While the people in Chang'an were chatting lively about football, students from Yanhuang Academy in Yunshan, outside Chang'an City, finally had their first class since arriving at the academy! The previous three and a half days of vacation are over!
This is also the first class after engineering was brought to this world. It is of great significance, so Li Zexuan chose to teach this class in person. The teaching location was the auditorium that was just built not long ago in the academy. The architectural style of this auditorium It was designed by Li Zexuan after he imitated the Beigong Building of Peking University in his previous life. This is a majestic palace-style building. The second floor can accommodate more than 600 people at the same time. This is why Li Zexuan chose this place to teach. Lessons are taught to all students.
More than 600 students and more than 70 teachers gathered together, making the newly built auditorium suddenly lively. After seeing Mo Zhong bring all the "tools", Li Zexuan coughed lightly and said: "Okay, everyone, be quiet! Class begins!”
The noisy classroom fell silent for an instant. Currently, no one in the academy dares to challenge Li Zexuan's majesty.
Li Zexuan stood on the podium, looked at the more than 600 students below, was silent for a moment, and said:
"From the day you decided to enter Yanhuang Academy, I believe you have already understood something about engineering! But that was just a brief introduction I gave in the "Datang Daily". What you learned was only literally Thing, today, I will show you with your own eyes what real engineering is like! Keep your spirits up and open your eyes, you are about to enter a new world!"
Seeing that Li Zexuan was so solemn, the students became very alert and stared at the podium without blinking, for fear that they would miss some magical phenomenon. The gentlemen in the academy also looked at Li Zexuan curiously. Today they came to "listen to the lecture" mainly because they wanted to learn Li Zexuan's teaching style. According to regulations, the academy will conduct professional title evaluations at the end of the year. Who doesn't want to improve their professional title as soon as possible?
I saw Li Zexuan on the podium smiling unhurriedly, and first asked: "Everyone here has studied arithmetic, so do you know what the ancestral rate is? If you know, raise your hands and answer!"
(Zu Chongzhi was the first person in the history of world mathematics to calculate the value of pi (π) to seven decimal places. This achievement led the world for nearly a thousand years. Later generations advocated calling the ratio of the circumference and diameter of a circle "Zu Chongzhi". ”, the predecessor of pi)
As soon as he finished speaking, forty or fifty students raised their hands in the audience.
Li Zexuan pointed at a thin student at random and said, "Tell me about this student! By the way, what is your name?"
Although he has a photographic memory, he has never taught any students except Class 1 before, so how could he possibly know the names of all the students?
The student who was selected by Li Zexuan did not have stage fright, but was slightly excited. He stood up and bowed to Li Zexuan, and said: "Student Sun Zhongzhi, what I said to you, sir, has been recorded in "Zhushu". The ancestor's rate was about three years ago." Between 1,415,926 and 3,141,5927!"
Li Zexuan nodded and continued to ask: "Yes, do you know how this result was obtained?"
The student suddenly looked embarrassed. He thought for a moment, shook his head and said, "Uh, sir, I forgot about this..."
"Haha, it's okay. It's pretty good. Please sit down first!"
Li Zexuan smiled and reassured, then looked at the others and asked, "Does anyone know how Zu rate was calculated~?"
After a moment of silence, a dozen students raised their hands. Li Zexuan pointed at Jia Jiayin, whom he had met several times before, and who was fourth in the Yanhuang Academy's opening exam, and said, "Jia Jiayin, tell me!"
Jia Jiayin stood up and said calmly: "Mr. Hui, Liu Hui, the arithmetic master in the Wei and Jin Dynasties, used the "circle cutting technique" to calculate the ancestral rate. He first connected the regular hexagon from the circle, and divided it one by one until the circle was reached. Inscribed in a regular 192-sided polygon. He said that if you cut it too thinly, you will lose very little; if you cut it again and again until it cannot be cut, it will fit into the circle and nothing will be lost. Based on his Method, Patriarch Zu Chongzhi took it a step further and came up with a more accurate result!"
(Zu Chongzhi once wrote a mathematical book "Zhu Shu", which recorded his research and results on pi. However, at that time, "no academic officials could study its profoundness, so they ignored it" and it was later lost. Because "Zu Chongzhi" Technique" has been lost. What method Zu Chongzhi used to calculate π to the seventh decimal place, and how he found a density that was both accurate and convenient, remains a mystery until the 21st century. However, many mathematicians have speculated , Zu Chongzhi probably used 12 circles to cut the circle on the basis of the circle cutting technique, and used the inscribed circle and the circumscribed circle to approximate the circumference of the circle in both directions. A total of 14 square roots were needed, and the accuracy of the square root must be at least to the decimal point. The last 14 digits determine the pi between 3)
Li Zexuan smiled inexplicably and continued to ask: "Then do you have other ways to obtain the ancestor's rate?"
In an instant, Jia Jiayin, known as the child prodigy, was also stumped.
"Students don't know, I hope you can teach me, sir!"
Li Zexuan said: "Sit down first, let's put this matter aside for now, and then we will play a little game together!"
Having said that, Li Zexuan picked up a piece of paper from the podium with black lines drawn on it (all parallel lines, and two adjacent parallel lines are equidistant), and then took out a box of fine needles (fine needles (the length of which is equal to half the distance of parallel lines), after doing all this, he raised his head and said:
"Next, every student and gentleman, come up in order of seating and throw these thin needles on this paper, once for each person. Come up quickly! Wang Meng, start from your side!"
Everyone was confused and didn't know what trick Li Zexuan was trying to play. The same was true for Wang Meng, but he was the first one in the front row. Since his name was called, of course he had to come up honestly.
When he came to the podium, he took out a thin needle from the needle box and hesitated: "Chief, did you just throw it away casually?"
"Well, just throw it casually, with your eyes closed, as long as you can throw it onto the paper!"
Li Zexuan said with a smile.
This is originally an experiment involving probability. If everyone throws it deliberately, it will affect the results.
Wang Meng is also a funny guy. Hearing what Li Zexuan said, he actually closed his eyes. With a "whoosh", the fine needle fell on the paper, and then he patted his butt and returned to his seat.
There was a burst of laughter from the students in the audience.
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 fine needles one after another.
The students and teachers who returned to their seats all turned their attention to the podium at this time, and saw Li Zexuan lowering his head as if counting something. Although they were surprised, they did not make a sound to disturb him. The whole classroom was quiet and could be heard. .
It didn't take long for Li Zexuan to raise his head. He picked up the chalk and wrote on the blackboard while saying: "I just counted the results of your needle throws. The total number of needle throws is 713, which intersects with the black line. There are a total of 227 times! The ratio of the total number to the number of intersections is 3.14096!"
At this point, he deliberately paused for a moment and then said coolly: "This is the approximate value of Zu rate!"
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