...... This is also reflected in many ways, interesting hobbies, making interesting opinions about something...... All sorts of things.

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

There really is such a boy in this world.

And along the way, he was not only a witness...... As a participant, now living under one roof, the feeling of wonder is even stronger.

Jiang Lili's eyes flickered when he thought about it, and Yi Yang smiled: "What's wrong?" ”

"Huh?" Jiang Lili came back to his senses and said, "The summer vacation is coming to an end, do you have anything to do tonight?" ”

"Not at the moment, but if there is, it's not anymore."

"Poor mouth." Jiang Lili laughed: "Accompany me to a concert." ”