Take a plane to the Ming Dynasty

Chapter 157 Circle Cutting Technique

Zhu Changyuan never imagined that the Ming Dynasty was so advanced that even Christians were there.

It is not surprising that there are Christians in the dynasty, after all, many Western missionaries have begun to infiltrate the East during this period.Thinking of this, Zhu Changyuan suddenly asked curiously: "Mr. Xu has seen Tang Ruowang?"

"Of course I've seen it before." Xu Ermo smiled coyly, took out a thin thread-bound book from his sleeve, handed it to Zhu Changyuan, and said, "When my grandfather was there, he often discussed Western learning with Tang Ruowang, Matteo Ricci and others. This is the book that my grandfather translated from them."

Zhu Changyuan took the book and took a closer look. The name of the book shocked him for a long time. It turned out to be "Elements of Geometry".Zhu Changyuan couldn't be more clear about the original geometry. It is said that this book was translated by Xu Guangqi, the crown prince of the Ming Dynasty, with great painstaking efforts.Suddenly thought of something, looked at Xu Ermo again, and finally realized that the grandfather he was talking about was Xu Guangqi.

"Hey, that's not right, Xu Guangqi has been a clean and honest official all his life, why did he accumulate such wealth!" Looking at this luxurious courtyard, with such suspicion, he followed Xu Ermo through the attic courtyard walls of Xu's mansion, and met along the way. I went to many servant girls of Xu Mansion.

If Xu Guangqi had been clean and honest all his life, Xu Ermo's grandfather should have bought this house.

Zhu Changyuan was thinking about this question in his heart, and unknowingly came to the outside of a courtyard wall, and suddenly heard a burst of laughter inside the wall, and the atmosphere was very lively.

Xu Ermo laughed and said, "Guys like Zhang Luan don't know what new tricks they are playing."

After these nobles in the Ming Dynasty, life can be described as rich and colorful, with cockfighting, running dogs, and romance.

After following Xu Ermo into the courtyard wall, the first thing that caught his eye was a lot of people, some of whom Zhu Changyuan was familiar with, such as the handsome guy Zhang Luan, Liu Yunzhou from the Ministry of Industry, and even the foreigner Li Ji.

Seeing Zhang Luan, he thought of his queen sister who turned all sentient beings upside down, and wondered when the waste could be reused, but since she is a queen, it should be extremely difficult to poach the emperor's corner to cuckold the first emperor.

But there is no need to worry, the Ming Dynasty will perish in a few years, so what kind of emperors will be there then?
Naturally, Zhu Changyuan didn't know most of the nobles in the small courtyard of the Xu Mansion, so he counted them. Apart from Zhang Luan, Li Ji and Liu Yunzhou, there were three other young people, all of whom had unrestrained looks. Sample.

"Come on, let me introduce you to your lord." Xu Ermo led Zhu Changyuan in front of everyone, pointed at Li Ji and Liu Yunzhou and said, "These two are your lord's colleagues, so I won't go into details."

"This is Uncle Xingyang, Zhang Luan!" Zhu Changyuan had seen Zhang Luan before, and seeing that he had no intention of coming forward to recognize him, he also pretended to bow to each other warmly with Zhang Luan.

"Uncle Xingyang is terrible, his elder sister was originally the empress of the former emperor in the inner palace, who ruled the six palaces." Xu Ermo smiled and pulled Zhang Luan, saying: "Uncle Xingyang is very good at poetry, calligraphy and painting, and he is also a hero at the moment. "

"Don't dare to take it." Although Zhang Luan said modestly, his face was full of joy.

Zhu Changyuan nodded inwardly, this guy really deserves his name when he says he is a genius.

"Come on! This is..."

Xu Ermo introduced the other three people one by one. One was Wen Yongyan, the grandson of Wen Tiren, the chief minister of the cabinet.

Zhu Changyuan is also drunk, you, the grandson of the chief assistant, are you so poor.

"This is Liang Chengxin, and this is Fu Kuang, both of them are people who are interested in mathematics, and they all have fame."

Zhu Changyuan looked at the two of them, it seemed that they were also descendants of aristocratic families.

"Everyone, please sit down." Xu Ermo led everyone to a pavilion on a high platform in the yard. There was a long table under the pavilion with tea and snacks on it.

Everyone sat down one by one, seeing that the vegetation in the courtyard seemed to be withering, Xu Ermo said: "The spring and autumn have passed, so fast, my grandfather has passed away for four years in a blink of an eye. Another month will be the anniversary of his death."

"Young Master, don't be sad!" Fu Kuang persuaded: "During the time Xu Ge was alive, he worked hard for me and other Ming students and made great contributions. He spared no time to compile "Elements of Geometry", so that we will have the opportunity Take a look at Western learning."

"Yes, let's offer a cup of tea to the old man first, and wish him all the best."

After Zhang Luan proposed, he raised his glass and drank it down.

"Okay, my lord respect!" Several people toasted and drank at the same time.

Zhu Changyuan looked down on the few people in front of him, and thought that he would pretend to be so aggressive after drinking J8 tea.

Fu Kuang took the "Elements of Geometry" from Xu Ermo's hand, and said with some emotion: "If there is no boss, I will wait for He De and He Neng to read such a wonderful book. But having said that, these barbarian countries, countless The technique is really good, and it is more unique than my Greater China."

"Master Fu, please forgive me for not accepting these words." Li Ji stood up and said, "It is not that the knowledge of mathematics in my Greater China is low, but that throughout the ages, not many people have paid attention to it. Over time, many techniques have been lost, which led to today's Like this."

"For example, how many chapters are still left in the ancient "Nine Chapters of Arithmetic"? Another example is the ratio of circumference to diameter. The specific value has been handed down, but how did Zu Chongzhi obtain it?"

The more Li Ji said, the more excited he became.

The so-called circumference-to-diameter ratio is also called pi in modern times. Anyone with middle school or even primary school knowledge knows that Zu Chongzhi in ancient China during the Southern and Northern Dynasties calculated the pi to be between 3.1415926 and 3.1415927.

People in the Ming Dynasty also knew the specific data of pi.

But how to find the pi is unknown, because the method used by Zu Chongzhi has been lost.

Xu Ermo gently put the teacup in his hand on the table, sighed, with deep sadness in his eyes, and said, "Speaking of this matter, it was my grandfather's heart disease."

"Oh?" Li Ji asked, "I would like to hear the details."

Xu Ermo said: "The relationship between my grandfather and Matteo Ricci was very unusual back then, but it is said that there was a dispute over this matter. The circumference-to-diameter ratio in the West has only developed in recent years. Matteo Ricci said that there was a guy named Wei Da. I have calculated it once with reason, and it is extremely accurate.”

"My grandfather refused to accept it, saying that China calculated the circumference-to-diameter ratio as early as 1000 years ago during the Southern and Northern Dynasties. Matteo Ricci did not believe it, so he insisted on asking his grandfather the specific method of cutting circles."

Hearing this, Zhu Changyuan laughed inwardly. If he guessed correctly, Wei Da used the formula to calculate pi.It is understandable that Matteo Ricci asked Xu Guangqi to prove it to him. Isn’t it because Westerners like to prove everything?

Without a rigorous and detailed proof process, people would naturally not believe it.In the words of Westerners, this is called without basis.

Only Xu Ermo said: "Later, my grandfather devoted himself to the study of Zu Chongzhi and even Liu Huizhi's circle cutting technique. After countless attempts, he finally failed to cut out an accurate number. Compared with Zu Chongzhi's, it is still far behind."

Li Ji next to him was also quite moved, and said: "When Xu Gebu cut the circle, I often came to help calculate it. I saw the hard work. Although today is not the anniversary of the death of the boss, I would like to cut it with my own hands on the occasion of the Mid-Autumn Festival. Round, pay homage to the old man."

"Okay!" Xu Ermo stood up and said: "When my grandfather cut the circle back then, the boy was still a naughty boy and couldn't see it in person. Today, Mr. Li cuts the old circle again, so that I can admire my grandfather's demeanor from it. Your Excellency please."

"Huh..." Li Ji stood up and took a deep breath, carefully recalled the scene when Xu Guangqi cut the circle, and said: "Please prepare the ruler and tools, I will prepare for it."

"My lord, take a break, and I will come later."

Xu Ermo didn't know what tools were needed to cut circles back then. He didn't know, but there was one person who knew, his father Xu Ji.

When Xu Guangqi cut the circle, Xu Ji was his greatest helper.

After Xu Ermo left, the pavilion fell into silence.

After a while, Fu Kuang asked: "Lord Li, I also have a little understanding of this technique of cutting circles. It should be part of the content described in Liu Hui's "Detailed Explanation of Nine Chapters of Arithmetic". Four cents, I don’t know how much Mr. Xu cut out?”

Li Ji shook his head and said: "I don't know much about the details, the jump is too big, sometimes three and one cent three cents, sometimes three and one cent four cents, sometimes three and one cent five cents, and so on. .”

After hearing what he said, Zhu Changyuan was puzzled.Decimals in the Ming Dynasty were represented by millimetres, and one cent four centimeters meant 0.14.Three and one cent four cents is 3.14.

It is undeniable that Liu Hui did cut 3.14 back then, but Xu Guangqi cut the circle and cut 3.13, 3.14 and 3.15.
wrong.

He also knew about the art of cutting circles. When he was in high school, his math teacher organized an outdoor activity of cutting circles. Zhu Changyuan still remembers it deeply. The principle of that thing is actually simple as hell, but the calculation is a bit complicated, and there is no calculator. It is more difficult to calculate, mainly because it involves the square root problem.

However, every time the cutting circle is cut, the formulas that can be used in it are all the same. After eleven consecutive cuts, the 3.1415926 that Zu Chongzhi said will appear. Why does the data that Xu Guangqi cuts out of the circle jump around? Woolen cloth?

Strange.

While Zhu Changyuan was thinking, he saw that Xu Ermo had already led a group of people running over from the courtyard gate.This time, not only servants, but also a few people in brocade robes and jade belts came here.

"Hey, Lord Xu is here too."

As soon as Fu Kuang finished speaking, everyone stood up. Zhu Changyuan naturally knew that this was the master of the Xu family. It should be Xu Ermo's brother.

"Let's go, let's pay respects to Mr. Xu." Zhang Luan led the crowd down from the high platform where the pavilion was, and walked slowly towards Xu Ji.

"Master Xu!" Everyone bowed and saluted.

"You don't need to be too polite!" Xu Ji also bowed to return the salute, looked at Li Ji and said, "I heard that Mr. Li is going to make a concubine in my Xu residence, and Mr. Xu is willing to accompany you and be at your command!"

　I only updated two chapters today, I had a fight with the foreman, and I was really not in the mood to type.

　　
　
(End of this chapter)