In the early counting form, there was no position value system. What is the position value system? The position value system is a number system, and the position of each number affects and changes the value of the number. For example, the number 3 in the decimal number 375 is not 3, but 300, because it is in hundreds.
Around 1700 BC, hexadecimal began to appear, which helped Mesopotamia a lot. Mesopotamia developed it and used it in their 360-day calendar. The oldest known actual position value system was designed by Babylonians, and this design was obtained from the hexadecimal system used by people in the Euphrates River basin. In order to replace what needs to be written, they only use two symbols, which can be used for complex mathematical calculations, except that there is no symbol of 0, but a space is left on the left side of the number to represent 0.
Around 300 BC, the symbol of zero began to appear and hexadecimal was widely developed. In the early years after A.D., Greeks and Indians began to use decimal system, but at that time they didn't have the notation of position. For calculation, they use the first ten letters of the alphabet. Finally, around 500 AD, Indians invented the decimal notation of position. This notation abandons the method of using letters to represent more than 9 numbers and unifies the first 9 symbols. Around 825 AD, mathematician Al Wahrazimi wrote a book about the worship of Indian numerals.
Decimal system was introduced to Spain almost in 1 1 century, that is, when the western * * * numbers were formed. Europe at this time is in a state of doubt and slow change. Scholars and scientists remain silent about the use of decimal, because it is not easy to express scores with it. But when merchants adopted it, it gradually became popular and showed unparalleled advantages in their work and records. Later, it was about.
Perhaps, one day in the future, with the change of our needs and calculation methods, a new system will replace our existing decimal system!
2. Decimal history (1) In the early counting form of decimal, there is no position value system. What is the position value system? The position value system is a number system, and the position of each number affects and changes the value of the number. For example, the number 3 in the decimal number 375 is not 3, but 300, because it is in the hundredth place. Around 1700 BC, hexadecimal began to appear, which helped Mesopotamia a lot. And use it in their 360-day calendar. The oldest known actual position value system was designed by Babylonians, and this design was obtained from the 60-based system used by people in the Euphrates River basin. In order to replace 60 symbols from 0 to 59, they only used two symbols, which can be used for complex mathematical calculations, but there is no symbol of 0. Instead, leave a space to the left of the number to indicate zero. Around 300 BC, the symbol of zero began to appear and hexadecimal was widely developed. In the early years after A.D., Greeks and Indians began to use decimal system, but at that time they didn't have the notation of position. For calculation, they use the first ten letters of the alphabet. Finally, around 500 AD, Indians invented the decimal position notation. This notation abandons the method of using letters to represent more than 9 numbers and unifies the first 9 symbols. Around 825 AD, the mathematician Al * * * Wah Razimi wrote a book about the worship of Indian numerals. Decimalization was introduced to Spain almost in 1 1 century. At that time, the western * * * had just taken shape. Europe at this time is in a state of doubt and slow change. Scholars and scientists remain silent about the use of decimals because it is not easy to express fractions. But when merchants adopted it, it gradually became popular and showed unparalleled advantages in their work and records. Later, in the16th century, decimals also appeared. And decimal point were proposed by J. Napier in 16 17. Maybe one day, with the change of our needs and calculation methods, a new system will replace our existing decimal system.
3. What is the origin of the decimal system? Decimalization is an outstanding creation of China people, which is of great significance in the history of mathematics in the world.
According to Oracle Bone Inscriptions, the Shang people had learned to remember any number within 65,438+million with the words 13 of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 10,000, and now the largest number that can be confirmed at that time is 30,000. There are even numbers, odd numbers, even numbers and multiples in Oracle Bone Inscriptions.
During the Spring and Autumn Period and the Warring States Period, the ancient people in China were able to skillfully use the decimal notation, which was basically the same as the decimal notation commonly used in modern times. Before Qin Dynasty, the system of weights and measures in China was not unified, including four, six, /V and decimal.
After Qin Shihuang unified China, he promulgated the decree of unified measurement system. Liu Hui, a native of Han Dynasty, introduced that when prescriptions are inexhaustible, they are approximated by decimals (the number of emblems, that is, decimals), and put forward the concept of decimals for the first time.
By the end of the Western Han Dynasty, new national standards had been formulated. At that time, the decimal system was basically used. In the Tang Dynasty, according to the need of weighing gold and silver, money was added to the unit of measurement, which was half of an inch, and cents, roots, cents, silk and sudden were borrowed as decimal units under the money.
Later, the two units "Jun" and "Shi" related to "Jin" were abolished, and "Dan" was added as the title of 100 Jin. Only the hexadecimal between "Jin" and "Liang" has been used for a long time.
By about 1300, Liu Jin's "Law Poetry" in Yuan Dynasty has been included in 106368. 63 12 is written as a decimal part, and it is written as a line after the integer part.
In foreign countries, most of them are hexadecimal and hexadecimal. The concept of decimal didn't come into being until 1585 in the west, and its expression method was far less advanced than that in China. It was not until 1799 that France first put forward the provisions of the metric system, and the world metric system began in 1840.
It was not until the 20th century that most countries took "meter", "liter" and "kilogram" as the decimal standard units of weights and measures. Professor Needham, a famous British historian of science, once spoke highly of China's ancient notation: "Without this decimal system, it is almost impossible to have our unified world now.
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4. The origin of decimal system: human beings use decimal system in arithmetic, which may be related to the fact that human beings have ten fingers. Aristotle said that the universal use of decimal system by human beings is only the result of an anatomical fact, that is, most people are born with 10 fingers. In fact, in the writing numeration system independently developed in the ancient world, except for the cuneiform numerals of Babylonian civilization, which adopted 60 decimal system, and the Mayan numerals adopted 20 decimal system, almost all of them were decimal system. However, these decimal notation systems are not bitwise.
5. Decimal system originated from binary system and decimal system in China or Indian China.
When it comes to the contribution of ancient * * * people to mathematics, people will naturally think of 1, 2, …, 9, 0, the ten "* * * numbers". In fact, these ten "* * * numbers" were first created by ancient Indians. Later, the ancient * * * people spread these ten numbers to Europe, and Europeans called them "* * * numbers". In the development of mathematics, ancient people mainly absorbed and preserved the mathematics of ancient Greece and India, and spread it to Europe, building a bridge of mathematics.
Arithmetically, the ancients adopted and improved India's numerical notation and carry notation, and also adopted India's irrational number operation, but gave up the negative number operation. The name of the subject "Algebra" was invented by people. * * * People have also solved some linear, quadratic and even cubic equations, and explained their solutions with geometric figures.
In addition, the ancients also used the intersection of conic curves to solve cubic equations, which is a great progress.
In ancient times, * * people also obtained more accurate pi. They calculated 2π = 6.283185307195865, and the π value has been calculated to 15 digits after the decimal point. In addition, they introduced tangent and cotangent of triangle and proved sine theorem.
The ancients also translated and wrote a large number of mathematical documents, which played a great role in promoting the development of mathematics in later generations after they were spread to Europe. Therefore, it is well-deserved to call ancient mathematics a bridge of mathematics.
Ancient China —— Hometown of Decimal System and Binary System
Ancient China is one of the four ancient civilizations in the world. In the history of world mathematics development, China's ancient mathematics achievements occupy a very important position.
In the early stage of the development of human culture, China's mathematical research results were actually far ahead of ancient Babylon and ancient Egypt. As early as five or six thousand years ago, people in ancient China invented simple mathematical symbols. By the Shang Dynasty more than 3,000 years ago (about16th century BC to1th century BC), the numbers engraved on Oracle Bone Inscriptions and pottery were very common. Through the study of Oracle Bone Inscriptions at that time, it was found that there were 13 counting units representing 1, 10, 100, 1000 and 10,000 respectively, which indicated that the counting method of China people at that time had adopted the current human decimal system.
Another example of China people's earliest use of decimal system is that the number symbol "0" originated from ancient books in China. The ancients in China used the method of "circling" when deleting typos in articles. Over time, this "○" has become a symbol of "non-existence", that is, "zero". Around 876 AD, the symbol "0" was officially used in ancient India. The decimal system invented by human beings is not complete until the symbol "0" representing "zero" is produced. Therefore, China is a well-deserved "hometown of metrication".
In the process of operation, the ancient people in China used the tool of "calculation and preparation". "Counting chips" are some symmetrical sticks made of wood and bamboo. The ancient people in China arranged these sticks vertically and horizontally, so they could represent any natural number. According to research, at least in the Spring and Autumn Period more than 2,500 years ago, the method of calculating and recording funds in ancient China was quite complete. This method of expressing numbers is undoubtedly in the forefront of the world.
Needless to say, the ancients in China studied pi. As early as the Wei and Jin Dynasties, the famous mathematician Liu Hui calculated an extremely accurate value π-3. 14 16. Zu Chongzhi, a great mathematician in the Northern and Southern Dynasties, further calculated the exact value of pi between 3. 14 15926 and 3. 14 15927. It was not until 1000 years later that Europeans calculated such an accurate pi.
Shang Gao, a mathematician of the Zhou Dynasty in China, was the first person to put forward Pythagorean theorem in the world, earlier than Pythagoras in ancient Greece. Yang Hui, a mathematician in the Southern Song Dynasty, founded the famous "Yang Hui Triangle" in the history of mathematics, which is the earliest exploration of binomial coefficient in the history of human mathematics.
In addition, the "multiplication formula" invented by the ancients in China (also called "Jiujiubiao") greatly improved the efficiency of the written calculation of multiplication and division. The abacus invented by the ancients in China is recognized as the predecessor of modern computer in the world.
The most wonderful thing is that Leibniz, one of the founders of calculus, thinks that China is the hometown of "binary" in modern computer theory. Leibniz made an in-depth study of the Book of Changes in ancient China. He believed that the gossip in the Book of Changes was recorded with the idea of "binary". According to him, "Tai Chi gives birth to two instruments, two instruments give birth to four images, and four images give birth to eight diagrams ..." The Book of Changes is undoubtedly the embodiment of the "binary" thought.
Therefore, the ancient mathematicians in China are worthy of being the founders of modern mathematical theory; China's achievements in ancient mathematics research are worthy of being the foundation of modern mathematics theory.
6. The origin of the decimal system was first used by people to count fingers, toes or pebbles, sticks and so on.
Represents 1, 2,3,4 objects, divided into 1, 2,3,4 fingers. Reach out with one hand when you meet five objects, and reach out with both hands when you meet 10 objects. When counting many pebbles, a pile of 10 pebbles is represented by a larger pebble.
China is one of the first countries in the world to use decimal notation. Oracle Bone Inscriptions in Shang Dynasty had decimal notation, which was an outstanding creation of China people and was of great significance in the history of mathematics in the world.
The commonly used number now is the Indian-* * * number, which is expressed in decimal. Use 0, 1, 2, 3...9 to represent any number, and the low-order number will go to the next one after reaching ten digits.
This decimal system looks simple and common now, but it has been evolved by human beings through long-term efforts. * * * There are only ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. However, with these ten numbers, you can remember an infinite number.
The counting method with the ratio of "ten" between every two adjacent counting units is called decimal counting method. It follows the principle of "one for every ten, ten for every ten".
Application: 10min = 1 angle 10cm = 1 decimeter, 1 sheet = 10 foot 1 kg = 10 beam.
7. With regard to the origin of the decimal system, almost every nation used the decimal counting method at the earliest, because human beings naturally count with ten fingers first.
But this does not mean that there is only one counting method, decimal counting. For example, all countries in the world use the decimal system when calculating the year, month and day (12 months is a year). For another example, in China, only 16 is considered as a catty, which is the "hexadecimal counting method"; Coincidentally, in the British weight unit, 1 constant pound is also equal to 16 ounce (also called "English ounce" or "pound"). Why is this happening? Because our ancestors often thought hexadecimal was convenient to divide things into two phases, I think the British probably thought so, too. Probably because it is more convenient to divide it into equal parts many times, people in the ancient two river basins first invented the method of calculating time and circumferential angle in hexadecimal, and later extended it to the whole world.
Interestingly, it is said that there is a village in Latin America where the same clan lives. Since the fingers and toes of residents are 12, the decimal method is used for daily counting.
In the past, conservative British people always insisted on carrying out the carry system, which is very complicated for foreigners: 1 =20 shillings; 1 shilling =12p. Dizzy! Foreigners in Britain often don't know how many pennies 1 pound can be exchanged, nor how many pennies 1 pound can be exchanged. Until 197 1, Britain * * * could not stop the world trend, and announced the currency decimal system:1=100p, and the shilling was cancelled.
There are other carry systems in the world, so I won't talk about those that are not commonly used.
In ancient times, it was inconvenient for people to count, and they would remember with the help of things around them. Of course, the hand is the most convenient, so it will count from 1 to 10. Then it became a habit, passed down from generation to generation. Rome also used 12.
Decimalization should be a habit, but there is no difference between good and bad. If I had to choose, I would choose binary.
From now on, 16 has one of the biggest weaknesses, that is, it needs to count letters, which makes many people unaccustomed. Only the decimal system is the most natural.