China's ancient mathematics has made great contributions to world culture. Algebra was undoubtedly created by China. China's ancient mathematics is reasonable and comes from practice, especially agricultural production? Found problems from rich production practice and created geometry with China characteristics? There are enough examples to show that ancient mathematics in China is rigorous and serves the actual needs of agricultural production?

Our motherland is vast and rich in resources? A large population? An ancient civilization with a long history? China has made great achievements in ancient literature and art. What is the compass of science and technology? Paper making? Printing? The four great inventions of gunpowder are world-famous? However, few people know about China's achievements in ancient mathematics, and some even mistakenly think that China has been lagging behind in mathematics?

In fact, ancient mathematics in China has made great contributions to world culture? China's ancient mathematics is reasonable, and there are enough examples to show that their argument is rigorous and ahead of the world. China's ancient mathematics won the "World Champion" in some important events? And ancient mathematics came from practice, especially agricultural production? This is because China has a long history of agriculture. Agriculture originated in ancient times and there is no written record. It happened in the economic matrix of primitive gathering and hunting. Because agricultural production is influenced by many factors such as social economy, natural environment and "land", the ancients regarded "land" as "the source of all things and the root of all life"? It is the basic means of production for agricultural production. With land, there must be measurement, calculation and, of course, mathematics? Publication of educational papers

Mathematics is a science that studies the quantitative relationship and spatial form of the objective world, while China's ancient mathematics only calculates? Shape? The combination of numbers and shapes has its own characteristics and system?

First of all, since the Spring and Autumn Period and the Warring States Period at the latest, China has generally used arithmetic to count, and adopted the decimal system. With a good counting tool, natural number operations can be carried out more easily; In addition to infinite division, there are fractional notation and its operation. By distinguishing positive numbers and negative numbers by two different colors, four operations of rational numbers can be carried out unimpeded, and the "current technology" that can solve various proportional problems is also carried out on this calculation system; From the Han Dynasty to the Sui, Tang, Song and Yuan Dynasties, right? List equations quickly? Equation? Indefinite equations and indefinite equations are also carried out on this computing system?

On the other hand, from the end of the Han Dynasty to the Three Kingdoms period, was this discrepancy complementary? The principle of damaging the breadth and benefiting Shaanxi plays a leading role in dealing with the problem of spatial form, which is reflected in the cutting and completion of plane graphics and the chess test of three-dimensional graphics. Interpreting Liu Wei's nine-difference technique with the complementary law of right-angle complementarity and supplementing Qin's triclinic quadrature formula will naturally break down, and the theory of "Qin inherited Helen from Greece" will also break down. Liu Wei's famous cyclotomy is the application of complementary forms. In the method, Zu used the special model of Mohe square cover to derive the volume formula of the ball. Theoretically, the result so far is beyond reproach. Is it the complementary principle of entry and exit?

Combination of numbers and shapes? Complementary square root? The issuer is undoubtedly the concrete application of Liu Wei's "disintegration diagram", just like peeling cocoons layer by layer? Batman? Shen Kuo? Yang Hui superimposed and compared with the corresponding three-dimensional volume formula, and got the correct result? On the other hand, the geometric problem depends on the quantitative relationship? For example, Zhao Shuang's Pythagorean Square Diagram proves the Pythagorean string relationship through calculation, and the principle of island gravity difference can only be revealed by means of right-angle coform. The limit of the number of sides multiplied by the number of sides of a circle as an inscribed regular polygon is also clarified by calculation?

One? Examples of Pythagorean Theorem in Agricultural Production

Ancient mathematicians in China studied the proof and application of Pythagorean Theorem, and formed their own system. Most of the proof methods use Green-Zhu method, which is today's fill-and-dig method? By proper division, divide the square area on the hook and the square area on the rope into several parts, and the sum of these parts can just fill the square on the rope. The so-called green ink in and out is to add green to the divided graphics? Zhu? Yellow and other colors are inferior (easy to identify when cutting and repairing), and the method is ingenious and simple, which is amazing?

According to historical records, Yu Xia (265,438 BC+040-2095 BC) used Pythagorean technique in water control, so can we say that Yu Xia is the first person in the world who has Pythagorean theorem?

The Classic of Weekly Parallel Calculations is the oldest arithmetic book in China, written about 100 BC? The book says, "Yu ruled the world because of this number"? Does this mean that Pythagorean theorem and measurement under special circumstances can be applied in Dayu? Zhao Shuang said in the annotation of Zhou Bi suan Jing: "Yu governs water, and he will definitely unify rivers, and only when he looks at mountains and rivers will he compete.". In addition to the catastrophic disaster, he released the people's distress and made him be injected into the sea without drowning. Is it the dice? " This shows that the success of Dayu's water control at that time was achieved by Pythagorean survey?

Nine Chapters Arithmetic is also the oldest mathematical masterpiece in China. It is the earliest and most important mathematical classic in China, and it is also an extremely precious classic document in the history of mathematics in the world. Written around 100? This book summed up China's brilliant achievements in the field of mathematics before Qin and Han dynasties, and created a unique theoretical system, which had a very far-reaching impact on the development of ancient mathematics in China, including many examples from agricultural production?

Example 1: Today, there is a square-foot pool, which was born in the center of the pool and one foot out of the water. It was introduced to the shore and adapted to the shore. What is the depth? What is the geometry of epiphysis? (selected from "Nine Chapters of Arithmetic")

There is a square pond with a side length of 65,438+0 feet. There is a reed in the middle of the pond, and the water surface is 1 foot. If the reed is pulled to the pond, the stem tip just touches the shore of the pond. What is the depth of the pond and the length of the reed?

This is the topic of Pythagorean theorem. Using Pythagorean theorem, after simple calculation, it is known that the water depth is one foot two feet and the length is one foot three feet.

Two? Profit and loss problem's Application in Agricultural Production: Published Computer Papers.

No important mathematical thought and method in history can be "water without a source, wood without a root", but it always has its practical background and theoretical origin? So what kind of mathematical historical background is the technique of surplus and deficiency produced, and what kind of mathematical thought and theory is it developed? The discussion of this problem is very valuable for understanding the evolution of solving problems in agricultural production before Qin and Han dynasties and the emergence of equation technology in ancient calculation?

As we all know, Nine Chapters Arithmetic is a summary of mathematical achievements before Qin and Han Dynasties in China. It is a mathematical work that has been gradually improved after a long period of historical development. This book is divided into nine chapters. The first chapter, "Square Field", talks about simple land survey and score algorithm in ancient times. Chapter VII What is "insufficient profit"? With the development of agricultural practice and the deepening of theoretical research, the quantitative relationship involved in mathematical application has gone far beyond the scope of proportional relationship. The appearance of various complex linear and nonlinear problems makes the original ratio algorithm powerless? On the one hand, the application of ratio algorithm in solving problems requires "the success rate of factors, the division of trial and argument, and the balance of its bias and uniformity", and requires high analytical ability and skills for complex ratio problems; On the other hand, the ratio algorithm can't solve all kinds of linear and nonlinear problems at all? This requires mathematicians to create a new and powerful general problem-solving method, and the residual technique is produced under such mathematical historical conditions?

Example 2: Today * * * buys cattle, seven * * * gives it to 190, less than 330, and nine * * * gives it to 270, with a profit of 30? Find out how to calculate the price of cattle (selected from "Nine Chapters of Arithmetic")

How many families buy cattle together Seven * * * contributions 190 is not 330. If nine * * * companies contribute 270 yuan, it will be 330 yuan more. What is the number of households and the price of cattle?

Translate the surplus and deficiency skills into today's equation, and the solution is:

Let x be the number of families and y be the price of cattle.

x/9×270-y=30

y-x/7× 190=330

Number of households solved 126, and the price of cattle is 3750 yuan?

According to Tang Shi, around 855 A.D., there was a great official in the Tang Dynasty named Yang Kui, who was famous for his integrity in selecting administrative officials? Once, there were two clerks, one of whom needed a promotion. The problem is that these two people have the same position, worked in the government for the same time, and even got exactly the same evaluation? So, who should be promoted? The official in charge of this work was very nervous about it, so he went to ask Yang for instructions? After careful consideration, Yang said, "One of the greatest advantages of clerks is their fast calculation speed. Now, let these two candidates listen to my question. Whoever gets the right answer first should be promoted "? His topic is: "someone was walking in the forest and overheard several thieves discussing how to divide the stolen cloth?" They said that if everyone divided six horses, there were five left, and if everyone divided seven horses, there were still eight missing? How many thieves are there here? What's the total number of cloth? "Yang's injury made two alternate personnel count on the stone steps of the hall with chips on the spot? Soon, one of them got the right answer, he was promoted, and everyone believed in the decision?

Three? Application of Volume Calculation in Agricultural Production —— Taking the publication of periodical papers as an example

In ancient China, due to water conservancy projects? National defense fortifications? Due to the need of architecture and road construction, earthwork calculation is very frequent? With the development of agricultural production, all kinds of barns? The calculation of grain depot volume is getting heavier and heavier? By the time Nine Chapters of Arithmetic was published, China had all kinds of geometric volume formulas except the common cuboid? Prism? Pyramid? Prism? Cylinder? A cone? Besides frustum of a cone, there are some prism volume formulas. These formulas are included in a large number of business articles in Nine Chapters of Arithmetic?

There was no derivation and proof of the volume formula in ancient countries, so China's achievements in geometric quadrature are far ahead, which is incomparable to foreign countries in the same period in terms of diversity and completeness of logical reasoning? It must also be pointed out that many color volume formulas used by our ancestors two thousand years ago are still useful today?

The following are some wonderful examples of Nine Chapters Arithmetic for readers' reference.

Example 3: There is a millet tablet today, which will be twelve feet high next Monday. Product and Xiaomi geometry?

There are a number of millet, piled in a conical shape on the flat ground. Its circumference at the bottom is 12 feet and its height is 2 feet. What is its volume and millet respectively?

A: Eight thousands of feet, two thousand nine hundred and sixty-two, twenty-seven minutes and twenty-six?

Exodus 4: Today there is a committee called One Yuan, and it will be ten feet tall next Wednesday. What is the dimension?

Today's translation: There are some cockroaches, stacked against the wall. Its bottom ring is 3.5 feet, and its height is 7 feet. How big is it and the cockroach?

Answer: 350 feet is 144 and 8 of 243?

Example 5: Today, the wall has an inner corner, which is eight feet next week and five feet high. What is the product of rice?

There are several meters, piled in the inner corner of the wall. A quarter of its circumference is 8 feet and its height is 5 feet. What is its volume and meters?

Answer: Five fifths of 35 feet and 9 feet is 69 1 meter, 2 1 minute, 729 minutes, 69 1 minute?

This method of calculating accumulation is widely used in our country, and these formulas have been compiled into songs and handed down? Song formula is:

The optical stacking method uses 36,

Stop against the wall in eighteen minutes.

When the inner corners get together, like 9 1,

Is the outer angle 39 clear?

These well-known songs may have been written by later generations according to this "entrusted millet technique" in "Nine Chapters of Arithmetic"? Obviously, the meaning of the first three sentences of the Song formula is tantamount to the technique of "supporting millet"? As for the fourth sentence of rhyme, it is to pile rice according to the outer corner of the wall. According to the script, it can be expressed as "twenty-seven and one against the outer corner of the wall (three-quarters cone)"? However, there is no such example in Nine Chapters of Arithmetic?

In a word, China's ancient mathematical thought is widely used in agricultural production, and what this article describes is only the tip of the iceberg. The function of this article is to attract jade at best?