"Boom~!"
Li Zexuan raised his hands in a gesture of "embracing the world", his posture was extremely chic, but the words he just said were like dropping a depth bomb, making everyone in the auditorium uneasy!
Zu rate! This has troubled our ancestors for countless 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 easily came up with the approximate value of the ancestral rate. This is simply a miracle!
"This...how is this possible?"
"It must be a coincidence, right?"
"But the mountain chief just mentioned Zu Lite to us first. If it was really a coincidence, wouldn't everything the mountain chief said before be in vain?"
"It's definitely not a coincidence. The chief's face has a confident 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, not only them, but also the academy teachers present felt incredible! How could Zu rate, a major problem in arithmetic circles, be calculated so casually?
Li Zexuan thought to himself, no one guessed it right! Because finally getting such an answer is both a coincidence and actually not a coincidence. This experiment is the famous Buffon needle experiment in previous generations:
One day in 1777 AD, the French scientist D. Buffon invited guests to his home and conducted an experiment previously done by Li Zexuan. In the end, the guests threw needles a total of 2212 times, of which 704 times intersected parallel lines. The ratio of the total number 2212 to the intersection number 704 is 3.142. He shouted to the guests: "Gentlemen, this is the approximate value of pi!"
The guests were in an uproar, and there were many doubts. Everyone felt puzzled: "Pi? This game has nothing to do with circles!"
The appearance of π in such a complicated and chaotic situation is really beyond people's expectation, but it is a true fact. Since the problem of the needle test was first raised by Mr. Buffon, it is called Buffon's problem in the history of mathematics. The general result obtained by Buffon is: If the distance between two parallel lines on the paper is d, the length of the small needle is l, the number of needle throws is n, so the number of needle throws that intersect with parallel lines is m, then when n is quite large and the needle length l used here is exactly equal to half of the distance d between parallel lines, so substitute it into the above The formula is simplified to: π≈n/m.
(This formula can be proved completely using the knowledge of probability and geometry, so I won’t go into details here)
It is worth mentioning that many people later followed Mr. Buffon's footsteps and used the same method to calculate the value of π.
The most amazing among them is the Italian mathematician Lazzrini. In 1901, he claimed that he had conducted many needle-throwing experiments. The number of needles each time was 3408, and the average number of intersections was 1808. He substituted Buffon's formula to obtain π. The needle length l he used was not equal to the distance between parallel lines. half of d). Compared with the exact value of π, the difference does not appear until the seventh decimal place! Using such a light and easy method to obtain such a high-precision π value is truly a masterpiece of heavenly creation and a beautiful creation! If Zu Chongzhi were reincarnated, he would be so surprised that he would be dumbfounded!
However, people have always criticized Lazreni's results a lot, but such results cannot be said to be unreasonable, because in mathematics it can be proved that the fractions closest to the true value of π are the fractions with smaller denominators. yes:
sparseness)
density)
And Lazreni actually threw at a high density. For a throw within 10,000 times, it is impossible to have a better result. No wonder many people have raised doubts: "Is it such a coincidence?" But most people think that Lazreni has indeed "got lucky" in view of his diligence and prudence throughout his life. What the facts are, there is no way to test them now!
So the result that Li Zexuan just got is neither a coincidence nor a coincidence. If he were not lucky, the error in the result would be slightly larger, but not much! This is a probability question!
In the auditorium, Xu Hongzhi had been doing arithmetic for most of his life, and the most shocked person was him. At this moment, he no longer cared about being polite, and stood up from his seat in an instant, and then walked quickly towards the podium!
Halfway through, he realized that he was being rude, and he quickly raised his hands to Li Zexuan and said, "Mountain Chief, can you allow me to go up and take a look? Well... I have no other intention, I just want to go up and see with my own eyes!"
The second half of the sentence was somewhat trying to hide the truth. In the final analysis, he would never believe such a miracle unless he saw it with his own eyes.
Li Zexuan felt happy and secretly thought that this old man still suspected that he was cheating? So he said with a smile: "Mr. Xu, if you want to take a look, just come up and take a look. Not only that, other teachers or students who have questions can come up and take a look! 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 more people immediately appeared below, including students and gentlemen from the academy, including Li Tai!
Several "questioners" quickly came to the podium and began to count the fine needles falling on the parallel lines on the paper.
"One, two, three... Two hundred and twenty-five, two hundred and twenty-six, two hundred and twenty-seven! There are exactly 227 fine needles falling on the black line!"
Half a quarter of an hour later, four or five "questioners" who came to the podium had already tallied up the results, and they couldn't help but exclaim again!
Xu Hongzhi was completely convinced at this moment, but he still couldn't figure out how a simple little game could be connected with Zu Sui? So he looked at Li Zexuan next to him and said excitedly:
"My mentor also used the circle cutting technique to deduce the ancestor's rate in the early years. However, after three days of calculation, only the first four digits after the decimal point were completely consistent with the ancestor's calculation. Many times, if one step is accidentally calculated incorrectly, it will lead to a full game. They are all wrong! Today, the mountain leader can accurately calculate to the first three decimal places through a casual game. I am deeply impressed! I wonder if the mountain leader can explain the principle for us? "
At this time, everyone turned their attention to Li Zexuan. Obviously they also wanted to know the reason? However, Li Zexuan smiled a little bit, and then said: "Everyone, you should go back to your seats first! Let's put this problem aside for now, and I will let you play a little game!"
Play your sister's game! We must listen to the truth! ! !
When everyone heard this, they almost vomited blood, and they all said crazy in their hearts.
But Li Zexuan's mouth is on his body and he doesn't want to say it. You can't find someone to beat him up and force him to say it, right? Who in the auditorium has the courage? Besides, who can beat him?
So, they could only sit down in their seats obediently (depressedly) and see what tricks Li Zexuan would do next!
.............................
