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

This is also the first class after engineering was brought to this world, and the significance is not insignificant, so Li Zexuan chose to teach this class in person, and the teaching location was chosen to be in the auditorium that had just been built not long before the academy, the architectural style of this auditorium was designed by Li Zexuan to imitate the Beibei Mansion in the previous life, this is a magnificent palace-like building, the second floor can accommodate more than 600 people at the same time, which is also the reason why Li Zexuan chose the teaching location here, and he taught this class to all students.

More than 600 students and more than 70 teachers gathered together, making the newly built auditorium suddenly lively, Li Zexuan saw that Mo Zhong took all the "tools", coughed lightly, and said, "Okay, it's quiet!" Classes are on! ”

The noisy classroom was silent in an instant, and at present, no one in the academy 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 you already know something about engineering! But that's just a brief introduction I made in the "Datang Daily", what you know is only literal, today, I will take you to see with your own eyes what real engineering is like! All of them cheer up, keep your eyes open, you are about to enter a new world! ”

Seeing Li Zexuan so solemn, the students raised their spirits one after another, staring at the podium without blinking, for fear that they would miss some magical phenomenon for 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 lecture method, according to the regulations, the academy will be evaluated at the end of the year, who doesn't want to improve their professional title as soon as possible?

Seeing Li Zexuan on the podium, he smiled unhurriedly, and first asked: "Everyone here has studied arithmetic, so do you know what the ancestral rate is?" Raise your hand and answer if you know! ”

(Zu Chongzhi was the first time in the history of world mathematics to calculate the value of pi (π) to seven decimal places, this achievement is nearly a thousand years ahead of the world, and later generations advocate that the ratio of circumference to diameter is called "ancestral rate", that is, the predecessor of pi)

As soon as the words fell, forty or fifty students raised their hands in an instant.

Li Zexuan casually pointed to a student with a thin physique, and said, "This student, let's talk about it!" By the way, what's your name! ”

Although he has the ability to remember everything, he has never taught a class of students except for one class before, so how can he know the names of all the students?

The student was hit by Li Zexuan, but he didn't have stage fright, but was faintly excited, he stood up and bowed to Li Zexuan, and said: "Student Sun Zhongzhi, Mr. Hui's words have been recorded in "Fixation", and the ancestral rate is about 3:1415926 to 3:1415927! ”

Li Zexuan nodded and continued to ask, "Yes, then do you know how this result was obtained?" ”

The student's face suddenly showed embarrassment, he thought for a moment, shook his head, and said, "Uh, sir, I forgot this...."

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

Li Zexuan smiled and comforted, then looked at the others and asked, "Does anyone know how the ancestral rate is calculated~?" ”

After a moment of silence, more than a dozen students raised their hands, Li Zexuan pointed to Jia Jiayin, who had a few previous encounters, and was also the fourth place in the opening examination of Yanhuang Academy, and said, "Jia Jiayin, you can talk about it!" ”

Jia Jiayin stood up and said unhurriedly: "Mr. Hui, Liu Hui, a master of arithmetic in the Wei and Jin dynasties, used the "circumcision technique" to calculate the ancestral rate, and he first connected the regular hexagon from the circle, and then divided it one by one until the circle was connected with one hundred and ninety-two sides. He said that if you cut it finely, you will lose a little, and if you cut it again, so that it cannot be cut, it will be combined with the circumference and there will be nothing lost. Based on his method, Zu Shi Chongzhi went one step further and obtained a more accurate result of pi! ”

(Zu Chongzhi once wrote a mathematical work called "The Art of Fixation", which recorded his research and results on pi.) However, at that time, "scholars could not investigate its profundity, and they ignored it", so that it was later lost. Because the "Fixation Technique" was lost, what method Zu Chongzhi used to calculate the π to the seventh decimal place, and how he found the accurate and convenient density, is still a mystery until the 21st century. However, many mathematicians have speculated that Zu Chongzhi is likely to use 12 circumcisions on the basis of circumcision, using the circumference of the circumference of the circumscribed circle and the circumscribed circle in both directions. A total of 14 times need to be squared, and the accuracy of the opening must be at least 14 decimal places before the pi is determined between 3.1415926 ~ 3.1415927)

Li Zexuan smiled inexplicably and continued to ask, "Then do you have any other ways to obtain the ancestral rate?" ”

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

"The students don't know, but I hope that Mr. will teach you!"

Li Zexuan said: "You sit down first, let's put this matter aside first, and then let's make a little game together!" ”

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

"Then each student and the gentleman, in order of their seats, come up and throw these thin needles on this piece of paper, each of them once at a time, come up quickly! Wang Meng, start from your side! ”

Everyone was confused, and they didn't know what trick Li Zexuan was going to play, and so was Wang Meng, but he was the first to sit in the first row, and 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: "Mountain Chief, are you throwing it casually?" ”

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

Li Zexuan said with a smile.

This is an experiment involving probability, and if everyone deliberately throws it, it will affect the outcome.

Wang Meng's product is also a joke, listening to Li Zexuan say this, he really closed his eyes, and with a "bang", the thin needle fell on the paper, and then patted his ass 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 in turn.

The students and teachers who returned to their seats all looked at the podium at this time, and saw Li Zexuan with his head down as if he was counting something, although they were strange in their hearts, they did not make a sound to disturb, and the whole classroom was quiet and the needle drop could be heard.

It didn't take long for Li Zexuan to raise his head, he picked up the chalk, wrote on the blackboard and said: "I just counted the results of your needle throwing, the total number of needle throws is 713 times, of which the number of times it intersects with the black line is a total of 227 times!" The ratio of the total number to the number of intersections is 3.14096! ”

Speaking of this, he deliberately paused for a moment before he said coolly: "This is the approximate value of the ancestral rate!" ”

……………………

(End of chapter)