Arithmetic is a tool used in ancient China to count, formulate formulas and calculate various numbers and formulas. Also called chips, strategies, operators, etc. At first, it was a natural object such as a small bamboo stick, and later it gradually developed into a special computing tool, and its texture and production became more and more exquisite.
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According to the records of historical books and the discovery of archaeological data, the ancient calculation map is actually a small stick with the same length and thickness, which is generally 13~ 14 cm long and 0.2 ~ 0.3 cm in diameter. It is made of bamboo, wood, animal bones, ivory, metal and other materials, and about 270 pieces are packed in a cloth bag.
When you need to count and calculate, take them out and play on the table, on the kang or on the ground. The origin of calculation and planning is very early in China. In Laozi during the Spring and Autumn Period and the Warring States Period, it was recorded that "those who are good at counting need not count".
In ancient China, calculation was not only a tool for four operations of positive and negative integers and fractions, but also included various concrete calculations. Before the invention of abacus, China was the most primitive and effective computing tool. The early and sustained development of ancient mathematics in China benefited from calculation.
In ancient China, there was an idiom called "strategizing", which meant carefully planning the overall situation of the war in a tent in a military camp. After Emperor Gaozu Liu Bang conquered the world, he once praised Sean, an adviser, saying that Sean could "achieve decisive victory thousands of miles away through strategic planning". The financing mentioned here is the calculation of financing. So how is the calculation used to calculate? In fact, the calculation of the chip is based on decimal values.
Why are there two different ways to put it vertically and horizontally? This is because of the need of decimal system. The so-called decimal system, also known as decimal numerical system, contains two meanings. One is "decimal system", that is, every ten decimal units, ten decimal units are ten, ten decimal units are hundred, and ten decimal units are thousands ... The other is "numerical system", that is, the value represented by each number depends not only on the number itself, but also on its position in the count.
For example, the same number "2" means 2 in one digit, 20 in the tenth digit, 200 in the hundredth digit and 2000 in the 1000 digit ... In the writing system of China Shang Dynasty, the decimal system has sprouted, and it is more standard in counting and calculation.
According to the ancient calculation rules of China, the counting method of counting is: one vertical, ten horizontal, one hundred vertical, one thousand horizontal, ten thousand vertical ... So from right to left, vertical and horizontal, etc., you can use calculation and counting to represent any large natural number.
Because there is vertical and horizontal conversion between its bits, and each bit has a fixed pendulum, it will not be confused or misplaced. The decimal notation in ancient China is a great creation in the history of mathematics in the world.
Compared with the notation of other ancient nations in the world, its advantages are obvious. The number system in ancient Rome had no ranking system, only seven basic symbols, so it was quite difficult to remember a slightly larger number. Although the Mayans in ancient America knew the value system, they used 20 decimal places. The ancient Babylonians also knew the value system, but they used 60 decimal places.
Decimal system needs at least 19 bits, and hexadecimal system needs 59 bits, which makes counting and operation very complicated, which is far less simple and convenient than decimal system which can represent any natural number with only 9 bits. China ancient mathematics has made many outstanding achievements in calculation, which should be attributed to this decimal notation to some extent. It was not until after the Ming Dynasty that the abacus was completely replaced.
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