As one of the four ancient civilizations in the world, our great motherland has made many outstanding contributions in the long history of mathematics development. These brilliant achievements are far in the forefront of the world and enjoy high honors in the history of world mathematics.

First, the earliest use of decimal position value system

The so-called position value system means that the same number has different values because of different positions. For example, in 365, the number 3 means 300 and 6 means 60.

Using this method to represent numbers is not only concise, but also convenient for calculation. The decimal value system is the earliest in China. During the archaeological excavation of Oracle Bone Inscriptions in Yin Ruins, the number 13 was found, namely:

With the symbols of nine numbers and four position values, thousands of natural numbers can be expressed, and the position value system has sprouted. By the Spring and Autumn Period and the Warring States Period, our ancestors had widely used computing chips for calculation. In the calculation, the decimal value system is completely used to count, which is more convenient than the 60-bit value system of Babylon and more advanced than the decimal value system of ancient Greece and Rome. This advanced counting system is human civilization.

Second, the earliest use of scores

Scholars such as Zhang Cang and Geng Shouchang in the Western Han Dynasty compiled Nine Chapters of Arithmetic by sorting out and deleting mathematical knowledge since Qin Dynasty. In this chapter of Tian Fang, a mathematical classic, a complete score algorithm is proposed.

From Liu Hui's Nine Chapters Arithmetic Notes, we can know that in Nine Chapters Arithmetic, the rules of dividing points, combining points (fractional addition), subtracting points (fractional subtraction), multiplying points (fractional multiplication) and dividing points (fractional division) are exactly the same as our current fractional operation rules. In addition, we also record scores (comparison scores) and equal scores.

The rules of fractional operation are the same as those introduced in Nine Chapters Arithmetic. Liu Hui's Nine Chapters Arithmetic Notes was written by Wei Jingyuan in 263.

Third, the earliest use of decimal places

Liu Hui introduced the use of decimals (the number of emblems, that is, decimals) to approximate the inexhaustible prescriptions in the Notes on Nine Chapters of Arithmetic, and put forward the concept of decimals for the first time. During the Song and Yuan Dynasties, Qin and he were expressed as 1863.2 inches, which was basically consistent with the current notation.

Fourth, the earliest use of negative numbers

The concept of negative number and the law of addition and subtraction of positive and negative numbers have been introduced in Nine Chapters of Arithmetic. Liu Hui said that "the gains and losses of the two calculations are opposite, and the positive and negative numbers should be named", which is a clear definition of positive and negative numbers. The addition and subtraction rules of positive and negative numbers given in the book are exactly the same as those introduced in textbooks now.

These contents appear in the equation chapter of the book and play a role in solving equations (groups). For example, the eighth question in this chapter is:

Today, we sold two cows and five sheep to buy thirteen tapirs, leaving a thousand dollars. Selling three cows and three tapirs and buying nine sheep is enough money; Selling six sheep, eight tapirs and buying five cows cost less than 600 yuan. What are the prices of cattle, sheep and tapirs?

The solution is:

Technically, if the equation holds, two cows and five sheep are positive, thirteen cows are negative, and the rest of the money is positive: three cows are positive, nine sheep are negative, and three cows are positive; The second time, the cow is five negative, the sheep is six positive, the tapir is eight positive, and the lack of money is negative.

What this means here is that if the price of each cow, sheep and tapir is represented by X, Y and Z respectively, the following equations (groups) can be listed:

Then use positive and negative numbers to calculate the result. Negative numbers appear in all the coefficients and constant terms of the equation, which is the first one used for calculation in the world.

The earliest discovery of binomial coefficient law

126 1 year, Yang Huizeng, a mathematician in the Song Dynasty, gave the origin map of cholesky decomposition in his book "Detailed Explanation of Nine Chapters of Algorithms", listed binomial coefficients with indices of 0-6 respectively, and pointed out that "cholesky decomposition's roots originated from the book" unlocking divination ",which was used by Jia Xian." Jia Xian was a mathematician in the Northern Song Dynasty. That is to say, China knew the binomial coefficient law as early as 1 1 century. Now, we call this law Jia Xian Triangle for short.

In addition, there are Sun Tzu's theorem and the solutions of higher-order equations. Wait a minute.