After the ancient Indians created Arabic numerals, they spread to the Arab region around the 7th century. By the 3rd century A.D./KLOC-0, the Italian mathematician Fibonacci wrote Abacus, in which he introduced Arabic numerals in detail. Later, these figures spread from the Arab region to Europe. Europeans only know that these numbers are imported from the Arab region, so they are called Arabic numbers. Later, these figures spread from Europe to all countries in the world.
Arabic numerals were introduced into China around 13 ~ 14 century. Because there was a number called "chip" in ancient China, which was easy to write, Arabic numerals were not popularized and used in China at that time. At the beginning of this century, with the absorption and introduction of foreign mathematical achievements by China, Arabic numerals began to be used slowly in China, and only now have they been popularized and used in China for more than 100 years. Arabic numerals have now become the most commonly used numbers in people's study, life and communication.
Due to the needs of life and labor, even the most primitive people know simple counting, and it has developed from counting with fingers or objects to counting with numbers. In China, at the latest in the Shang Dynasty, there was a method of expressing large numbers with decimals; As late as the Qin and Han Dynasties, there has been a perfect decimal numerical system. Written not later than 1 century, Nine Chapters Arithmetic already contains the calculation rules of square roots and cubes that are only possible in the value system, as well as various operations of fractions and solutions of linear simultaneous equations, and also introduces the concept of negative numbers. Liu Hui also proposed to use decimal fraction to represent the odd zero part of the square root of irrational numbers in his annotated Nine Chapters Arithmetic (3rd century), but it was not until the Tang and Song Dynasties (in Europe, after S. Steven in16th century) that decimal fraction became universal. Although China never had the concept of irrational numbers or real numbers in a general sense, in essence, China had already completed all the arithmetic and methods of the real number system at that time, which was indispensable not only in application, but also in early mathematics education. At first, the concept of numbers began with natural numbers, such as 1, 2, 3, 4 ... no matter where they are located, the symbols of counting are quite different.
The figures in ancient Rome were quite advanced, and now many old wall clocks are often used. In fact, Roman numerals have only seven symbols: I (for 1), V (for 5), X (for 10), L (for 50), C (for 100), D (for 500) and M (for 65438). No matter how the positions of these seven symbols change, the numbers they represent are the same. They can be combined to represent any number according to the following laws:
1. Repetition: How many times a Roman numeral symbol is repeated means several times this number. For example, "II" means "3"; "XX" means "30".
2. Right plus left minus: symbols representing large numbers are attached to the right of symbols representing decimals, indicating that Osuka is on decimals, such as "VI" for "6" and "DC" for "600". The symbol representing big numbers is accompanied by the symbol representing small numbers to the left, indicating the number of big numbers minus small numbers, such as "IV" for "4", "XL" for "40" and "VD" for "495".
3. Add a horizontal line: add a horizontal line to the Roman numeral, indicating that it is 1000 times that number.
People in other countries and regions generally agree with the decimal notation, namely 1, 2, 3, 4, 5, 6, 7, 8, 9. When zero is encountered, it is represented by a black dot, such as "6708", which can be represented as "67.8". Later, this "zero" gradually became "0".
If you look closely, you will find that there is no "0" in Roman numerals. In fact, in the 5th century, "0" was introduced to Rome. But the Pope is cruel and old-fashioned. He doesn't allow any use of "0". A Roman scholar recorded some benefits and explanations about the usage of "0" in his notes, so he was called by the Pope to be whipped so that he could no longer hold a pen and write.
The commonly used numerical symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 in the world are called Arabic numerals. In fact, they were first used by ancient Indians. Later, Arabs integrated ancient Greek mathematics into their own mathematics, and this simple and easy-to-remember decimal notation spread all over Europe, gradually evolving into today's Arabic numerals.
P.S. later discovered that it was not enough to express only natural numbers. If five people share four things when distributing prey, how much should each person get? So the score is generated. Natural numbers, fractions and zeros are usually called arithmetic numbers. Natural numbers are also called positive integers.
Then people find that many quantities have opposite meanings, such as increase and decrease, forward and backward. In order to express such a quantity, a negative number is generated. Positive integers, negative integers and zero are collectively called integers. If you add a positive score and a negative score, they are collectively called rational numbers. In 2500 BC, when Pythagoras' students studied the middle term in the ratio of 1 2, they found that none of them could be expressed by integer ratio. Pythagoras was shocked by the appearance of this new number, and then people found many numbers that could not be written by the ratio of two integers, such as pi, which is the most important one. People called these numbers irrational numbers. Rational numbers and irrational numbers are collectively called real numbers. But when solving equations, you often need to find a square root. If the number of square roots is negative, is there any solution to this problem? If there is no solution, then mathematical operation is like walking into a dead end. So mathematicians stipulated that the symbol "I" was used to represent the square root of "-1", that is, the imaginary number was born.
After the concept of number developed to imaginary number, for a long time, even mathematicians thought that the concept of number was perfect and all the members of the mathematical family had arrived. However, in June 1843+16 10, British mathematician Hamilton put forward the concept of "quaternion". Quaternion is a number consisting of a scalar (real number) and a vector (where x, y and z are real numbers). Quaternions are widely used in number theory, group theory, quantum theory and relativity. At the same time, people have also studied the theory of "multivariate number". Up to now, several families have developed greatly.