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Chapter 128 Fibonacci Sequence
As soon as Shi Bo entered the classroom, he saw Wang Ziqi chatting with his classmates. Of course, the topic could not avoid the Premier League match last night.

Everyone gathered around Wang Ziqi, praising Wang Lie's performance in the game. Among them were people who had stood on his side before...

With Wang Lie's outstanding performance, Wang Ziqi is now the celebrity in Class 2, Grade 1.

Weeds!
Shi Bo only dared to despise these traitors in his heart, but did not dare to actually go up and confront them.

Not only that, he also planned to sneak into the classroom along the wall and try to avoid that group of people.

But when he was halfway there, tiptoeing like a thief, he was discovered...

"Shibo!"

Wang Ziqi shouted, causing Shi Bo to tremble. Then he stood still, turned his head, and asked calmly, "What are you doing?"

"Three points! Three points!" Wang Ziqi proudly raised three fingers to remind Shi Bo.

"What three points?" Shi Bo pretended not to understand.

"There's only three points between Tyne and Sofia United. Are you ready to change your idol?"

Shi Bo said stubbornly: "When Sofol United beats Tyne in the next game, we will be six points behind again!"

Wang Ziqi sneered: "Haha."

"What are you saying? A football is round. How can you be sure that Tyne can beat Sofia United?!"

"I can be sure of it!" Wang Ziqi held his head high and spoke confidently.

This time it was Shi Bo who sneered: "Just lose, Wang Ziqi, and ruin Wang Lie's reputation! I tell you, when Taien loses to Sofol, it will all be your fault!"

Wang Ziqi still had a fake smile on his face: "Haha."

Shi Bo acted as if to say "I don't want to bother with you", returned to his seat calmly, and then pretended to be calm as he took out textbooks and stationery from his schoolbag.

But in his mind, there was one thought that never left his mind:
What if Tyne really gets the Champions League qualification? Do I really have to like Wang Lie? No, he looks so daddy, who would like him?
※※※

"Are you ready, Mr. Sven Helden? I am."

Looking at Wang Lie on his phone screen, who was smiling and pointing at the camera and asking questions, Stanley Harris sighed and said to his best friend Matthews Weaver:
"I really don't know how I will face Wang in the weekend's game..."

Weaver, who was lying on the sofa, held the controller in his hand, staring at the game screen on the TV screen intently, and comforted his friend: "What are you worried about, Stanley? It's not you who forced Wang to leave."

"But it's all about me and Wang. You know, it was the boss who gave me the opportunity to play in the first team. No matter what the outside world says, I am still very grateful to the boss. In order to prove myself and to prove that the boss's choice was correct, I always tried my best to perform and win for the team... So when the team's performance was getting better and better, they felt that the team no longer needed Wang..."

Stanley Harris kept talking.

But his best friend Matthews Weaver responded with an absentminded "hmm", his attention still on the game, where he was controlling a character with three heads and six arms to fight a BOSS.

"...So they said that I accelerated Wang's departure from the team, and I was also responsible for Wang's forced departure from Sofo United..."

Weaver quickly pressed the keys and dodged the boss's killing move, then said: "Don't take yourself too seriously, Stanley. Whether you perform well or not, it will not affect Wang and Sofulian's farewell... FUCK!"

He didn't finish his words, but because of his distraction, he was hit by the BOSS's next change of moves, and the protagonist, who already had little health, died instantly.

The game screen on the TV gradually turned black and white, and a huge subtitle "You are dead" appeared.

"Ah! Damn it!" After cursing, Weaver simply threw the controller aside and said to his friend very seriously: "You know the team needs to be renewed. Without your outstanding performance, Wang would have left the team for other reasons. Besides, his performance was not good during that time. This matter has nothing to do with you, and you should not make yourself more dramatic just because Helden thinks highly of you. Really, otherwise you should call Wang now and ask him what he thinks of you..."

Stanley Harris immediately waved his hands: "No, no, no, I won't do it! Besides, Wang told me before that he has never complained about me..."

"That's it, isn't it?" Waver spread his hands, intending to pick up the controller again to continue challenging the BOSS that had killed him repeatedly for more than an hour.

"But do you think Wang would say to me, 'Yeah, all my problems at SOF are because of you,' " Harris asked.

Then, to his surprise, Weaver blurted out: "Why not? Hasn't he always been such a frank person? Look at what he said in the interview yesterday? He was not even willing to pretend to forget the old relationship..."

Harris was stunned.

Because his friend was right. When asked by reporters whether it would be awkward for him to meet his old club again in such a crucial game, he answered directly:

“We’re going to go all out to win.”

Seeing Harris's reaction, Weaver knew he had hit the nail on the head, so he continued, "Wang has been preparing to defeat you in the weekend game and help Tyne take fourth place in the league. But you are here, presumptuous and entangled in how to face him... Ha, you are almost making me laugh, Stanley! Or do you think you can easily deal with Wang now?"

The look on Stanley Harris's face is brilliant.

Seeing that he didn't say anything else, Weaver started a new round and immersed himself in the game.

His best friend turned his attention back to his phone.

The voices on the Internet were so noisy that he seemed to have been led astray...

Matthews is right, I should focus on the game itself.

Just like Wang said, I will also do my best to pursue victory!

※※※

The day after the match between Tyne and Southampton, all of England and half of Europe were discussing Tyne's road to the Champions League.

Because this matter is really too magical and too topical - if Tyne really does qualify for the Champions League in the end, combined with Wang Lie’s previous declaration on the live TV program, the whole thing will seem extremely legendary.

You should know that just before Wang Lie joined Tyne, that is, five months ago, Tyne was still hovering on the edge of the relegation zone and could fall into it at any time.

All critics and fans believe that the team will have accomplished its mission as long as they can successfully avoid relegation this season.

That’s why when Wang Lie publicly pushed for the team to qualify for the Champions League, he attracted so much ridicule and confusion:

Why choose a goal that is impossible to achieve when there is a task that is easy to accomplish?
During that time, countless people were slandering Wang Lie and Taien on the Internet.

But now the comments of these haters have become boomerangs hitting their own faces.

Just today, the internet was filled with Wang Lie's fans digging up old grudges.

"'Tain will soon learn the price they paid for signing the king!' So this is the 'price'? Can there be more 'prices' like this?"

"If Sofia United loses to Tyne in the away game, the two teams will have the same points. But because Sofia United now has two fewer goals than Tyne, Tyne's league ranking will be above Sofia United... I remember what those people said before? 'Goals hurt the team'? Ah, I finally found the reason why Sofia United has fewer goals and a smaller goal difference now - these Sofia United players don't have the heart to hurt the team! It's really touching. The players care so much about the team, how can Sofia United not revive!"

"Who said that no matter how Wang performed in Tyne, it was considered a great achievement for Heldon to clean up Wang? As a Tyne fan, I strongly agree! Thank you Mr. Sven Heldon, and thank you to Sofia United for generously terminating the contract, so that we can sign Wang! Regardless of whether Mr. Heldon can continue to stay in Sofia United, his status in the hearts of us Tyne fans will always be lofty!"

"I heard someone scolding Wang for being too cold and heartless when he was interviewed yesterday? Come on, he is a Tyne player. If he doesn't speak from the perspective of Tyne, should he speak from the perspective of Sofia United? Thinking of 'heartless' now, wasn't it heartless when Wang was sent to the youth team in January this year? If I were to ask you, Wang was very grateful that he didn't say 'I am very happy to see Sofia United fall to this point' in front of so many media reporters yesterday! He just showed a strong desire to win, isn't it normal?"

There was a heated argument online, with forces supporting and opposing Wang Lie attacking each other, and those who were just watching and enjoying the show were also enjoying the show.

So what is Wang Lie, the person involved, doing?

※※※

1, 2, 3, 5, 8
Wang Lie stared at the numbers he had written on the paper in a daze.

This is the number of goals he scored each time he was young, and he tried to find some pattern in it.

After the system notified him yesterday that he was one year younger, he proved on his wife that his body functions had indeed become younger that night.

In three months, his physical functions really became five years younger, from thirty-eight years old to thirty-three years old, and he only scored nineteen goals in total!
Even with the support of the system, Wang Lie was still shocked by the speed - he felt it was too fast, so fast that it seemed like "getting something for nothing".

Although the "traveler" said it was a "gift" with absolutely no side effects.

But the effect was so good that Wang Lie couldn't help but wonder:
The better the effect was, the more unreal it seemed to him, and the more he worried that a heavy price was waiting for him.

To put it bluntly, it is actually the worry that "if someone shows you kindness for no reason, he is either a traitor or a thief."

Because he was still in the game yesterday, he didn't delve into this issue.

Now it is the second day after the game. He has half a day to rest and naturally has time to study what is going on.

He wanted to know the pattern between these numbers so that he could calculate how many balls he would need to get younger next time.

If I don't need that many balls, then if I continue like this, can I really be as young as eighteen?
What if my knee is suddenly injured again? Is that the price of this "gift"?
Don’t say that Wang Lie is worrying too much, he really does have this worry because of the unknown future.

The first time his body became younger, he only used one ball.

The second time he was young and scored two more goals.

The third time he was young, he scored three more goals. He once thought that he only needed to score four more goals to be young for the fourth time.

The result, of course, was a slap in the face.

It wasn't until he scored five goals that his physical function reached that of a thirty-four-year-old.

1, 2, 3, 5...

What is this rule?
Is there no pattern? The specific number of goals you score to get younger depends entirely on the mood of the system?

Now the fifth time young, with eight balls.

8和5之间，差了3，可是5和3之间却差了2，3和2之间又差了1……完全不相同嘛。

With Wang Lie's limited cultural knowledge, this set of numbers is almost the same as "chaotic" in his eyes.

Just then, his wife's curious voice came from behind him: "What are you doing?"

Wang Lie turned around and saw his wife coming towards him.

After seeing the string of numbers he wrote on the paper, he joked, "Are you researching the Double Color Ball?"

Wang Lie rolled his eyes at her, then drew a question mark after the number "8": "Let me test you, what should be the number after eight?"

"You're testing me on this?"

After hearing her husband's question, Tang Xingmei smiled.

"Yes, see if you know..."

Without waiting for her husband to finish his words, Tang Xingmei snatched the pen from him, crossed out the question mark, and wrote the answer:
13
"Thirteen? Why?" Wang Lie didn't understand.

"The Fibonacci sequence."

"What? What sequence? What is a sequence?" Wang Lie was confused.

Tang Xingmei pointed at the set of numbers on his paper and said, "These numbers can be collectively called 'sequences'. There are many types of sequences, and yours is called the 'Fibonacci sequence'."

As she spoke, she drew a spiral line on the paper with her hand: "Have you seen this picture?"

Wang Lie frowned and guessed, "Nautilus?"

Tang Xingmei was speechless. She could only draw a few auxiliary lines and then said, "You must have heard of the golden ratio, right?"

"Oh, this, I know this. But what does this have to do with that number series?" Wang Lie was still very confused.

Tang Xingmei explained: "Because when the Fibonacci sequence tends to infinity, the ratio of the previous term to the next term will get closer and closer to the golden ratio of 0.618. So the Fibonacci sequence can also be called the 'golden ratio sequence'..."

Then she looked at Wang Lie's pure expression, which seemed uncontaminated by the vast knowledge, and explained to her husband in a different way: "The characteristic of the Fibonacci sequence is that starting from the third number, each number is equal to the sum of the previous two numbers. You see, one plus two equals three, two plus three equals five, and three plus five equals eight. Then according to this rule, we can deduce that the number after the number eight should be the previous eight plus five, which is equal to thirteen."

As if she was afraid that her husband wouldn't understand, she simply wrote the equation on paper with a pen.

Wang Lie could still understand simple addition. After she listed these equations, Wang Lie suddenly understood: "Interesting..."

“其实严格意义上来说，斐波那契数列应该是‘1、1、2、3、5、8’以此类推。你写的这组数列少了个‘1’。不过无所谓，反正规律是斐波那契数列的规律。”

Tang Xingmei explained further.

"Because of the relationship between the Fibonacci sequence and the golden ratio, some people say that the Fibonacci sequence is the most beautiful sequence in nature. The golden ratio is used to draw a spiral curve. Many beautiful designs are designed with the golden ratio in mind. For example, the five-pointed star on our national flag has five isosceles triangles on each star. The ratio of the base to the waist of the triangle is the golden ratio. This kind of triangle is called a golden triangle."

"So that's why..." His wife used the five-pointed star on the national flag as an example, and the new knowledge in Wang Lie's mind immediately came to life. "No wonder our national flag is so beautiful!"

Tang Xingmei finished her popular science work with her husband and asked casually, "Why did you start studying this?"

Of course, Wang Lie couldn't tell his wife that he was cheating. This string of numbers was the password for cheating, so he just made up an excuse: "Someone in the team asked us this question, so I thought about it..."

Although it was just a random excuse, Tang Xingmei didn't doubt it at all.

Because this is very consistent with my husband's personality of wanting to win in everything - when teammates use this kind of question to test everyone, it is normal for my husband to want to put in some effort to answer this question correctly...

So Tang Xingmei didn't ask any further questions.

Wang Lie also put away the note. After he had figured out the pattern of the number string, he no longer needed to stare at the numbers in a daze. Instead, he silently calculated in his mind:
According to the pattern his wife told him, each number in this series is equal to the sum of the previous two numbers. So if he wants to make his body one year younger, he has to score thirteen more goals.

Given his current condition, thirteen goals doesn't seem very difficult, at least not far away.

By analogy, he felt he might be able to roughly guess what age his body would be in before next year's World Cup.

He now has the body of a thirty-three-year-old, and if he scores thirteen more goals, his body will be as young as that of a thirty-two-year-old.

If he is younger than 31, he needs to score 21 goals after 13 goals.

If you are young enough to be thirty, you have to continue to score thirty-four goals.

Young enough to be 29 years old, and score 55 more goals...

He didn't continue calculating because he felt that the number was already exaggerated.

Today is May 2037, 5, and there are still thirteen months until the opening of the World Cup next year.

If he wants to participate in the World Cup with the physical function of a 29-year-old, it means that he has to score in the next 13 months from now...

One hundred and twenty-three balls!

This is obviously impossible. Even at his peak, he could not score 123 goals in 13 months.

In fact, in Wang Lie's best season, the 2029-2030 season when he helped Sofa League win the "Quadruple Crown", he set a personal career single-season goal record, which is also a single-season goal record in world football history.

That season he scored a total of 79 goals in the Premier League, FA Cup, League Cup, Champions League, and national team matches.

This is the number of goals scored in one season, and a season is certainly not equal to thirteen months.

But there are not competitions every month in these thirteen months.

There are four league games and one national team World Cup qualifier left this season.

In other words, the so-called thirteen months is actually just five more games than a full season...

Five more games and scoring 42 more goals than in his peak period is absolutely impossible.

Through these simple mathematical additions, Wang Lie can conclude that it is difficult for him to be as young as 29 years old before the World Cup.

There is hope at the age of 30 - he only needs to score another 68 goals, which is not difficult for him with his cheats.

Going to the World Cup with the physical functions of a 30-year-old...it's really exciting just to think about it!

Just when Wang Lie was aiming for this, his brows, which had originally relaxed, suddenly frowned again.

Because he thought about his birthday on February 17 next year, which would make him one year older. That means if he wants to achieve his goal of participating in the World Cup at the age of 30, he still has to score 123 goals...

Fuck!
Wang Lie, who had just ignited some hope, cursed in his heart.

Then continue to lower your expectations in your mind.

Fine, it’s okay to participate in the World Cup at the age of 31... 31 is also my peak.

This is not his self-consolation, but the fact.

Because Wang Lie was 31 years old in the season when he won four championships and the year when he won seven championships.

At that time, his physical function had not yet declined from its peak. At the same time, he also had rich experience and excellent awareness, which allowed him to lead the team to accomplish unprecedented feats.

There is indeed not much difference between Wang Lie at the age of 30 and Wang Lie at the age of 31.

To reach the age of 31 before the World Cup, Wang Lie must score at least 68 goals.

This is not difficult.

Wang Lie was thinking in his mind.

Let’s leave it like this for now, the minimum bottom line is sixty-eight balls, and the more the better!

(End of this chapter)