Take a plane to the Ming Dynasty

Chapter 158 The result is wrong (three more)
Although Xu Ji was called an adult by those on the opposite side, he had no fame because he didn't like being an official at all.

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

It is conceivable how comfortable this guy's life is. Apart from reading, he usually studies those numerology.I used to study with my father, but now that my father is gone, I can figure it out by myself.

But Xu Ji's comprehension is really bad, and he can't figure out many things at all!

"How dare you!" Although Xu Ji offered to help Li Ji, how could Li Ji let him do the job of a servant.The person standing in front of me is also the head of the contemporary Xu family, the son of Xu Guangqi, the former cabinet assistant.

To put it bluntly, if it is in modern society, he is the son of the Deputy Prime Minister of the Republic, formerly.

"Hehe." Li Ji smiled, looked at the things Xu Ji brought, and thought about others when he saw things, and said with a lot of feeling: "I was lucky enough to cut the circle with the old man back then, and I still feel it. Admiring the demeanor of the old man, use the art of cutting circles learned from the old man to calculate the ratio of circumference to diameter."

Li Ji took a step forward, first took out a thin nail from the tray in the hands of the servants behind Xu Ji, and said, "Li has made a fool of himself, please follow me."

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

Tie the other end of the fifteen-foot-long cotton thread to a movable nail.

Gently tightening it, Li Ji drew a big circle on the ground himself.

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

Then Li Ji pulled out the nail in the center of the circle, drew a regular hexagon inscribed in the circle with the radius as the side length, and explained to everyone: "There is a saying in "Zhou Pi Suan Jing": The diameter of a circle is one and three weeks. .It means that the length of a circle of a circle is equal to three times the radius, which is actually wrong.”

Pointing to the regular hexagon inscribed under his feet, Li Ji said, "Actually, Wednesday is exactly the circumference of the hexagon, and the circumference of the circle is naturally larger than the hexagon."

"Therefore, Liu Hui, a master of numerology in the Wei and Jin Dynasties, used the method of continuously increasing this regular shape, so that the perimeter of the polygon was infinitely close to the perimeter of a circle. Therefore, he speculated that when the number of sides of this shape increases, the perimeter increases. is close to the circumference."

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

Xu Ji also nodded, muttering something in his mouth, and said: "The more you cut, the less you will lose. If you cut it again and again until it cannot be cut, then it will fit into the circle and nothing will be lost. Master Li, you can start now."

What Xu Ji said is a theory annotated by Liu Hui in "Detailed Explanation of Nine Chapters of Arithmetic", which means: cut a regular hexagon into a regular dodecagon, and then cut it into 24-gon and 48-gon . . .By analogy, the smaller the cut, the less the error, cut and cut, and finally to the extent that it cannot be cut, the regular polygon and the circle become one.

"Okay!" 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 the ruler." Li Ji took out the ruler from the servant and began to measure the side length of the regular dodecagon cut out for the first time.

For the regular dodecagon cut out for the first time, Li Ji only measured one side, and reported the length to Xu Ermo, saying: "Mr. "

Xu Ermo wrote down the number in the book, and a special Mr. Abacus next to him dialed the abacus.Calculating pi with this method is actually very simple, because its assumption is that the side length of a regular polygon = the circumference of a circle.

Therefore, Mr. Abacus quickly calculated the answer: first, 7.76*12 (because it is a dodecagon), and the perimeter of the dodecagon is 93.12, which is only an approximate long-distance perimeter.And the ratio of the circumference to the diameter should be divided by this number and the diameter is 30.
After Mr. Abacus had calculated it completely, Xu Ermo reported from the side: "Three, one and four."

In this simplified way of reporting numbers in ancient times, there was a slight pause when it came to three, and the latter represented decimals.Through the first calculation, it can be known that the pi that Li Ji cut out for the first time is 3.104.

This data is far from the known pi 3.14.

It was the first time for Zhu Changyuan to see someone calculate pi in this way, and he laughed deep in his heart.If the ancients were unable to fathom Zu Chongzhi's true method of cutting the circle, Zhu Changyuan can only say one thing: it is still far away.

With this result, Li Ji was not surprised, and continued to cut the twelve-sided shape on the great circle into 24-sided shapes.

Measure the length of one side and report to Xu Ermo: "Three feet nine inches two."

Xu Ermo wrote it down, and then Mr. Abacus crackled the abacus, and within ten seconds he got the answer. The second time he cut the circle, the pi was 3.136.

This number is very far from the real pi, and as long as it is rounded to six, you can get the answer of 3.14, but it is still thousands of times worse than Zu Chongzhi's pi with seven decimal places.

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

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

Then cut the circle to a 48-sided shape with a side length of one foot nine inches six, and obtain the pi ratio: 3.136
Cut the circle to 96 sides, the side length is 3.136 inches and [-], and the pi remains unchanged, still: [-]
Cut the circle to 182 polygons, the side length is 3.136 inches and [-], and the calculated pi is still unchanged, still: [-]
When the circle is cut to 384 sides, the side length is already very small, only two and a half inches, and the calculated pi becomes: 3.2
This means that the error of Li Ji's method is getting bigger and bigger.

Sure enough, in Zhu Changyuan's smiling eyes, the circle was cut to 768 polygons. At this time, the side length of the regular polygon is only one inch and two, and the obtained pi becomes 3.072, which has already run away from the real pi. up.

"Cut again!" Li Ji shouted.

Li Ji wants to continue cutting, but the conditions are no longer allowed, because the length of the deformed side is too short, less than an inch, and it is impossible to measure it with the ruler of this era.

Li Ji wiped the sweat from his brow, although no one commented, but there is no doubt that this time the circle cutting failed.Not to mention catching up with Zu Chongzhi's seven decimals, it is still far behind Liu Hui's 3.14. Even if Liu Hui is not counted, even Xu Guangqi's half-assed is more accurate than him.

At least the number 3.14 was actually cut several times before.

The scene was silent for a while, Li Ji raised his head, shook his head again, and said, "Oh, it still doesn't work, after all, I still don't know how Zu Chongzhi and Liu Hui got married."

After saying this, no one at the scene responded.Suddenly seeing Zhu Changyuan's smile with disdain, Li Ji felt that his face was dull, and said to Zhu Changyuan: "Master Zhu also seems to know the art of cutting circles?"

"Pfft!" Zhu Changyuan didn't have a good impression of the guy from the beginning. Seeing that he was upset, he wanted to take him into a knife. Technique, you are clearly the technique of measuring circles, it really opened Zhu's eyes."

"You!" Faced with Zhu Changyuan's ridicule, Li Ji was slightly angry, and calmly took hatred towards the Xu family, saying: "Master Zhu, you should be more cautious when speaking. This method is not my Li Ji's. But I was cutting circles for the boss, and the boss also used this method back then..."

"Measure round?" Zhu Changyuan smiled slightly, interrupting Li Ji's words.I can't let this guy talk anymore, and that old boy Xu Ji is impatient, "I don't care whether Mr. Li cuts the circle or measures it, and let me ask you a few questions."

"Please enlighten me!"

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

"The 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, isn't the diameter thirty feet?

"No, I don't think it's thirty feet." Zhu Changyuan said with a mysterious smile.

"Heh, heh." If it wasn't for the same yamen with this guy, Li Ji would really want to go up and beat Zhu Changyuan up. Are you talking nonsense with your eyes open? The radius I measured just now is exactly fifteen feet. What the hell are you saying? Isn't it thirty feet in diameter?
"Lord Zhu, many people here have seen it, please don't make trouble for no reason."

Li Ji was proud, and secretly thought that Zhu Changyuan, a rascal, took the blame on himself, just to relieve everyone's eyes on me just now.

"I only trust the ruler, not the thread in your hand, otherwise, you'll have to measure it." Zhu Changyuan pointed to the big circle on the ground.

Li Ji snorted and said: "Just measure it, I don't believe it. Can the circle drawn by me be changed in length?" With the help of two servants, stretch a cotton thread through the center of the circle, Take a diameter direction and start measuring.

After measuring one foot by one, he was suddenly stunned. The diameter of this big circle was exactly 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 couldn't believe it, so he repeated the measurement, and it was still thirty feet and three inches, not too much, not too little.

"Why, the radius I measured before drawing the circle was fifteen feet. Could it be that I made a mistake before?" Li Ji was puzzled.

"That's right, Master Zhu, why is this? Please help me, sir?"

Xu Ji stood respectfully beside Zhu Changyuan, and asked with the same doubt.

　Forget it, although I am in a bad mood, but this has nothing to do with the readers. It is because I am too self-righteous. I still need to update what should be updated, even if I work overtime.Good night everyone. . .

　　
　
(End of this chapter)