Otaku Engineer in Great Tang Dynasty

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"Boom~!"

Li Zexuan raised his hands in a gesture of "embracing the world", and his posture was extremely unrestrained, but what he just said was like dropping a depth bomb, making everyone in the auditorium uneasy!

Zu rate! This is the ancestral rate that has troubled the ancestors for many years! Even now, there are very few people who can accurately calculate the ancestral rate, but Li Zexuan just played a small game with everyone, and he easily obtained the approximate value of the ancestral rate. This is a miracle!

"This... how is this possible?"

"It must be a coincidence, right?"

"But the mountain chief just mentioned Zu Su to us first. If it's really a coincidence, isn't everything the mountain chief said before?"

"It's definitely not a coincidence. The mountain chief's face has always been a sure-shot expression from beginning to end. How could it be a coincidence?"

The students were talking a lot below, and they all felt incredible. In fact, it was not only them, but also the teachers of the academy present. A major problem in the field of arithmetic, how could Zu rate be calculated so casually?

Li Zexuan thought to himself, no one guessed right! Because in the end getting such an answer is not only a coincidence, but it is not a coincidence. This experiment is the famous Buffon needle injection experiment in the previous life:

One day in 1777, the French scientist D. Buffon invited the guests to perform an experiment that Li Zexuan had done at home. In the end, the guests cast a total of 2,212 needles, of which 704 times intersected with parallel lines. The ratio of the total number of 2212 to the number of intersections of 704 is 3.142. He shouted to the guests: "Gentlemen, this is an approximation of pi!"

The audience was in an uproar, and there was a lot of doubts for a while, and everyone felt inexplicable: "Pi? This game has nothing to do with the circle!"

The appearance of π in such chaotic occasions is really beyond people's expectations, but it is a true fact. Since the problem of the needle-throwing test was first proposed by Mr. Buffon, it is called the Buffon problem in the history of mathematics. is l, and the number of needles is n, so the number of times the needles are thrown to intersect with the parallel line is m, then when n is quite large, there are: π≈(2ln)/(dm). The needle length l used here is exactly equal to half of the distance d between parallel lines, so it is simplified by substituting the above formula: π≈n/m.

(This formula uses the knowledge of probability and geometry, which can be fully proved, so I won't go into details here.)

It is worth mentioning that many people followed in the footsteps of Mr. Buffon and used the same method to calculate the value of π.

One of the most amazing is the Italian mathematician Razrini. In 1901, he claimed to have carried out many needle-throwing experiments. The number of needles was 3408 times each time, and the average number of intersections was 1808 times. Substituting into Buffon's formula, he obtained π≈3.1415929 (the needle length l he used was not equal to parallel half the distance d between lines). This is compared to the exact value of pi, which does not appear different until the seventh decimal place! Using such a light method to obtain such a high-precision value of π, this is really a creation of heaven, and it is so beautiful! If Zu Chongzhi were to be reborn, he would be astonished and dumbfounded!

However, people have always criticized Razreni's result a lot, but getting such a result cannot be said to be unreasonable, because it can be proved in mathematics that the fractions with smaller denominators that are closest to the true value of π Yes:

(22)/7≈3.14 (sparse rate)

(333)/(106)≈3.1415

(355)/(113) ≈ 3.1415929 (density)

(103993)/(33102)≈3.141592653

And Lazreni actually threw the density rate, for the throws within 10,000 times, there can be no better results. It's no wonder that many people are skeptical: "Is there such a coincidence?" But most people think that Lazreni has indeed "had good luck", given his life of diligence and prudence. What the truth is, there is no way to test it now!

Therefore, the result Li Zexuan just got is both a coincidence and not a coincidence. If he is unlucky, the error of the result obtained will be slightly larger, but it is not too big! This is a probability question!

In the auditorium, Xu Hongzhi has been doing math for most of his life, and the one who was most shocked was him. At this moment, he didn't care about humility, he stood up from his seat in an instant, and then walked directly to the podium!

Halfway through, he realized the rudeness, and hurriedly cupped his hands to Li Zexuan: "Master, can I let this old man go up and take a look? This... This old man has no other intentions, just wants to go up and see for himself!"

In the second half of the sentence, there is a sense of concealment. After all, if he had not seen such miracles with his own eyes, he would never have believed them.

Li Zexuan was happy, and secretly said that the old man still suspected that he was cheating? So he laughed and said, "Mr. Xu can come up to check it if he wants to see it. Not only that, other gentlemen or students who have questions can come and check it out! Be careful not to touch the podium and disturb the position of the fine needle!"

"Thank you, Chief!"

As soon as he finished speaking, several people immediately appeared below, including students and teachers from the academy, including Li Tai!

Several "skeptics" quickly came to the podium and began to count the thin needles that fell on parallel lines on the piece of paper.

"One, two, three... two hundred and twenty-five, two hundred and twenty-six, two hundred and twenty-seven! It turns out that there are exactly two hundred

Twenty-seven fine needles fell on the black line! "

Half an hour later, four or five "doubters" who walked onto the podium had already counted the results, and suddenly they couldn't help but exclaimed!

Xu Hongzhi was completely convinced at this moment, but he still couldn't understand, how could a simple little game be linked to Zu rate? So he looked at Li Zexuan next to him and said excitedly:

"My teacher also used the cutting circle technique to deduce the ancestral rate in the early years, but after three days of calculation, only the first four digits after the decimal point are exactly the same as the ancestral calculation result. Many times, if one step is accidentally miscalculated, it will lead to a full plate. It's all wrong! Today, the chief of the mountain can accurately count the first three digits after the decimal point with his random game. This old man is deeply impressed! I wonder if the chief of the mountain can clarify the principle for us?"

At this time, everyone turned their attention to Li Zexuan, obviously they also wanted to know the principle? However, I saw Li Zexuan smiled a bit cheaply, and then said: "Everyone, go back to your seats first! Let's put this question aside for the time being, and I'll show you a little game!"

Play your sister's game! We must listen to the truth! ! !

When everyone heard it, they almost vomited blood, and they all went crazy in their hearts.

But the mouth is on Li Zexuan's body, he doesn't want to say it, he can't find someone to beat him up and force him to speak, right? Who has the guts in the auditorium? Besides, who can beat it?

So, they could only sit down obediently (depressed) in their seats and see what Li Zexuan will do next!

......................

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