The Great Industrial Ming Dynasty Started from Beiping

Chapter 515 The Big Bang of Mathematics

Jiyang, Shandong.

Mr. Zhou has organized his books again, and his book boy is two years older.

"Sir, are we going to the capital this time?"

The scholar has become Mr. Zhou's disciple.

Mr. Zhou went to Peiping and was received by the former Crown Prince Yan, and was praised by the young prince himself as a great talent.

The Science and Technology Department registered its name and received the talent subsidy.

The subsidy is nothing to a wealthy family, but for ordinary people who have no source of livelihood, it can solve the problem of food and clothing.

"Ah."

Mr. Zhou nodded.

Mathematicians in the capital have proposed new definitions of symbols. How could such a mathematics festival be without them?

at this time.

Mr. Zhou's father stopped him.

"The capital is not peaceful recently, and there may be major cases involved. It is better to wait until the storm is over before you go to the capital."

The old man's face showed concern.

Someone dared to plot to assassinate the saint. When the news spread, it caused an uproar and everyone was frightened.

This heinous act of rebellion will implicate many people.

Even the social atmosphere in Shandong has become serious recently. I wonder what the situation in the capital is like, the old man said comfortingly.

"We are scholars and do not participate in political affairs."

Mr. Zhou said indifferently.

Those who receive talent allowances, even if they do nothing, will not have to worry about their livelihood and will have more political privileges.

The government cannot govern them. Even if they commit a crime, the local government has no right to punish them. The interrogation must involve the participation of the Department of Science and Technology.

They cannot be tortured or mistreated, they are held in separate places, a good environment is ensured, and they must have adequate food and clothing.

In the past, their political privileges were limited to Peiping, and then extended to the north. Now that Prince Yan has become the emperor's grandson, their privileges have also expanded to the entire Ming Dynasty.

Like overnight.

After being identified by the Department of Science and Technology, scholars who receive talent allowances from the Department of Science and Technology have become the most comfortable group.

The old man felt helpless when he saw his son being so innocent.

Not wanting to miss the opportunity, Mr. Zhou took his Shutong disciple with him, and the two took a train in Shandong and arrived in the capital on the third day.

Peiping initially attracted many scholars from other places.

During the Hongwu Dynasty of the Ming Dynasty, the literary style flourished in the south. Only with the flourishing literary style was there the soil to breed scholars who were interested in studying various kinds of knowledge. There were not many scholars in Peiping.

The Jianghuai area is the place with the most scholars. Most of them returned to their hometowns and received subsidies and privileges in the capital. Scholars flocked to the capital.

Mr. Zhou did not expect that his father’s reminder was right.

The banks of the Jianghuai River in the Jianghuai area were completely empty. Instead of seeing the luxury and beautiful scenery that my friends mentioned, there were only lonely flower boats.

But what does it have to do with him?

He doesn't care.

Several mathematicians were counting using chips at one of their homes.

Shuangchang is the writing method of the Chinese numerical abbreviation system.

Very simple and scientific.

It is at the same level as the smoothness and simplicity of ancient Indian numeral writing, but more comprehensive.

Use the vertical form for the ones place, the horizontal form for the tens place, the vertical form for the hundreds place, the horizontal form for the thousands place, the vertical form for the ten thousand place, etc.

In this way, from right to left, vertically and horizontally, and so on, you can use arithmetic chips to represent any large natural number.

Because of the vertical and horizontal transformation between bits, and each bit has a fixed writing method, there will be neither confusion nor misalignment.

There is no doubt that such a calculation method is completely consistent with the modern popular decimal notation method.

"In "Shuowen Jiezi" of the Eastern Han Dynasty, it is recorded that rice weighs one, twenty dou of millet, ten dou of rice, and is called Kou; six dou of rice weighs more than half a dou, and it is called Can."

A mathematician talks and describes in a mathematical way.

"Rice is written as twenty, Kou is written as ten, and Can is written as six and two-thirds."

"Twenty to ten to six and two-thirds."

(Because the writing method of calculation is not included in the input method, it can only be replaced by text. This is also the price of lagging behind.)
Then the mathematician wrote another set of numbers.

"Sixty to thirty to twenty."

The mathematician wrote the word "equal" between the two sets of numbers.

In ancient times, there was no equal symbol. When written, it was represented by the Chinese character "equal" or "equal".

"=" sign.

When it first appeared, it did not mean equal. The French mathematician Veyette stated in his work that "=" is used to add two quantities.

These messy symbols have no clear definition, they are just everyone's writing habits.

For example, some people use "" to represent equal, some people use the letter equivalent to pha to represent equal, and some people use one to represent equal.

Finally, because the works of the French mathematician David Wade in the [-]th century were widely spread, his habitual use of "=" made more people aware of it and spread wider, gradually becoming a tacit understanding and even a recognized equal sign in later generations.

Today, the Ming Dynasty mathematician casually drew an apostrophe at the end of a slash, and everyone knew it meant equal.

Mr. Zhou became more and more fascinated as he watched.

"Do you understand this equation?"

"Isn't this a rudimentary equation? Even more advanced is Mr. Zhu Shijie's eternal equation. You're bullying us because we are ignorant." Mr. Zhou was dissatisfied with the other party's showoff.

The man smiled sheepishly.

The Zhu Shijie mentioned by Mr. Zhou was a Han Chinese. When the Southern Song Dynasty collapsed, he was born in the north and traveled around the south to exchange knowledge with southern mathematicians. Later generations called it Zhu Shijie's identity.

Several mathematicians quickly discussed a set of symbols.

The words equal, multiply, divide, add, divide, etc. are marked with detailed concepts and accompanied by the symbols they drew.

Their results were published in the Technical Journal - Mathematics.

This issue of Mathematics Journal caused dissatisfaction among many mathematicians.

"Why did they define symbols and why should they use his symbols?" Another scholar complained to the Technical Newspaper and asked the Technical Newspaper to withdraw the article.

Many scholars have complained.

This article in the Technical News caused an earthquake in the academic world.

People inside and outside the capital cannot understand.

cabinet.

Huang Huai said incredulously: "People nowadays don't dare to express their anger for fear of being implicated. Why don't they care."

"His Royal Highness the Emperor Taisun treats scholars the most. They stay out of the matter. What should they care about?"

Xie Jin understands.

"Isn't it just a symbol? I think they are eager to fight."

"Haha."

Xie Jin couldn't help but laugh: "This is a battle for the right to speak. Let alone a quarrel, I wouldn't be surprised if someone started a fight."

Whatever you say comes.

The day after Xie Jincai finished speaking, two scholars actually got into a fight on the streets of the capital.

Alarming the inspector, they could only separate the two of them. The first lesson of their training was the privileges of scholars.

They have no authority to deal with scholars and can only ask scholars if they want to be held accountable.

If you want to investigate the responsibility, you have to ask officials from the Department of Science and Technology to come forward. The regulations are very cumbersome, energy-consuming and time-consuming.The two scholars glared at each other, neither pursuing the other.

Mr. Zhou's actions opened another door and aroused the interest of scholars in formulating definitions.

This is not a difficult task, and you can publish articles in technical newspapers, gain fame, and leave your name in history.

Who wouldn’t rush to do it?

There is fast hand, no hand is slow.

Mr. Zhou came to the capital, and of course he would not return empty-handed. "Encyclopedia of Mathematical Symbols" was jointly published by several people, which does not show his ability.

If the library in Beijing didn't provide accommodation, he would even live here.

After a period of time.

Zhu Gaochi heard the arrangements for the actions of officials from the Ministry of Rites to welcome Zhu Di and approved them. In his free time, he read today's newspapers.

As a rule, read the technical report first.

"During the Shang Dynasty, Mr. Shang Gao, the ancestor of the people, was the greatest mathematician in the world at that time. He invented the Pythagorean theory and completed the proof."

"The agricultural technology of our Chinese civilization is unparalleled in the world, and agriculture is inseparable from astronomy, and astronomy is inseparable from mathematics."

"As early as the Shang Dynasty, we observed astronomy, made astronomical measurements and established calendars in ancient times. We raised the problem that there are no steps to climb up to the sky, and the earth cannot be measured with dimensions. How do we get numbers?"

"Mr. Shang Gao, the ancestor of the Chinese people, proposed his theory of moments. Numbers are derived from the principles of circles and squares. Circles come from squares, and squares come from moments."

"Moments are calculated based on multiplication and division."

"The "moment" proposed by Mr. Shang Gao originally refers to the drawing tool including right angles, Pythagorean measurement, and he used 3:4:5 as an example to analyze and prove it."

"During the proof process, the uses of moments were also pointed out: square moments are used to straighten ropes, yanked moments are used to see heights, overlapping moments are used to measure depth, lying moments are used to know distances, circumferential moments are used to determine circles, and combined moments are used to determine squares."

Zhu Gaochi found it difficult to watch.

It was as if long-dead memories were attacking him.

"After the Shang Dynasty and the Zhou Dynasty, people needed more accurate calculation methods. The ancestor Mr. Rongfang raised the difficult problem of how to calculate the diameter of the sun and the distance between the sun and the earth."

"Mr. Chen Zi, the ancestor of Zhou Dynasty, completed the proof."

"He proposed to point a hollow bamboo pole eight feet long (note: one foot at that time was equal to sixty-nine feet today) towards the sun. Then he observed at one end of the pole that the sun just covered the middle hole at the other end of the pole. From this, Obtain the distance from the sun to the ground observation point/sun diameter=bamboo pole length/aperture=[-]:[-].”

"In addition, an eight-foot-long bamboo pole was erected in an open space in the King of Zhou's city as a "biao", also called "bi"; it can be observed that at noon on the summer solstice every year, the sun's shadow of the table is the shortest, which is one foot six. inches, and facing due south and due north, for every thousand miles, the surface shadow becomes one inch shorter."

"So, at noon on the day when the apparent shadow is six feet long, there is no shadow 250 miles due south. Using the Pythagorean theorem and the proportion method, we can calculate that the distance from the sun to the shadowless point on the ground at that time is [-] miles. miles, the distance from the sun to the observation point in the royal city is one hundred thousand miles. Further calculations show that the diameter of the sun is one thousand and two hundred and fifty miles.

After Zhu Gaochi read it.

Can't help but laugh.

The average distance from the sun to the earth is 960 kilometers, and the diameter of the sun is 130 million kilometers.

So the ratio of the distance between the sun and the earth to the diameter of the sun is about [-]:[-].

The result here is wrong.

What was wrong was not the formula, but the ancients of the Zhou Dynasty who believed that the earth was flat, so even though they used correct mathematical principles, the error in their calculations was still very large.

It includes the right-angled triangle theory and the Pythagorean theorem of three strands, four strings and five strings. It is thousands of years earlier than Pythagoras proposed and proved the Pythagorean theorem in ancient Greece in the sixth century BC.

If someone says that there was no geometry in ancient China, you can directly photograph his face. This is more than 1000 years earlier than "Elements of Geometry".

The Western "Elements of Geometry" came out in 300 BC, but was soon completely lost, unlike China's "Zhou Bi Suan Jing" and "Nine Chapters of Arithmetic" which were passed down from generation to generation.

of course.

The content in the later "Elements" is great, but no one knows what is said in the original "Elements", and it has become a historical secret.

"Shang Gao, the ancestor mathematician of the Shang Dynasty, invented the Pythagorean theorem, the square of a right triangle, and the theory of square area, and proposed concepts such as rectangle, circle, square, etc."

[-] BC to [-] BC.

"Chen Zi, the ancestor mathematician of the Zhou Dynasty, perfected the Pythagorean theorem and had a mature formula."

[-] BC to [-] BC.

"In the Jin Dynasty, the squares of various figures were solved, equations were solved, and even Sun Tzu's theorem was born."

Zhu Gaochi couldn't understand.

The large written record above, converted into the writing method of later generations, Zhu Gaochi could recognize every word, but he could not recognize them together.

The big words in the content mean that for a set of integers Z, each number in Z is divided by the same number m, and the remainder can be 0, 1, 2, .m-1, a total of m types.Then Z is divided into m categories based on the size of the remainder.Each category has the same remainder.

Written according to the equation:
Assume b (x) is an integer coefficient polynomial, then the congruence equation f (x) = 0 (mod m) is equivalent to f (x) + b (x) = b (x) ( mod m);
Assume b is an integer, (b, m) = 1, then the congruence equation f(x) = 0 (mod m) is equivalent to bf(x) = 0 (mod m);
Assume m is a prime number, f(x)=g(x)h(x), g(x) and h (x) are both integer coefficient polynomials, and xo is the same spinning process f(x)= 0 (mod m ), then xo must be the solution of the congruence equation g(x)= 0 (mod m) or h(x)= 0(mod m).

Proof: (1) If f(xo)= 0(modm), then f(xo)+ b(xo)= b(xo)(mod m) is established, conversely, if f(xo)+ b(xo)= b(x0)(mod m), then f(xo)= 0(mod m) holds;
(2) If f(xo)= 0(mod m), then bf(xo)= 0(mod m) is established. On the contrary, if bf(xo)= 0(mod m), then (b, m)= 1: f(xo)=0(modm) is established;
(3) If g(xo)h (xo)= 0(mod m), then since m is a prime number, g (xo)= 0 (mod m) or h (xo)= 0(mod m).Certification completed.

Zhu Gaochi could still solve the mathematical problems of the Shang Dynasty and the Zhou Dynasty, and he could see the meaning.

By the Northern and Southern Dynasties, Zhu Gaochi could no longer do it.

"Mathematics can only be understood by the smartest people, no matter what era." Zhu Gaochi murmured, giving up the act of competing with himself.

"Mr. Yang Hui, a mathematician in the Southern Song Dynasty, invented the geometric arrangement of Yang Hui's triangle and the coefficient law expanded on Sun Tzu's theorem. For example, in Yang Hui's triangle, the three numbers in the third row exactly correspond to each of the expansions of the sum of the squares of the two numbers. The four numbers in the fourth row exactly correspond to the coefficients of each term in the expansion of the cube of the sum of the two numbers, and so on.”

……

Zhu Gaochi stopped watching.

It was really a headache to read. In short, the famous scholar named Zhou whom he had met in Peiping had sorted out the mathematics and physics of the past dynasties. What was different from others was that he formulated and symbolized it.

And each theory, theorem, equation, etc. is given annotations and origins, forming a complete system.

For example, people in the Shang Dynasty had limited knowledge and formed an algorithm for triangulation. Then with the development of civilization, by the Zhou Dynasty, people not only had an algorithm for triangular area, but also formed a formula.

In the Han Dynasty, Liu Hui, a mathematician during the Three Kingdoms period, wrote "Nine Chapters of Arithmetic", which used the naked eye and tools to calculate the height of the island and various advanced mathematical theories.

Then in the Jin Dynasty, there were more complex equations and algorithms, and in the Southern Song Dynasty, mathematics reached its climax.

After the fall of the Southern Song Dynasty and the early Yuan Dynasty, Zhu Shijie, the greatest mathematician in the world at that time, summarized and optimized Chinese mathematics and pushed it to unprecedented heights.

He even studied the essence of mathematics and formed the concepts of spatial patterns and quantitative relationships.

Zhu Gaochi was very happy.

I almost forgot to greet Zhu Di.

The importance of mathematics is very important both in ancient and modern times.

Not to mention the technology in other industries, where did the excellent agricultural technology in ancient times come from?Did it fall from the sky?

A developed agricultural society is inseparable from a high level of understanding of celestial phenomena.

The excellent calendar allowed ancient farmers to clearly know how to farm, which required the support of science and technology rather than random imagination.

Nowadays, with a more complete mathematical system, the development of industrial technology has a solid support.

How can Zhu Gaochi promote the entire society?

He relied on the advanced technological civilization of ancient China.

"We must pay the greatest attention to scholars." Zhu Gaochi said in the cabinet, asking the cabinet to discuss laws.

He wants to formulate legal provisions to protect the social status of scholars and provide them with an adequate environment.

No one can suppress scholars.

any scholar.

As long as he passes the assessment of the Department of Science and Technology, he will have enough food and clothing, even if he doesn't produce a single result.

It’s the same reason that ancient times valued scholars.

Zhu Gaochi just pointed out the group of people he valued.

scholar.

From readers.

It is also not born out of thin air.

　There is something going on in the company today, and there may only be one chapter. It is a big chapter, with nearly [-] words, so I will send it out first. If I have time in the evening, I will try to write another chapter.

　　
　
(End of this chapter)