What were the studies on negative numbers in ancient China?

According to archaeologists, in addition to the "Nine Chapters of Arithmetic", many ancient Chinese mathematical works and even calendars mention the arithmetic of negative numbers and negative numbers. Qin Jiushao of the Southern Song Dynasty recorded in the book "Nine Chapters of Mathematics" that the result as a constant term of a higher-order equation is "often negative". In the book "Detailed Explanation of the Nine Chapters of Algorithm", Yang Hui changed "benefit", "from", "division" and "elimination" to "addition" and "subtraction" respectively, which more clearly clarified the relationship between positive and negative and addition and subtraction.

Zhu Shijie of the Yuan Dynasty included "positive and negative techniques" in the book "Enlightenment of Arithmetic" for the first time in the "Overview" of the book, which shows that people at that time had taken positive and negative numbers as a special mathematical research subject. In this book, Zhu Shijie also wrote the multiplication rule of positive and negative numbers, which is a new step in the study of positive and negative numbers.

According to historical records, as early as more than 2,000 years ago, China had the concept of positive and negative numbers, and mastered the operation of positive and negative numbers, and Liu Hui, a scholar in the Three Kingdoms period of China, made significant contributions to the establishment of the concept of negative numbers. Liu Hui first gave the definition of positive and negative numbers, Liu Hui first gave the method of distinguishing positive and negative numbers, in the famous mathematical treatise "Nine Chapters of Arithmetic" (written in the first century AD), the first to put forward the law of addition and subtraction of positive and negative numbers, in addition to the definition of positive and negative arithmetic methods in the "Nine Chapters of Arithmetic", Liu Yan (206 AD) in the late Eastern Han Dynasty and Yang Hui (1261) also discussed the law of addition and subtraction of positive and negative numbers, which are completely consistent with what the nine chapters of arithmetic said. It is particularly worth mentioning that Zhu Shijie of the Yuan Dynasty not only clearly gave the addition and subtraction rules of positive and negative numbers with the same sign and different signs, but also gave the multiplication and division rules of positive and negative numbers.

In his algorithm enlightenment, negative numbers were recognized and recognized abroad, much later than in China. In India, the mathematician Brahmagupta did not realize until 628 AD that negative numbers could be the root of quadratic equations. And in Europe, the most accomplished French mathematician in the 14th century, Chucquet, described negative numbers as absurd numbers.

It was not until the seventeenth century that the Dutchman Gerard (1629) first recognized and used negative numbers to solve geometric problems.

It was only with the establishment of the theoretical foundations of integer numbers in the 19th century that the logical rationality of negative numbers was truly established.

Negative numbers are mathematical terms that refer to real numbers less than 0.

The generation of negative numbers is closely related to people's production and life. For example, when calculating the amount of rice stored in the granary, sometimes the amount of grain received should be recorded, and sometimes the amount of grain lent should be recorded; When it comes to bookkeeping, sometimes you make a profit, sometimes you lose money. In order to record such numbers with opposite meanings, the concept of positive and negative numbers was introduced, and the received grain or surplus money was recorded as positive, and the borrowed grain or lost money was recorded as negative.

In ancient China, people realized the value of negative numbers very early. The concept of positive and negative numbers was already proposed in the Nine Chapters of Arithmetic, written in the Han Dynasty. Liu Hui, a mathematician during the Three Kingdoms period, also gave a way to distinguish between positive and negative numbers when he annotated the book:

When using arithmetic chips for calculations, black chips are often used to represent negative numbers, and red chips are used to represent positive numbers; Or use oblique columns to represent negative numbers, and positive columns to represent positive numbers; Alternatively, use a rectangle for negative numbers and triangles for positive numbers. Among them, the practice of using different colors to distinguish positive and negative numbers has been retained until now. Nowadays, red is generally used to indicate negative numbers – newspapers that a country's economy is running a deficit indicates that spending is greater than its revenues and that the country's finances are in deficit.

In addition to the "Nine Chapters of Arithmetic", there are many mathematical works in ancient China that mention the operation of negative numbers and negative numbers: for example, the addition of negative and negative is negative, the multiplication of negative and negative is positive, and so on. Yang Hui, a mathematician in the Southern Song Dynasty, emphasized the close relationship between positive and negative numbers and addition and subtraction in his "Detailed Explanation of Nine Chapters of Arithmetic"; Zhu Shijie, a mathematician of the Yuan Dynasty, not only summarized the law of addition and subtraction of positive and negative numbers, but also proposed the law of multiplication of positive and negative numbers in "Enlightenment of Arithmetic".

At this time, people have officially taken positive and negative numbers as a special mathematical research direction, and have worked tirelessly in this direction.

Summary: Indians recognized the existence of negative numbers more than 700 years later than our country, and Europeans more than 1000 years later than our country, and it was not until after the Renaissance that mathematicians began to study negative numbers. Negative numbers are now widely used around the world, solving many of the difficult problems that were left in the past.

The ancients generally used black to represent negative numbers, red to represent positive numbers, or oblique columns to represent complex numbers, and this method is also very simple.

In ancient China, black chips were often used to represent negative numbers, and red chips were used to represent positive numbers.

Later, some advanced ones used oblique columns to represent negative numbers, and positive columns to represent positive numbers.

Alternatively, use a rectangle for negative numbers and triangles for positive numbers.

In ancient times, they would generally use black chips to represent negative numbers, and sometimes they would also use rectangles to represent negative numbers.

The deficit is used to represent negative numbers, and this negative number is set as a loss, and the mathematical technology in ancient China is still quite high, and there are many ways to deal with mathematics.

1. Generation.

Negative numbers are also generated in production practice. People often encounter various amounts of opposite meanings in their lives. For example, there are surpluses and losses in the bookkeeping; When calculating the rice stored in the granary, sometimes it is necessary to record the grain, and sometimes the grain must be recorded.

For the sake of convenience, people consider the number of opposite meanings. Therefore, people introduced the concept of positive and negative numbers, and recorded the surplus money into the grain as positive, and the loss of money and the loss of grain as negative.

Liu Hui, a scholar during the Three Kingdoms period in China, made significant contributions to the establishment of the concept of negative numbers. Liu Hui first gave the definition of positive and negative numbers, he said: "Today, the two are opposite to the gains and losses, and the positive and negative should be named."

This means that when you encounter quantities with opposite meanings during the calculation, you should distinguish them by positive and negative numbers.

In the famous mathematical treatise "Nine Chapters of Arithmetic" (written in the first century AD) in ancient China, the law of addition and subtraction of positive and negative numbers was first proposed: "Positive and negative numbers are said: the same name is divided, different names are beneficial, positive and negative are not negative, and negative is not positive; Its different names are divided by each other, the same name is beneficial, the positive is not into the positive, and the negative is not into the negative.

The "name" here is the "number", the "division" is "subtraction", the "benefit" and "division" are the absolute values of the two numbers "add" and "subtract", and "none" is "zero".

In today's words: "The law of addition and subtraction of positive and negative numbers is: the subtraction of two numbers with the same sign is equal to the subtraction of their absolute values, and the subtraction of two numbers with different signs is equal to the addition of their absolute values."

Zero minus positive numbers gives negative numbers, and zero minus negative numbers get positive numbers. The addition of two numbers with different signs is equal to the subtraction of their absolute values, and the addition of two numbers with the same sign is equal to the addition of their absolute values. Zero plus a positive number equals a positive number, and a zero plus negative number equals a negative number.

2. The earliest period when negative numbers appeared in China.

According to historical records, China recognized negative numbers during the Warring States period. For example, Li Kui (c. 455-395 BC) wrote in the Book of Laws, "The five people in clothes use 1,500 and less than 450 at the end of the year."

In the Han Jian unearthed in Juyan, Gansu, there are similar descriptions such as "dividing by minus one hundred and twenty-four", minus two thousand two hundred and forty-five, minus four counting, getting seven, dividing to get three", etc., here the "negative" is compared with "gain", which means lack and deficit, which is the prototype of today's negative number.

China is the first country to use negative numbers, and during the Western Han Dynasty (second century BC), China began to use negative numbers. The "Nine Chapters of Arithmetic" has given the rules of operation of positive and negative numbers, people use two colors of arithmetic chips to represent positive and negative numbers respectively when calculating, and use empty spaces to represent "0", but there is no special symbol for 0, the symbol "0" was first used by the Indians in the fifth century AD.

Hello dear, I'm Teacher Donna, and I'm happy to answer for you. In foreign antiquity, the method of expressing negative numbers is as follows: 1

Leave a blank space above the number to indicate a negative number, such as leaving a blank space above 5 to indicate -5. Ancient India and Eggplant Collapse Ancient China used this method. 2.

Extra notation precedes a digit with an extra minus sign or other symbol to indicate a negative number, such as 5"-"Or add two dots before 5 to indicate -5. This method is more common in Europe. 3.

The color method uses numbers of different colors to distinguish between positive and negative numbers, such as black for positive numbers and red for negative numbers. This method was used in both ancient Greece and Rome. 4.

The position method judges the positive and negative numbers according to their position, such as the positive number on the right lead rock side and the negative number on the left. Arabic numerals were also originally notated. 5.

The borrowing method is expressed by subtracting the absolute value of this negative number from a positive number, e.g. 3-5 for -5. This method is used in India and China. 6.

The negative bar method adds a horizontal line below the number to indicate that the number is negative, similar to today's representation. It began to be gradually accepted in Europe from the 16th century.

In the "Equations" chapter of "Nine Chapters of Arithmetic", the concept of negative numbers was proposed, and the operation rules of addition and subtraction of negative numbers were written. Liu Hui, a famous great mathematician in ancient China, commented in his book that when the ancient Chinese people performed arithmetic operations on the abacus, they generally used black chips to represent negative numbers and red chips to represent positive numbers. Or a slashed column for negative numbers, and positive columns for positive numbers.

In addition, there is also a way to represent positive and negative numbers with a triangle on a plane for positive numbers and a rectangle for negative numbers.