readx;??? Although Xu Ji was called an adult by the other side, he had no merit because he didn't like to be an official at all. Pen? Interesting? Pavilion wWw. ｂiquge。 ｉｎfo

Of course, if it's for life, it's even more unnecessary. Aside from Xu Guangqi, Xu Ji's father-in-law is a native of Shanghai County, Songjiang Prefecture, and is known as Gu Bancheng in Songjiang, and it is said that his wealth alone can buy half of Songjiang Mansion.

It can be imagined how comfortable the life of this product is, in addition to reading, Ping Suli is to study those mathematical techniques. I used to study with my father, but now that my father is gone, I think about it myself.

But Xu Ji's comprehension is really too poor, and he can't understand many things at all!

"How dare you!" Although Xu Ji took the initiative to ask to help Li Ji, how could Li Ji let him do the work of the next person. The person standing in front of him is also the head of the contemporary Xu family, the son of Xu Guangqi, the former deputy assistant of the cabinet.

To put it mildly, if it were in modern society, he would be the son of the Deputy Prime Minister of the Republic, former.

"Huh." Li Ji smiled, looked at these things that Xu Ji brought, saw things and thought about people, and said with feeling: "I was fortunate to follow the boss to cut the circle together, and I still feel nostalgic." Anyway, today, the official admires the demeanor of the old man, and uses the technique of cutting the circle learned from the old man to calculate the circumference ratio. ”

Li Ji took a step forward, first took out a thin nail from the tray in the hands of the people behind Xu Ji, and said, "Li is ugly, please come with me." ”

Walking to a fairly flat ground in the courtyard of Xufu, he first smashed a nail in the center, then took out the cotton thread, tied a piece of the cotton thread to the nail, and measured the length of fifteen feet.

He tied a movable nail to the other end of the fifteen-foot cotton thread.

Pulling it tightly, Li Ji personally drew a big circle on the ground.

With a radius of fifteen feet, the diameter of the circle is thirty feet long, and it looks quite large and round.

Then Li Ji pulled out the nail in the center of the circle, drew an inscribed regular hexagon in the circle with the radius of the circle as the side length, and explained to everyone at the same time: "The Zhou Spleen Sutra has a saying: the diameter of the circle is one and Wednesday. Meaning: The length of the circumference of the circle is equal to three times the radius. In fact, this statement is wrong. ”

Pointing to the circle under his feet, Li Ji said: "Actually, Wednesday is exactly the circumference of this hexagon, the circumference of the circle." Naturally, it's a bit larger than this hexagon. ”

Therefore, during the Wei and Jin dynasties, Liu Hui, a master of mathematics, used the practice of increasing this regular side. Let the circumference of the polygon be infinitely close to the circumference of the circle, so, he speculated. The more sides of the shape, the closer the circumference is to the circumference. ”

Zhu Changyuan couldn't help but nodded. What Li Ji said naturally makes sense. And it's a very simple truth. The more sides of the inscribed regular polygon, the closer they are to the circumference of the circle, and the closer their perimeter is to the circumference of the circle.

Xu Ji also nodded. There are words in his mouth, and he says: "Cut it finely." What is lost is too little, and it is cut and cut, so that it cannot be cut. It is combined with the circle, and nothing is lost. Master Lee, you can get started. ”

Xu Ji's words are a theory annotated by Liu Hui in "Detailed Explanation of Nine Chapters of Arithmetic", which means that the regular hexagon is cut into a regular twelve-sided shape, and then cut into twenty-four and forty-eight sides in turn... And so on, the smaller the cut, the less the error, cut back and forth, and finally to the point of being uncutable, the regular polygon and the circle become one.

"Good!" Li Ji first took the midpoint of one side of the regular hexagon, passed through the center of the circle and extended to the circumference, turning the regular hexagon into a dodecagon.

"Bring me a ruler." Li Ji took out a ruler from his subordinate and began to measure the length of the sides of the regular dodecagonal shape that was cut for the first time.

The first time he cut out the regular twelve-sided shape, Li Ji only measured one of the sides, and reported it to Xu Ermo after getting the length, and said: "Xu Gongzi remembered that the length of the twelve sides is seven feet seven inches and six inches. ”

Xu Ermo wrote down this number in the book, and there was a special abacus gentleman next to him who turned the abacus with a rattle. Calculating pi in this way is actually quite simple, as it assumes that the side length of a regular polygon = the circumference of the circle.

Therefore, Mr. Abacus quickly calculated the answer: first, 7.76*12 (because it is a dodecagon), the circumference of the dodecagonal is 93.12, which is only an approximation of the far perimeter. And the circumference ratio has to take this number to remove it to a diameter of 30.

After Mr. Abacus fully calculated, Xu Ermo reported next to him: "Three, one zero four." ”

In ancient times, this simplified way of reporting numbers, when talking about three, there was a slight pause, and the following represented the decimal number. Through the first calculation of the takeover, it can be seen that the pi of Li Ji for the first time is 3.104.

This figure is too far off from the known pi rate of 3.14.

It was the first time for Zhu Changyuan to see someone calculate pi like this, and he smiled deep in his heart. To say that the ancients could not figure out the real method of cutting the circle through the ancestor Chongzhi, Zhu Changyuan could only say one sentence: it is still far away.

Getting this result, Li Ji was not surprised, and continued to cut the twelve-sided shape on the big circle into twenty-four sides.

Measuring the length of one of the sides, he reported to Xu Ermo: "Three feet nine inches two." ”

Xu Ermo wrote it down, and then Mr. Abacus crackled the abacus, and got the answer in less than ten seconds, the second time he cut the circle, and the pi cut out was: 3.136.

This number is very little different from the real pi, and as long as it is rounded to six or four, you can get the answer of 3.14, but it is still thousands of times different from Zu Chongzhi's seven-decimal place.

"It's close, it's close." Xu Ji said excitedly.

Li Ji nodded and continued to cut the circle, Xu Ermo continued to record, and Mr. Abacus continued to calculate.

Then cut the circle to 48 sides, the side length is one foot nine inches six, and the pi is obtained: 3.136

Cut the circle to 96 sides, the side length is nine inches and eight, and the pi is unchanged, or: 3.136

Cut the circle to 182 sides, the side length is four inches and nine, and the pi is still unchanged, still: 3.136

When the circumcision circle reaches 384 sides, the side length is already very small, only two and a half inches, and the pi becomes 3.2

This means that Li Ji's method is becoming more and more incorrect.

Sure enough, in Zhu Changyuan's smiling gaze, the circle was cut to 768 sides, and the side length of the regular polygon at this time was only one inch and two, and the pi obtained became 3.072, which had run out of 108,000 miles with the real pi.

"Cut again!" Li Ji shouted.

Li Ji wanted to continue cutting, but the conditions no longer allowed it, because the side length of the deformation was so short that it couldn't be shorter. It's less than an inch. It is completely impossible to measure with the ruler of this era.

Li Ji wiped the sweat from his head, although no one commented, there was no doubt that this time the circle had failed. Not to mention catching up with Zu Chongzhi's seven decimal places, it is also much worse than Liu Hui's 3.14. Even if you don't count Liu Hui, even Xu Guangqi's half-hung son is more accurate than him.

At least in the past, people have really cut out the number 3.14 several times.

The scene was silent for a while. Li Ji raised his head, shook his head again, and said, "Alas. Still no, after all, I still don't know how Zu Chongzhi and Liu Hui cut the circle. ”

After saying this. None of the people on the scene responded. Suddenly seeing the smile on the corner of Zhu Changyuan's mouth with some disdain, Li Ji felt that his face was very dull, and said to Zhu Changyuan: "Lord Zhu also seems to understand this technique of cutting circles?" ”

"Poof!" Zhu Changyuan didn't have a good impression of the guy from the beginning. Seeing that he was unhappy, he wanted to cut him out, and finally laughed after holding back his heart for a long time. "Hehe, Master Li, what kind of technique do you have to cut the circle. You are clearly the art of measuring circles, which is really an eye-opener for someone Zhu. ”

"You!" In the face of Zhu Changyuan's ridicule, Li Ji was slightly angry in his heart, and quietly pulled hatred towards the Xu family, and said: "Lord Zhu should be cautious when he speaks, this method is not used by me Li Ji, but I am cutting the circle for the boss, and the boss also used this method back then... ”

"Measuring round?" Zhu Changyuan smiled slightly and interrupted Li Ji's words. I can't let this thing go on anymore, and Xu Ji's old boy will be anxious, "I don't care whether Master Li cuts or measures it, and let me ask you a few questions." ”

"Please advise!"

Li Ji is Zhu Changyuan's top boss, and his position is one level higher than him, so he still has this bearing. Of course, in public, even if you don't have it, you have to pretend to have it.

"First question, I dare to ask my lord, what is the diameter of your circle?"

Li Ji replied, "Thirty feet." "Just kidding, the radius is fifteen feet, and the diameter is thirty feet.

"No, I don't think it's thirty feet." Zhu Changyuan smiled mysteriously and said.

"Heh, hehe." If it weren't for the same yamen with this goods, Li Ji really wanted to go up and beat Zhu Changyuan wildly, aren't you talking nonsense with your eyes open, the radius I measured just now is exactly fifteen feet, why do you say that the diameter is not thirty feet?

"Master Zhu, many people here have seen it, please don't be unreasonable."

Li Ji was proud, and secretly said that now Zhu Changyuan, you rammer, take the spearhead on yourself, just to soothe everyone's gaze on the official just now.

"I only believe in the ruler, not the thread in your hand, otherwise, you will weigh it." Zhu Changyuan stretched out his finger and pointed to the big circle on the ground.

Li Ji snorted and said, "The amount is measured, I don't believe it, can the circle drawn by the official himself be changed to length?" "Let the two subordinates assist, taut a cotton thread through the center of the circle, take out the direction of a diameter, and start to measure it.

After measuring one foot at a time, he was suddenly stunned, the diameter of this big circle was indeed as Zhu Changyuan said, not thirty feet, but thirty feet and three inches.

"This, this, why, why is there an extra three inches?" Li Ji didn't believe it, and measured it again, it was still thirty feet and three inches, not much at all, no less.

"Why, before I drew the circle, I had a radius of fifteen feet. Could it be that I did it wrong? Li Ji was puzzled.

"Yes, Master Zhu, why is this? Do you want to answer your questions? ”

Xu Ji stood respectfully next to Zhu Changyuan and asked with the same doubts. (To be continued.) )

ps: Forget it, although I'm in a bad mood, but this has nothing to do with the reader, it's the old man who is too self-righteous, and the one who should be updated still has to be updated, and the overtime must be updated. Good night everybody... Intranet unique URL: