Abacus

Abacus (abacus)

A traditional Chinese calculation tool. An important invention in ancient China, it was a widely used calculation tool before the emergence of Arabic numerals.

Existing abacuses come in different shapes and materials. The general abacus is mostly made of wood (or plastic products). The abacus consists of a series of equal numbers of beads arranged in a rectangular wooden frame. There is a beam in the middle that divides the beads into upper and lower parts. The beads run through straight columns, commonly known as "Gear" is generally 9th gear, 11th gear or 15th gear. There is a beam in the middle, with 2 beads on the beam (1 bead for accounting, each bead is 5); 5 beads below the beam (4 beads for accounting), each bead is 1. Calculating with an abacus is called abacus, and abacus has four corresponding operations. The corresponding rules are collectively called abacus rules. Compared with general calculations, skilled abacus calculations are not inferior to calculators, especially in addition and subtraction. You can move the abacus up and down according to your mouth to make calculations quickly and easily. It is a calculation tool commonly used in shops in my country.

The origin and popularity of the abacus

The abacus gradually evolved from the abacus which was commonly used as early as the Spring and Autumn Period. The most cited document is the Eastern Han Dynasty's "Shu Shu Ji Yi". It can be seen that the method and theory of abacus calculation using beads appeared in the Han Dynasty. In the Song Dynasty, the large abacus with cross-beams had appeared. By the Yuan Dynasty, the use of abacus had become very popular. Liu Yin wrote more poems about it in the Ming Dynasty, such as "Yingya Shenglan". "" and "Nine Chapters with Detailed Annotations on Analogous Algorithms" have records about abacus. In the early Ming Dynasty, Chinese abacus spread to Japan, and then to Russia, and from Russia to Western European countries, which had a profound impact on modern civilization. Great influence. In the mid-15th century, the "Luban Wooden Classic" contained specifications for making abacus. The materials for abacus we can see now include wood, bamboo, copper, iron, jade, cloisonne, ivory, bone, etc. It can be hidden in a pocket, and the big one needs to be carried.

With the use of abacus, people have summarized many calculation formulas to make calculations faster. This method of calculation with abacus is called abacus. In the Ming Dynasty, abacus calculations were quite popular, and many books on abacus calculations were published. Among them, the most influential one that has been passed down to this day is "Zhizhi Algorithm Tongzong" (1592) by Cheng Dawei (1533~1606).

"Algorithm Tongzong" is an abacus calculation book. It has 17 volumes and 595 application questions. Most of the questions are taken from other abacus calculations, but all calculations in the book are based on abacus calculations. It contains abacus diagrams and abacus formulas, and gives examples of how to perform calculations on an abacus. Among them, the abacus algorithm for square root and cube root was first proposed by Cheng Dawei. Most of the 51 mathematical book titles since then have been lost, and this appendix has become a valuable historical material on mathematics.

Types of abacus

It is worth noting that the word abacus does not exist. It does not specifically refer to Chinese abacus. Judging from the existing literature, many ancient civilizations have their own abacus. /p>

① A sand table is spread on a flat surface such as a tabletop or a stone slab, and people use wooden sticks to write, draw and calculate on the fine sand. ② Later, they gradually stopped spreading sand and carved on the board. There are a number of parallel lines on it, and small stones (called "calculators") are placed on it to record numbers and calculations. This is a marble abacus board more than 1 meter long found in Salamis, Greece in the mid-19th century. , the ancient Greek abacus, now in the Athens Museum. The abacus board has always been an important calculation tool in the European Middle Ages, but the form varies greatly. The lines are straight or horizontal, the counters are round or flat, and sometimes they are conical (similar to today's checkers), and there are numbers marked on them. . ③Abacus cross refers to Chinese abacus, Japanese abacus and Russian abacus. The Japanese abacus is called "Shilu Pan". It is different from the Chinese abacus in that the longitudinal section of the beads is not oblate but rhombus, with smaller size and more steps. The Russian abacus has a number of curved wooden bars set horizontally in a wooden frame, each with 10 abacus beads. Among the various ancient abacus in the world, the Chinese abacus is the most advanced abacus tool.

Were there any accountants in the Huangdi era, or in other words, were there any "accountants" who could do calculations? People today don't know.

Legend has it that the abacus and arithmetic were invented by a man named Li Shou under the Yellow Emperor. The Chinese-style "Arabic" alphabet invented by Li Shou when he was settling accounts is still circulated in rural areas. Young people over 80 years old can still write and use it. The ten letters are written as follows: |, ‖, ?, ×, ?, ?, ?, ?, Xi, Shi. For example, three pounds and eight taels is written as "?"; two buckets and four liters are written as "‖×"; eighteen feet of cloth is written as "十?"; three feet and four inches of wood is written as "?×".

After the Yellow Emperor unified the tribes, the ancestors fished and hunted all day long, made clothes and crowns, built boats and vehicles, and production flourished. With more and more materials, accounting and accounting have become things that everyone in every household often encounters. In the beginning, I had no choice but to tie knots to record events and carve wooden numbers to deal with daily accounting problems. One time, Yu Ze, a hunting expert, handed over 7 goats, but the stone used to store the prey only allowed one to be returned. When Yu Ze checked the actual goats, he found exactly 7 goats. Why only remember 1? It turns out that the stone heard seven as 1 and only tied one knot on the straw rope.

Another time, Huangdi's granddaughter Heiying received 9 tiger skins for Leizu. The stone only tied 6 knots on the straw rope, and 3 pieces were missing. Therefore, the number of physical objects coming in and out is becoming more and more chaotic, and false claims and false claims often occur. Huang Di was very angry about this.

One day, Li Shou from the Huangdi Palace went up the mountain to pick wild fruits and found a ripe mountain peach tree. He climbed up the tree and picked and ate. He didn't know how much he ate, but his mouth was sour and his stomach was bloated. He didn't dare to eat more, so he jumped down from the tree and sat on the ground to rest.

Suddenly I found that the pecan stones thrown on the ground were very beautiful. He picked them up from the ground one by one and counted them, exactly 20. He thought: These ten peach stones are like 10 tiger skins, and the other ten are like 10 goat skins. From now on, whoever returns as much prey as possible will be given as many hickory nuts as possible. Whoever takes away as much prey as possible will be given a number of hickory nuts. This way no one will be able to default on their debt. Lishou returned to Huangdi's palace and told Huangdi his idea. Huang Di thought about it and thought it made sense. He ordered the chief minister to manage all the property accounts in the palace. After Li Shou served as the chief "accountant" in Huangdi's palace, he ordered people to collect various wild fruits and separate them into categories. For example, mountain fruit represents goats; chestnut fruits represent wild boars; mountain peach fruits represent birds; papaya fruits represent tigers and leopards... No matter which hunting team catches any prey, the capital will record accounts according to different wild fruits. Unexpectedly, the good times don't last long. After being stored for a long time, all kinds of wild fruits changed color and rotted. It was difficult to distinguish the colors of various wild fruits for a while, and the accounts were all confused. Lishou stomped his feet angrily because of this. Finally, he figured out a way. He went to the river beach to pick up many pieces of stones of different colors and put them into ceramic plates. Now the accounting is no longer afraid of discoloration and rot. Because Li Shou was happy for a while, he did not keep it strictly. One day, when he was out on business, his children attracted a group of children. They saw that there were many plates in Lishou's house, containing beautiful stone flakes of different colors. The children were curious and tried to look at them accidentally. The plate fell to the ground and broke into pieces, and all the stone pieces were scattered. Li Shou's accounts were in chaos again. He squatted on the ground and had to pick them up one by one. Li Shou's wife, Hua Nu, came over, pointed at Li Shou with her finger and said, "What a fool! Pierce a hole in the stone piece and string it together with a rope. It will be safer!" Smart people are afraid of being tricked. Li Shou was immediately enlightened. He put holes in each stone piece of different colors and tied them one by one with a string. Every time you wear ten numbers or 100 numbers, wear a stone piece of a different color in the middle. It will be much easier to clean up this way. Li Shou himself often knew what was going on. From then on, inside and outside the palace, up and down, there was no more false reporting or claiming. As production continues to develop, the numbers and types of various prey and skins obtained are getting larger and larger, and there are more and more varieties. We can no longer keep using stone tablets to record accounts. Li Shou seems to be unable to think of any good solutions. Once, he went up the mountain to look for his children and found ripe red chestnuts all over the mountains and fields. There are only ten flowers on each plant, all bright red, very beautiful. He broke off a few branches and held them in his hand, looking at them from left to right. He also wanted to use the red chestnut seeds as a tool to settle accounts, but then he thought, no, it has failed in the past. Li Shou sat alone on the ground, the more he thought about it, the more he ran out of ideas. At this time, Qi Bo, Feng Hou, and Limu went up the mountain to collect herbs and found several bunches of red millet seeds in Li Shou's hand. People sit on the ground in a daze. Feng Hou asked Li Shou what he was thinking about. Li Shou turned around and saw that they were three old ministers. He quickly stood up and told the three senior ministers his idea of ??keeping accounts and settling accounts. Fenghou is one of the founders of Compass. After listening to Li Shou's idea, he took Li Shou's words and said: "I think in the future, we will no longer use so many stone flakes for accounting. Only 100 stone flakes can be used to support the number of one hundred and eight thousand." Li Shou hurriedly asked: "What's the way to do it?" Feng Hou asked Li Shou to pick off all the red European millet, then folded back ten thin bamboo sticks, put ten on each stick, and inserted ten strings in a row. On the ground. Feng Hou said: "For example, if the hunting team returns 5 deer today, you will push 5 red chestnuts up from the bamboo stick. If 6 deer are returned tomorrow, you will push 6 more red chestnuts." Li Li The first said: "That won't work! There are only ten pods on a stick, 5 have been pushed up, and 6 more have to be pushed up, then there will be no more red chestnuts to push." ??The queen of the wind said, "Let me ask you, What’s 5 plus 6?” Lishou said, “Of course it’s 11!” Fenghou said, “Yes! You should move forward by one. Judging from the number of stars, it’s actually only 11.” Number. Also, if the hunting team returns nine deer, how do you count them? Add one more; what is 9 plus 11? Of course it is 20. Judging from the number of deer on the bamboo stick, there are only two. A red chestnut actually equals 20 numbers. That is to say, for every ten numbers and every 100 numbers, one must move forward. For example, if a hunting team returns 80 deer, then how to record the algorithm. "Add 20 to 80, count to 100, and then round up, the number of bamboo sticks will become a red chestnut. In fact, it equals 100." Li Shou asked again: "How can I remember it after rounding up?" Said: "This is easy to do. After carrying, you should draw a mark. For example, draw a circle after the number ten (10); draw two circles after the number 100 (100); draw three circles after the number 1000 (1000) ); after the number 10,000, draw four circles (10,000), which are called one, ten, one hundred, one thousand, and ten thousand. After Li Shou understood the principle of carrying, he went home and made a big clay plate. Dig out the white pearls from the turtle's belly, punch them into holes, and pierce every 10 pearls into an "abacus" with a number of 100, and then write the digits on them; such as tens, hundreds, and thousands. From then on, we no longer need so many stone tablets for counting and accounting.

The abacus, the predecessor of the contemporary "computer" of the Chinese nation, was born 5,000 years ago. As the times continue to advance, the abacus has been continuously improved and became today's "abacus". Especially among the people, not many people were literate at first, but as long as they understood the basic principles and operating procedures of abacus, everyone could use it.

Therefore, abacus quickly spread and was widely used among ancient Chinese people.