Boom ~!
Li Zexuan raised his hands and made a gesture of "embracing the world." His posture was extremely dashing. However, what he had just said was tantamount to dropping a deep-water bomb, causing everyone in the auditorium to lose their composure!
The ancestral rate! This was the ancestral rate that had troubled the ancestors for who knew how many years! Even now, there were very few people who could accurately calculate the ancestral rate. However, Li Zexuan had easily obtained an approximate value of the ancestral rate just by playing a small game with everyone. This was simply a miracle!
"This... How is this possible?"
"It should be a coincidence, right?"
"But Yamachō mentioned the ancestral rate to us first. If it really is a coincidence, then wouldn't all the things that Yamachō said before be in vain?"
"It's definitely not a coincidence. Yamachō's expression was that of certainty from the beginning to the end. How can it be a coincidence?"
The students discussed animatedly below the stage, all of them feeling incredulous. In fact, it wasn't just them. The academy teachers present also felt incredulous! How could the ancestral rate, one of the biggest problems in the field of mathematics, be calculated so casually?
Li Zexuan thought to himself. No one guessed correctly! Because the answer he got was both a coincidence and not a coincidence at the same time. This experiment was the famous Buffon Needle Throwing Experiment in his previous life:
On a day in 1777 AD, the French scientist D. Buffon invited guests to do the same experiment that Li Zexuan had done previously at home. In the end, the guests threw in a total of 2,212 needles, of which the needles intersected with parallel lines 704 times. The ratio of the total 2,212 needles to the number of intersections 704 was 3.142. He said loudly to the guests, "Gentlemen, this is the approximate value of pi!"
The guests were in an uproar, and there were doubts for a while. Everyone was baffled. "Pi? This game has nothing to do with circles at all! "
The appearance of pi on such a chaotic occasion was really unexpected, but it was absolutely true. Since the problem of the needle throwing experiment was first proposed by Mr. Buffon, it was called the Buffon problem in the history of mathematics. The general result obtained by Buffon was: if the distance between two parallel lines on the paper was d, the length of the small needle was l, and the number of times the needle was thrown in was n, so the number of times the needle intersected with the parallel lines was m. Then, when n was relatively large, it was: pi ≈ (2ln) (dm). The needle length l used here was exactly half of the distance d between parallel lines, so substituting the above formula was simplified to be: pi ≈ nm.
(This formula could be completely proven using the knowledge of probability and geometry, so I won't go into detail here for the time being.
It was worth mentioning that later, many people followed Buffon Buffon's footsteps and used the same method to calculate the value of pi.
The most amazing of them all was the Italian mathematician. In 1901, he claimed to have conducted many needle throwing experiments. The number of needles thrown in each experiment was 3,408 times, and the average number of intersections was 1,808 times. Substituting it into the Buffon formula, he got pi ≈ 3.1415929 (the needle length l he used was not equal to half of the distance d between parallel lines). Compared with the accurate value of pi, the difference only appeared up to the seventh decimal point! Using such a simple method to obtain such a high precision value of pi, this was really a work of God, a work of God, too beautiful! If Zu Chongzhi were still alive, he would be flabbergasted!
However, people had always criticized Lazreini's results, but it was not unreasonable to get such a result, because it could be proved in mathematics that the fractions closest to the true value of pi, but with a smaller denominator, were:
(22) 7 ≈ 3.14 (Probability)
(333)(106)≈3.1415
(355) (113) ≈ 3.1415929 (Probability)
(103993)(33102)≈3.141592653
And Lazreini actually threw the probability. For a throw within 10,000 times, it was impossible to get a better result. No wonder many people doubted, "Could it be such a coincidence?" But most people thought that Lazreini was really "lucky" because he had been diligent and cautious all his life. As for the truth, there was no way to investigate it now!
Therefore, the result that Li Zexuan had just obtained was both a coincidence and not a coincidence. If he had been unlucky, the error in the result would have been slightly larger, but not by much! This was a probability problem!
In the auditorium, Xu Hongzhi, who had been studying mathematics for most of his life, was the most shocked person. At this moment, he did not care about being polite. He instantly stood up from his seat and walked directly to the podium!
Halfway there, he realized that he had been rude. He quickly bowed to Li Zexuan and said, "Yamachō, can I go up and take a look? This... I don't mean anything else. I just want to go up and take a look with my own eyes! "
The second half of his sentence seemed to be a cover-up. After all, if he had not seen such a miracle with his own eyes, he would never have believed it.
Li Zexuan was amused. Is this old man still suspecting that I cheated? So he laughed and said, "Mr. Xu, if you want to take a look, please come up and take a look. Not only that, other teachers or students who have doubts can also come up and take a look! Be careful not to touch the podium and mess up the position of the thin needles! "
"Thank you, Yamachō!"
As soon as he finished speaking, a few people immediately came up from below. There were students and teachers from the academy. Li Tai was also among them!
Several "doubters" quickly came to the podium and began to count the thin needles that fell on the parallel lines on the paper.
"One, two, three … two hundred twenty-five, two hundred twenty-six, two hundred twenty-seven! There are exactly 227 thin needles on the black line! "
After a quarter of an hour, four or five "doubters" walked up to the podium and counted the numbers. They could not help but exclaim!
Xu Hongzhi was completely convinced at this moment, but he still could not understand how a simple game could be related to the ancestral rate. So he looked at Li Zexuan next to him and said excitedly,
"A few years ago, my teacher had also used the Circle Cutting Technique to calculate the ancestral rate. However, after three days of calculation, only the first four digits after the decimal point were exactly the same as the ancestral master's calculation. Many times, if one careless miscalculation was wrong, it would lead to a complete miscalculation! Today, Yamachō casually played a game and accurately calculated the first three decimal places. I am deeply impressed! I wonder if Yamachō can explain the principle to us? "
At this moment, everyone's eyes were on Li Zexuan. Obviously, they also wanted to know the theory behind this. However, Li Zexuan smiled and said, "Everyone, please go back to your seats first! Let's put this question aside for the time being. I will play a small game with you! "
"F * ck your game!" "We want to hear the truth!"
When everyone heard this, they almost vomited blood. They were all going crazy in their hearts.
However, Li Zexuan was the one who spoke. If he did not want to say it, they could not find someone to beat him up and force him to say it, right? Who in the auditorium had the guts to do that? Besides, who could beat him?
Therefore, they could only sit down obediently and wait to see what Li Zexuan would do next!
.....
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