While the people of Chang 'an were talking about football, the students of Yanhuang College in Yunshan, outside of Chang' an City, finally welcomed their first class after coming to the Academy! The previous three and a half days of vacation had ended!
This was also the first class of engineering after being brought to this world. It was very significant, so Li Zexuan chose to teach this class in person. The venue was the recently built auditorium of the Academy. The architectural style of the auditorium was designed by Li Zexuan by imitating the Beibei Building in his previous life. It was a magnificent palace-like building, and the second floor could accommodate more than six hundred people at the same time. This was also the reason why Li Zexuan chose to teach here. His class was for all the students.
More than six hundred students and more than seventy teachers gathered together, making the newly built auditorium very lively. Li Zexuan saw that Mo Zhong had brought the "tools" over. He coughed lightly and said, "Okay, quiet down! The class has started! "
The noisy classroom suddenly became silent. Currently, in the Academy, no one dared to challenge Li Zexuan's prestige.
Li Zexuan stood on the podium and looked at the more than 600 students below. After a moment of silence, he said,
After a moment of silence, he said, "From the day you decided to enter Yanhuang College, I believe you already have some understanding of engineering! But that was just a simple introduction I made on Datang Daily. What you understood was just the literal things. Today, I will let you see what real engineering is like with your own eyes! Everyone, brace yourselves and open your eyes wide. You are about to enter a new world! "
Seeing that Li Zexuan was so serious, the students all raised their spirits and stared at the podium without blinking, afraid that they would miss some magical phenomenon. The teachers of the Academy also looked at Li Zexuan curiously. Today, they came to "listen" mainly because they wanted to learn from Li Zexuan's teaching style. According to the rules, the Academy would have a title evaluation at the end of the year. Who didn't want to improve their title quickly?
On the podium, Li Zexuan smiled unhurriedly and asked first, "Everyone here has learned mathematics. Do you know what the ancestral ratio is? If you know, raise your hand and answer! "
(Zu Chongzhi was the first to calculate the value of pi to seven decimal places in the history of mathematics in the world. This achievement was ahead of the world by nearly a thousand years. Later generations advocated that the ratio of the circumference to the diameter of a circle be called the "Zu ratio," which was the predecessor of pi.)
As soon as he finished speaking, forty to fifty students below the stage immediately raised their hands.
Li Zexuan casually pointed at a skinny student and said, "This student, why don't you say something? By the way, tell me your name! "
Although he had the ability to remember everything he saw, he had never taught a class before. How could he know the names of all the students?
When the student was pointed out by Li Zexuan, he didn't have stage fright. Instead, he was faintly excited. He stood up and saluted Li Zexuan, saying, "Student Sun Zhongzhi. In response to Mister's question, it has been recorded in the 'Fixing Technique' that the ancestral rate is approximately 3.1415926 to 3.1415927!
Li Zexuan nodded and continued to ask, "Not bad. Then do you know how this result is calculated?"
That student's face suddenly became awkward. He thought for a moment and shook his head, "Uh, teacher, I forgot about this …"
"Haha, it's okay. It's already very good. Sit down first!"
Li Zexuan comforted her with a smile, then looked at the others and asked, "Does anyone know how the ancestral rate is calculated?"
After a moment of silence, a dozen students raised their hands. Li Zexuan pointed to Jia Jiayin, whom he had met several times before. She was also the fourth in the opening examination of Yanhuang College and said, "Jia Jiayin, you say something!"
Jia Jiayin stood up and said unhurriedly, "Sir, during the Wei and Jin Dynasties, the master of arithmetic, Liu Hui, used the" Circle Cutting Technique "to calculate the ancestral rate. He first calculated from the inside of the circle to the inside of the circle to the inside of the circle to the outside of the circle to the outside of the circle to the outside of the circle to the outside of the circle to the outside of the circle to the outside of the circle to the outside of the circle. He once said that if you cut it thin, you will lose less. If you cut it again and again until it cannot be cut, then you will merge with the circumference and nothing will be lost. Based on his method, Ancestor Ancestor Chong Zhi went one step further and obtained an even more accurate result! "
(Zu Chongzhi once wrote a mathematical book, "Pi Technique", which recorded his research and results on pi. But at that time, "Scholars couldn't delve into the profoundness of it, so they ignored it", and it was later lost. Because the "Pi Technique" was lost, how Zu Chongzhi calculated pi to the seventh decimal place, and how he found the accurate and convenient ratio, was still a mystery until the 21st century. But many mathematicians speculated that Zu Chongzhi was likely to use 12 circular cuts on the basis of the circular cutting method, using the inscribed circle and the circumscribed circle to approximate the circumference of the circle in both directions. A total of 14 square cubes were needed, and the precision of the square cubes had to be at least 14 decimal places to determine pi between 3.1415926 and 3.1415927.)
Li Zexuan smiled inexplicably and continued to ask, "Then do you have any other methods to obtain the ancestral rate?"
Suddenly, Jia Jiayin, who was known as a child prodigy, was stumped.
"I don't know, please enlighten me!"
Li Zexuan said, "Sit down first, let's put this matter aside first. Next, let's play a little game together!"
After that, Li Zexuan picked up a piece of paper from the podium. There were black lines drawn on the paper (all parallel lines, and two parallel lines were equidistant from each other), and then took out a box of thin needles (the length of the thin needles was equal to half the distance between the parallel lines). After doing all this, he raised his head and said,
"Next, every student and teacher, come up according to the order of your seat and throw these thin needles on this piece of paper. Everyone throw once, come up quickly! Wang Meng, start with you! "
Everyone was confused. They didn't know what kind of trick Li Zexuan was playing. Wang Meng was the same, but he was the first in the first row. Since he was called, of course, he had to come up obediently.
When he came to the podium, he took out a thin needle from the needle box and hesitated, "Yamachō, do I just throw it casually?"
"Yes, just throw it casually. You can throw it with your eyes closed, as long as you can throw it on the paper!"
Li Zexuan said with a smile.
This was an experiment that involved probability. If everyone deliberately threw the needles, it would affect the results.
Wang Meng was also a joker. When he heard Li Zexuan say that, he actually closed his eyes. "Xiu!" The thin needle fell on the paper, and then he patted his butt and went back to his seat.
The students in the audience suddenly burst into laughter.
Li Zexuan shook his head and said, "Next, continue!"
In this way, it took more than half an hour for everyone to go up and throw the thin needles one by one.
The students and teachers who returned to their seats all looked at the podium. They saw Li Zexuan with his head down as if he was counting something. Although they were curious, they didn't disturb him. The whole classroom was so quiet that you could hear a pin drop.
Not long after, Li Zexuan raised his head. He picked up the chalk and wrote on the blackboard as he said, "I just calculated the results of your needles. The total number of times you threw the needles is 713, and the number of times you intersected with the black line is 227! The ratio of the total number to the number of times you intersected with the black line is 3.1496! "
At this point, he deliberately paused for a moment, and then said coolly, "This is the approximate value of the ancestral rate!"
…
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