Li Zexuan didn't have any grudges against the Imperial College. At most, some people in the Imperial College didn't like him. He didn't take these things to heart.
Back then, when he had angrily resigned, it had not been to deliberately target Kong Yingda. On the contrary, when he had been teaching at the Imperial College, Kong Yingda had taken good care of him. In the end, he had just been a little dissatisfied with the Imperial College, where Confucianism was prevalent.
Besides, it had been so long. He only wanted to do well at Yanhuang College. How could he have the time to care about these small grudges?
"Haha, Mr. Xu, Mr. Liu, come in and have a seat! Mo Zhong, serve the tea! "
Mo Zhong welcomed Xu Hongzhi and Liu Hongyuan in. Li Zexuan hurriedly stood up and greeted them warmly.
Xu Hongzhi cupped his hands and said sincerely, "Yamachō, this is my teacher. He has something to ask you. I hope you won't mind …"
"Hey! Mr. Xu, you're too serious. This is the first time I've met Dr. Liu. There's no such thing as past grudges. Come in and have a seat. Dr. Liu, please! "
Li Zexuan interrupted Xu Hongzhi without waiting for him to finish.
Liu Hongyuan looked at Li Zexuan appreciatively and followed Li Zexuan inside. He smiled and said, "Marquis Yong 'an is so young, but you have such a big heart. No wonder you can build up such a big business in just a few months!"
They sat down one after another. Li Zexuan smiled and said, "Dr. Liu, you're too kind. You've been working hard at the Imperial College for decades, teaching and educating people. You're the role model of my generation!"
Li Zexuan knew that Liu Hongyuan was Xu Hongzhi's teacher. He also investigated Liu Hongyuan's past deeds. He was a respectable "teacher of the people"!
Seeing Li Zexuan's kind face without any displeasure, Xu Hongzhi, who was still worried, was relieved.
Liu Hongyuan said, "Haha! Forget it, forget it. That's all in the past. Don't mention it again! Today, this old man has come to find the Marquis of Yong 'an because I have a request! "
The old man had been teaching for his entire life, but he did not put on any airs at all. His attitude was also quite humble. He was completely different from those rotten scholars!
Li Zexuan admired him in his heart, but he quickly said, "Old Mister, you're too kind. If you have something to ask, just say it. There's no need to talk about asking for it. Isn't this too much for this junior? "
When Liu Hongyuan heard Li Zexuan's reply, he didn't bother to be courteous. His pale old face was now flushed red. He was probably very excited at this moment. "A few days ago, I saw the needle toss game that Marquis Yong 'an made. Out of curiosity, I also made a similar game at the School of Mathematics. I'm sure Marquis Yong' an has already heard of the results. To be able to accurately calculate the sixth decimal point of the ancestral rate in my lifetime, this old man is naturally excited, but … "
Speaking of this, the old man paused for a moment. Li Zexuan cooperated and asked, "But what? Professor Liu, there's no harm in saying it directly! "
Liu Hongyuan nodded and continued, "But no matter how much I thought about it, I still couldn't figure out how to calculate the ancestral rate through a simple needle toss game. This seems like child's play! This old man thought about it for four whole days and still couldn't figure it out. Thus, I shamelessly came here to ask Marquis Yong 'an for advice. I hope you don't blame this old man for coming uninvited! "
So it was for the needle toss experiment!
After hearing this, Li Zexuan finally understood why the old man came. However, he couldn't help but feel that it was a little funny. To be troubled over a question for four whole days, this was really a stubborn old man!
Actually, regarding the theory behind the needle toss experiment, many teachers from Yanhuang College, including Xu Hongzhi, had come to ask him. However, he didn't say anything. He wanted to let the teachers from the college slowly find the answer themselves.
Now that the old man came all the way here just for this, Li Zexuan couldn't continue to keep him in suspense.
"Since Professor Liu wants to know the theory behind this game, then this junior will explain it today. If there are any mistakes, I hope the two of you can point them out ~!"
Li Zexuan said politely. Then, he took out a pencil from the pencil box on his desk and a piece of white paper. He began to explain as he drew:
"Let's assume that there is an iron wire bent into a circle. Its diameter is exactly the distance between the parallel lines that I drew on the paper when I was doing the needle toss game. We will use d (de) to represent this distance.
It can be imagined that for such a circle, no matter how it is thrown, there will be two points of intersection with the parallel lines. Thus, if the circle is thrown n (en) times, then the total number of intersection points must be 2n (en). "
Cough cough, the people of Tang Dynasty didn't understand English, let alone the pronunciation of the English alphabet. Thus, when Li Zexuan set the unknown variables, he used Hanyu Pinyin to read it so that others wouldn't understand.
(To make it easier to read, there will be no additional labels for the letters.)
Liu Hongyuan and Xu Hongzhi both nodded thoughtfully. Both of them had learned Li Zexuan's new mathematics and had read about equations in the textbooks, so they could understand Li Zexuan's method of setting the unknown variables.
Li Zexuan continued: "Let's now imagine that the circle is straightened, then the length of the iron wire is π d. Oh, right, I usually like to use π to represent the ancestral rate. After the circle was straightened, the situation of such an iron wire intersecting with parallel lines when it was thrown down was obviously more complicated than that of a circle. There might be 4 points of intersection, 3 points of intersection, 2 points of intersection, 1 point of intersection, or even no intersection at all.
Since the length of a circle and a straight line are both π d, according to the principle of equal opportunity, when they are thrown a large number of times and are equal, the total number of intersection points between the two and a set of parallel lines is approximately the same. That is to say, when a wire of length π d is thrown n times, the total number of intersection points between the wire and a set of parallel lines should be approximately 2n.
Now let's talk about the case of the iron wire length l. When the number of throws n increases, the total number of intersection points of the iron wire with the parallel lines, m, should be proportional to the length l, thus: m = kl, where k is the coefficient of proportionality.
In order to find k, we only need to note that for the special case of l = π d, we have m = 2n. Thus, we get k = (2n) (π d). Substituting the former formula, we get: m ≈ (2ln) (π d), and thus π ≈ (2ln) (dm)!
When the length of the line is half the distance between the parallel lines, the above formula can be written as π ≈ nm. These are the two needle throwing games we did before! "
There were some "beyond the scope" of the knowledge, so Li Zexuan forgot to explain. He didn't care whether they could understand or not, he just said it all.
Sure enough, Liu Hongyuan and Xu Hongzhi both frowned. The two silently "digested" the information. After a while, Liu Hongyuan asked:
"I have something I don't understand. What is the principle of equal opportunity?"
…
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