Tracing China: Through history, dialogue between ancient and modern

Chapter 277
"Want to try "Nine Chapters of Arithmetic"?"

""Nine Chapters of Arithmetic" is a monograph on mathematics written by our ancient Zhang Cang. Does Zhang Cang know who it is? He was the prime minister in the early Western Han Dynasty."

"Mathematics 2000 years ago, isn't it?"

"It's probably to test some quadratic equations of chickens and ducks in the same cage."

"Naturally, it is not comparable to modern people, but you must know that the contribution of creation is always more difficult than the subsequent improvement."

"Yes, for example, in modern times, any professor-level talent in physics and mathematics has a more comprehensive knowledge reserve than the great gods Newton and Einstein. When you can say that these professors can be at the same level as Newton and Einstein of?"

""Nine Chapters of Arithmetic" contains a total of 246 mathematical problems, which are divided into nine chapters, and the amount of knowledge is not small."

"Don't underestimate the wisdom of the ancients! Papermaking in the Western Han Dynasty, just this technology, allowed knowledge to spread around the world, and allowed the knowledge of civilization that originally belonged to the aristocracy to spread among the common people at the bottom. student."

"A poor family? Brother, what does it mean to be a poor family? A poor family refers to the children of a poor nobleman."

"In short, mathematics in the Qin and Han Dynasties was remarkable. Looking at the world of Bluestar at that time, it was said to be second, and no one dared to say first."

……

In the live camera.

In the Huanghuang Hall, the emperors are sitting in all directions, waiting for the start of this competition of six arts.

Unexpectedly, in this competition of emperors, the Western Han Dynasty sent Liu Ying, the last child emperor of the Han Dynasty.

The one sent by the Eastern Han Dynasty will also be the last Emperor Xiandi Liu Xie of the Han Dynasty.

Two subjugated kings.

Compete in the same field.

The host Lin Feng looked forward and couldn't help frowning, why?Because Liu Ying, the last emperor of the Western Han Dynasty, looks like a fool?
Liu Bang said indifferently, "Mr. Lin, is there any question?"

Lin Feng said, "Emperor Gaozu, don't you think that Liu Ying..."

Liu Bang waved his hand and said, "It's okay, just give way to the Eastern Han Dynasty."

Unspoken.

In the Han Yuefu poetry competition just now, "Son of the Plane" Liu Xiu took the initiative to admit defeat, and was very open-minded.

They Western Han Dynasty can't be small, can't they?
Some people may be unfamiliar with Liu Ying, the child of the Han Dynasty. This is the prince of the Han Dynasty controlled by the "traveler" Wang Mang.

He is the great-great-grandson of Emperor Xuan of the Han Dynasty.

Liu Ying only served as the crown prince for three years in his life. He was imprisoned at the age of 4, and an order was issued to prohibit anyone from talking to him. In February, Liu Ying, who was only 25 years old, was killed by Li Song in Linjing.

Fool Liu Ying VS Han Xiandi Liu Xie.

A set of competitions without any suspense.

of course.

Lin Feng's purpose is not to compete, but to let modern audiences understand our ancient Chinese achievements in mathematics, and to know a little about the ancient book "Nine Chapters of Arithmetic".

Modern mathematics is controlled by the Westland countries.

In ancient mathematics, we once stood on the top of the world and looked down on the world.

Lin Feng walked to the center of the main hall, faced the camera, and began to talk cheerfully, talking about the general situation of "Nine Chapters of Arithmetic".

"Nine Chapters of Arithmetic" contains a total of 246 mathematical problems, which are divided into nine chapters.

Their main contents are:
Chapter 1 "Fang Tian": mainly describes the calculation method of the area of ​​plane geometric figures.Including rectangle, isosceles triangle, right angle trapezoid, isosceles trapezoid, circle, sector, bow and ring, the calculation methods of the area of ​​eight graphics.

In addition, it also systematically describes the four arithmetic rules of fractions, and methods of finding the greatest common divisor of numerator and denominator.

Among them, there are 38 sample questions and 21 standing techniques.

Chapter 2 "Corn": Proportional conversion of grains and grains, a proportional algorithm is proposed, which is called Jinyoushu, and the chapter of Decay Fen proposes a proportional distribution rule, called Decay Fen Technique.

Among them, there are 46 sample questions and 33 standing techniques.

Chapter 3 "Decline": Proportional distribution problems, including 20 sample questions and 22 standing techniques.

Chapter 4 "Shaoguang": Knowing the area and volume, find the length of one side and the length of the diameter, etc., and introduce the methods of square root and cube root.

Among them, there are 24 sample questions and 16 standing techniques.

Chapter 5 "Commercial work": earth and rock engineering, volume calculation; in addition to giving various three-dimensional volume formulas, there are also engineering allocation methods.

Among them, there are 28 sample questions and 24 standing techniques.

Chapter 6 "Equal Loss": Reasonable apportionment of taxes; using the technique of decay to solve the problem of reasonable burden of taxes and servitude.Jin Youshu, Decaying Technique and their application methods constitute a complete set of proportional theories including today's positive and negative proportions, proportional distribution, compound proportions, and chained proportions.The West did not form a similar set of methods until after the end of the 15th century.

Among them, there are 28 sample questions and 28 standing techniques.

Chapter 7 "Insufficiency of surplus": that is, the problem of double thinking; three types of profit and loss problems, namely, surplus and deficiency, surplus and deficiency, double surplus and double deficiency, are proposed, and some problems that can be transformed into surplus and deficiency through two assumptions Solutions to general problems.This is also the result of being in a leading position in the world. After it spread to the West, it has had a great impact.

Among them, there are 20 sample questions and 27 standing techniques.

Chapter 8 "Equations": the problem of linear equations; the method of separating coefficients is used to express linear equations, which is equivalent to the current matrix; the direct division method used in solving linear equations is consistent with the elementary transformation of matrices.

This is the world's first complete solution of linear equations.

In the West, it was not until the 17th century that Leibniz proposed a complete solution rule for linear equations.

This chapter also introduces and uses negative numbers, and proposes positive and negative techniques—the rules of addition and subtraction of positive and negative numbers, which are exactly the same as those in modern algebra; when solving linear equations, the multiplication and division of positive and negative numbers are actually performed.

This is a major achievement in the history of world mathematics. For the first time, it broke through the range of positive numbers and expanded the number system.

In foreign countries, it was not until the Brahma and Duo of India in the 7th century that negative numbers were recognized.

Among them, there are 18 sample questions and 19 standing techniques.

Chapter 9 "Pythagorean": various problems solved by using the Pythagorean theorem.Most of the content is closely related to the social life at that time.

A general solution formula for the problem of Pythagorean numbers is proposed: if a, b, and c are the hooks, strands, and chords of the Pythagorean shape respectively, then a+b=c.

In the West, Pythagoras, Euclid, etc. only obtained a few special cases of this formula, and it was not until Diophantus in the 3rd century that similar results were obtained, which is about 3 years later than "Nine Chapters on Arithmetic". century.

There are still some contents in the Pythagorean chapter, but they are still modern in the West. For example, a set of formulas given in the last question of the Pythagorean chapter was not derived by American number theorist Dixon until the end of the 19th century abroad.

Among them, there are 24 sample questions and 19 standing techniques.

……

Most mathematicians of later generations began to learn and research mathematics from "Nine Chapters on Arithmetic", and many people have commented on it.

Among them, Liu Hui, Li Chunfeng and others are the most famous.

The annotations by Liu, Li and others have been handed down to this day together with "Nine Chapters on Arithmetic".

In the Tang and Song dynasties, "Nine Chapters of Arithmetic" was clearly stipulated as a textbook by the state.

In the Northern Song Dynasty, "Nine Chapters of Arithmetic" was published by the government, which is the earliest printed mathematics book in the world.

In the current version of "Nine Chapters of Arithmetic", the earliest version is the Southern Song reprint of the above-mentioned Northern Song version, which is now stored in the Shanghai Library (only the first five volumes are left alone).

Dai Zhen in the Qing Dynasty copied out the complete book "Nine Chapters of Arithmetic" from "Yongle Dadian" and made a collation.Most of the subsequent "Siku Quanshu", the rare edition of Wuyingdian, and the "Ten Books of Suanjing" engraved by Kong Jihan are based on Dai Xiaoben.

As a world famous work of mathematics, "Nine Chapters of Arithmetic" was introduced to the Northern Dynasties and Japan as early as the Sui and Tang Dynasties.It has been translated into Japanese, Russian, German, French and other language versions.

"Nine Chapters of Arithmetic" is a thousand-year masterpiece.

The disadvantages are also very obvious.

It does not define any mathematical concepts, nor does it give any derivations and proofs.

This also led to a situation where in this ancient oriental land, the discipline of mathematics could not be unified.

After thousands of years, Western mathematicians dominated this field.

It has to be embarrassing, our learned people are too numerous to enumerate, mentioning Confucianism, Chinese studies, and master-level figures, the number is dazzling. It is really rare, especially mathematicians. Zu Chong seems to be the only one who left an impression on people in ancient times.

If it has to be related to chemistry, I am afraid that there are still a few alchemy scholars who seem to be "pretending to be gods and ghosts", and they are only used to fill in the numbers.

In addition, scholars in the field of science are simply blank.

Therefore, many scholars will have such a question, since it is a broad and profound country that can produce many talents in the field of thought, why can't it cultivate excellent science talents?

After all, the field of science is far easier to explore than the field of thought.

However, in everyone's exploration, we gradually discovered that such extreme consequences were caused by the system of selecting talents in feudal society.

At that time, the most important form of selecting talents was the scientific examination. The scope of the imperial examination was only in the "Four Books and Five Classics". Educational career developed around the "Four Books and Five Classics".

To make a joke that is not very respectful, if the imperial examination at that time was about how to get pedicures, then, in the history of China, it is estimated that a large number of pedicure masters will emerge.This is the exam-oriented education that has not changed since ancient times, and its sadness lies!
The major dynasties have never paid much attention to mathematics, which is also our major shortcoming!

no way.

In the field of mathematics, it cannot help the rulers of the feudal dynasty to govern the country, but metaphysics and Chinese studies can.

Finally, Lin Feng made a conclusion: "In the field of mathematics, 2000 years ago, we were brilliant, and it seems that we have never been brilliant."

in the hall.

Lin Feng still gave Liu Ying and Han Xiandi Liu Xie a few questions for the assessment.

For example: the topic of bringing reeds to shore.

"Today there is a pond with a square of ten feet, and the reeds grow in the center. Out of the water one foot, lead the reeds to the shore, so that they are at the same level as the shore. Ask about the depth of the water and the length of the reeds."

The translation is--the existing pool is one foot square, and there is a new reed growing in the pool, which is one foot above the water surface. If it is led to the shore, it is just flush with the shore. How deep is the water? How deep is the reed? how long?

……

For example: round wood buried wall problem.

"Now there is a log buried in the wall. I don't know the size. I saw it with a saw. It is one inch deep and one chi long. What is the diameter?"

Modern means - the existing cylindrical wood, buried in the walls.I don't know its width, so I saw it with a saw. When the depth is one inch, the width of the saw is one foot. What is the diameter of the wood?
……

For example: the problem of folding bamboo to the ground.

"Today there is a bamboo that is one zhang high, and the end is folded to reach the ground, and it is three feet away from the original. Ask how tall the one that was folded is?"

The translation is--the existing bamboo is one foot high, and the broken end is propped up on the ground, three feet away from the bamboo root on the ground. How high is the broken part from the ground?

……

For example: meet the topic.

Today there are ducks that travel from the South China Sea to the North Sea in seven days, and geese that travel from the North Sea to the South China Sea in nine days.Today all the ducks and geese got up and asked, "When will we meet again?"
The translation means that the wild ducks take off from the South China Sea and reach the North Sea in 7 days; the wild geese take off from the North Sea and reach the South China Sea in 9 days. Today, the wild ducks and wild geese take off from the South China Sea and the North Sea at the same time, and how many days later will they meet?
……

These questions are very simple in the eyes of modern people. It is easy to get the answer by establishing one or two equations to solve.

What about the two subjugated emperors?
Han Xiandi, who was once imprisoned by the hero Cao Cao, was obviously stronger. He answered all three questions with ease. Han Xiandi also said bluntly, "I, when I was bored, I once studied "Nine Chapters of Arithmetic"!"

The idiot Liu Ying stood there for a while, then was dragged back to his seat. Xihan lost the round.

……

(End of this chapter)