Otaku Engineer in Great Tang Dynasty

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When the people of Chang'an were talking about football, the students of Yanhuang Academy in Yunshan, outside Chang'an City, finally ushered in their first class after coming to the academy! The previous three-and-a-half-day vacation is over!

This is also the first class after engineering was brought to this world, and it is of great significance, so Li Zexuan chose to teach this class in person. It was designed by Li Zexuan's imitation of the former Peking University Bei Gong Building. This is a magnificent palace-style building. The second floor can accommodate more than 600 people at the same time. This is why Li Zexuan chose the teaching location here. Lessons are taught to all students.

More than 600 students and more than 70 teachers gathered together, which made the newly built auditorium suddenly lively. Seeing Mo Zhong brought all the "tools", Li Zexuan coughed lightly and said, "Okay, be quiet! Class starts!"

The noisy classroom was silent for a moment. At present, in the academy, no one dared 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 that you already have some understanding of engineering! But that was just a brief introduction I made in the "Datang Daily", and what you have learned is only literal Thing, today, I will show you with your own eyes what real engineering is like! All cheer up, keep your eyes open, you are about to enter a new world!"

Seeing that Li Zexuan was so serious, the students raised their spirits one after another, staring at the podium without blinking, for fear that they would miss some magical phenomenon in a while. The gentlemen of the academy also looked at Li Zexuan curiously. Today, they came to "listen to the lecture", mainly to learn Li Zexuan's teaching method. According to the regulations, the academy will conduct professional title evaluation at the end of the year. Who doesn't want to hurry up and improve their professional title?

Seeing Li Zexuan on the podium smiling unhurriedly, he first asked, "Everyone here has studied arithmetic, so do you know what the Zu rate is? Those who know raise their hands and answer!"

(Zu Chongzhi calculated the value of pi to seven decimal places for the first time in the history of mathematics in the world. This achievement has been ahead of the world for nearly a thousand years. Later generations advocated that the ratio of the circumference and diameter of a circle should be called "Zu Ratio". ", the predecessor of pi)

As soon as the voice fell, forty or fifty students immediately raised their hands off the field.

Li Zexuan casually pointed at a thin student and said, "This student, tell me! By the way, what is your name!"

Although he has the ability to remember, but he has not taught the students in the class except the first class before, how can he know the names of all the students?

The student was picked by Li Zexuan, but he didn't have stage fright. Instead, he was a little excited. He stood up and bowed to Li Zexuan, and said, "Student Sun Zhongzhi, Mr. Hui's words have been recorded in "Xiaoshu", Zu rate is probably in the third Between 1415926 and 3.1415927!"

Li Zexuan nodded and continued to ask: "Yes, then do you know how this result came out?"

The student suddenly looked embarrassed, he thought for a moment, then shook his head and said, "Uh, sir, I forgot about this..."

"Hehe, it's okay, it's already very good, you sit down first!"

Li Zexuan smiled to reassure him, then looked at the others and asked, "Does anyone know how Zu rate was calculated~?"

After being quiet for a while, a dozen or so students raised their hands. Li Zexuan pointed to Jia Jiayin, who had met several times before and who was also the fourth place in the Yanhuang Academy entrance exam, and said, "Jia Jiayin, talk about it!"

Jia Jiayin stood up and said calmly, "Mr. Hui, Liu Hui, a math master in the Wei and Jin Dynasties, used the "circle cutting technique" to calculate the ancestral rate. Inscribed is a regular one hundred and ninety-two polygons. He said that if you cut it finely, you will lose very little. If you cut it again and again, so that it cannot be cut, it will be integrated with the circle and nothing will be lost. method, the ancestor Zu Chongzhi went a step further and came up with a more accurate result of pi!"

(Zu Chongzhi once wrote a mathematical book "Suspension", which recorded his research and achievements on pi. However, at that time, "the academics could not study the profoundness of it, so it was abandoned and ignored", so it was lost later. "The Technique" has been lost. What method did Zu Chongzhi use to calculate π to the seventh decimal place, and how he found the density that is both accurate and convenient will remain a mystery until the 21st century. However, many mathematicians speculate that , Zu Chongzhi is very likely to use 12 times to cut the circle on the basis of cutting the circle, and use the inscribed circle and the circumscribed circle to approximate the circumference of the circle in both directions. A total of 14 square rootings are required, and the accuracy of the square rooting must be at least the decimal point. The last 14 digits are used to determine the pi between 3.1415926 and 3.1415927)

Li Zexuan smiled inexplicably, and continued to ask: "Then do you have other ways to get the ancestors?"

In an instant, Jia Jiayin, known as a child prodigy, was also stumped.

"Students don't know, I hope you can enlighten me!"

Li Zexuan said: "You sit down first, let's put this matter aside for now, and then let's play a small game together!"

After all, Li Zexuan picked up a piece of paper from the podium on which black lines were drawn (all parallel lines, and two adjacent parallel lines were equidistant), and then took out a box of fine needles (fine needles) is equal to half the distance of the parallel lines), and having done all this, he raised his head and said:

"Next, each student and gentleman, in the order of seats, come up and throw these fine needles on this piece of paper, and each person throws

Once, hurry up! Wang Meng, start from your side! "

Everyone was at a loss, and they didn't know what trick Li Zexuan was going to play. Wang Meng was also the same, but he was the first in the first row. Since he was named, 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: "Shan Chang, did you just throw it away?"

"Well, just throw it casually, you can throw it with your eyes closed, as long as you can throw it on paper!"

Li Zexuan said with a smile.

This is originally an experiment involving probability. If everyone deliberately throws it, it will affect the result.

Wang Meng is also a funny guy. Hearing what Li Zexuan said, he actually closed his eyes. With a "huh", the thin needle fell on the paper, and then he patted his butt and went back to his seat.

There was a burst of laughter from the students off the field.

Li Zexuan shook his head and said, "Next, continue!"

In this way, it took more than half an hour, and everyone went up and threw the fine needle in turn.

The students and teachers who returned to their seats all turned their attention to the podium. They saw Li Zexuan lowered his head as if he was counting something. Although they were strange in their hearts, they did not make a sound. .

It didn't take long for Li Zexuan to raise his head, he picked up the chalk, and said while writing on the blackboard: "I just counted the results of your needles, and the total number of needles was 713, of which intersected the black line. A total of 227 times! The ratio of the total number to the number of intersections is 3.14096!"

Having said that, he deliberately paused for a while before saying coolly: "This is the approximate value of the Zu rate!"

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