Decimal notation is an outstanding creation of working people in ancient China. Decimal notation brings great convenience to calculation and has a far-reaching impact on the development of mathematics. The decimal notation was once called "one of the most wonderful inventions of mankind" by Marx.
Once upon a time, people in Huaxia didn't know why there were clouds in the sky and rain, lightning, strong winds and fog on the ground. Fuxi, the tribal leader, has been trying to figure out these things.
One day, Fuxi fished in Cai He and caught a white turtle. White turtles are rare in the world, he thought. When the sky were to fall, the ancestors of the white turtle saved my brother and sister and never met again. Is this white turtle a descendant of its ancestors? Well, I have to keep it.
He dug a hole and filled it with water, put the white turtle in it, caught some small fish and shrimp and put them in the hole for the white turtle to eat.
Strange to say, there are white turtles, and the water in the pit is particularly clear. Every time Fuxi went to feed it, it would go to Fuxi and lie motionless by the pit.
Fuxi sat by the pit, looking at the white turtle and thinking about the problems in the world. Looking at it, he saw a pattern on the white turtle shell, so he folded a straw and drew it on the ground according to the pattern on the white turtle shell.
Painting thinking, painting thinking, painting 998 1 day, a famous painter. He used two symbols "-"and "-"to describe his feelings and experiences. The former represents a yang and the latter represents a yin. Yin and yang go back and forth, one yang and two yin, one yin and two yang, three yang and three yin, and draw them into gossip.
The binary idea in Fuxi's eight diagrams was used by the later German mathematician Leibniz, and a mechanical computer was designed in 1694. Now, binary has become the basis of electronic computers.
Fuxi Bagua not only contains binary thoughts, but also China is the first country in the world to use both decimal and binary.
The difference between binary and decimal lies in the number of digits and the law of carry. The counting rule of binary is every binary one, which is a counting system based on 2. In decimal system, what we usually call 10 is the value equivalent to 2 in binary system.
Decimal system, that is, with 10 as the base, one digit is added after each decimal point. The key point of the mathematical concept of bit value is to make the same digital symbol have different values because of its different positions.
Since we have written records, the notation has always followed the decimal system. Oracle Bone Inscriptions in the Shang Dynasty and Zhong Dingwen in the Western Zhou Dynasty used the words "one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand and ten thousand" to record natural numbers within 654.38+ million. This symbol has obvious value system significance.
Oracle Bone Inscriptions also has the concepts of odd number, even number and multiple.
Archaeologists have verified that in the Spring and Autumn Period and the Warring States Period in the 3rd century BC, the Chinese ancients had skillfully used the decimal notation, which was basically the same as the decimal notation commonly used in the world.
Historical facts show that China was the first country in the world to invent and use the decimal system. China used the decimal system at least 1000 years earlier than the second country in the world, ancient India.
Decimal notation includes two principles: decimal and decimal. "Decimal" refers to a complete decimal one; "Bit value" means that the same number represents different values in different positions. All numbers are represented by 10 basic symbols, which are full of ten into one.
At the same time, the same symbol has different values in different positions, so the position of the symbol is very important.
For example, three numbers "1 1", the right "1" means 1 one, the middle "1" means1ten, and the left "/kloc". This makes it easier to express and calculate extremely difficult integers.
The decimal notation is widely used. In computational mathematics, there were already four operations in Shang and Zhou Dynasties, and by the Spring and Autumn Period and the Warring States Period, the four operations of integers and fractions were quite complete.
Among them, the positive integer multiplication melody "Jiujiuge", which appeared in the Spring and Autumn Period, can be called the crystallization of the combination of advanced decimal notation and concise Chinese, which can not be produced by any other notation and language.
Since then, 99 pine has become one of the most basic foundations for the popularization and development of mathematics, and it has continued to this day. It only changed from "998 1" in ancient Jiujiu songs to "22 gets 4", and now it is from "1 1 de 1" to "998 1".
The application of decimal notation is also reflected in the invention of weights and measures. Since ancient times, the carry system of units of measurement in all countries of the world is very complicated. At that time, the units in various countries and even cities were not unified, and even the decimal system was different. This system is very chaotic. Few countries use decimal, mostly decimal or hexadecimal.
In fact, before the Qin dynasty unified the whole country, the system of weights and measures was also very inconsistent. At that time, the vassal States had four, six, eight and decimal systems.
After Qin Shihuang unified China, he promulgated the decree of unified measurement system. By the end of the Western Han Dynasty, the imperial court had formulated a new national standard. Except for the units of "balance", the decimal system was basically used throughout the country.
According to the need of weighing gold and silver, the unit of "money" was added in the Tang Dynasty. At that time, "Hu", "Si", "Millie", "Li" and "fen" were used together, and "Liang" was one tenth of what it is now, and the decimal unit below "Qian" was used.
Later, the Tang court abolished the Jun and Shi units used at that time and added the load unit as the abbreviation of "100 Jin". However, at that time, the two units of Jin and Liang were not decimal, but hexadecimal, and they were used for a long time.
Decimal notation brought great convenience to calculation and had a great influence on the high development of ancient computing technology in China. Compared with other areas with earlier civilizations in the world, such as ancient Babylon, ancient Egypt and ancient Greece, the calculation method used is much better.
Decimal notation is produced by people's expanding understanding of natural numbers and practical needs, which embodies the causal relationship between the development of mathematics and the development of human thinking and the needs of human life, and reveals the essential characteristics of mathematics as a thinking science.
In his book Mathematical Manuscripts, Marx praised decimal notation as one of the most wonderful inventions, and accurately summarized the inherent characteristics of this mathematical method and its position in the mathematical kingdom. Our ancestors were the earliest inventors of this "most wonderful invention".
Professor Needham, a famous British historian of science, once spoke highly of the notation of Shang Dynasty in China: "Without this decimal system, it is almost impossible to have our unified world now." Needham said: "Generally speaking, the number system of Shang Dynasty is more advanced and scientific than that of ancient Babylon and ancient Egypt."