How does the traditional abacus work?

The abacus

The traditional Chinese calculation tool. An important ancient Chinese invention, widely used as a calculation tool before the advent of Arabic numerals.

The existing abacus is of different shapes and materials. General abacus is mostly wooden (or plastic), abacus by the rectangular wooden frame arranged in a string of equal number of beads, there is a beam to the bead system is divided into the upper and lower parts of the beads within the straight columns, commonly known as the "file", generally 9, 11 or 15 gears. Stalls across the beam, the beam on the 2 beads (1 bead for the financial club, each bead for 5; beam under the 5 beads (4 beads for the financial club), each bead for 1. Calculated with an abacus is called the bead counting, the bead counting corresponds to the four rules of operation of the corresponding law, collectively referred to as the laws of the bead counting. Relative to general arithmetic point of view, skilled bead calculator is not inferior to the calculator, especially in the addition and subtraction. When you use it, you can dial the beads up and down according to Kou Liao to do the calculations. Bead calculations are simple and quick, for our store commonly used calculation tools.

The origin and popularity of the abacus

The abacus was gradually evolved from a chip counting which was in common use as early as the Spring and Autumn Period. The earliest bead calculation in the literature when push the Eastern Han Dynasty, "the counting of records" book, visible in the Han Dynasty has appeared with the bead calculation bead calculation methods and theories. The name of the abacus in the book of calculations to the Song Dynasty, "Xie Chaiwei calculating scripture" for the earliest, it can be determined that as late as in the Song Dynasty, there are beams through the stalls of the large bead abacus has appeared. To the Yuan Dynasty, the use of abacus has been very popular. Between the Song and Yuan dynasties, Liu Yin wrote a poem about the abacus. More records in the Ming Dynasty, such as "Yingya Shengwan", "nine chapters of the detailed notes than the class algorithm of the book have records on the abacus. At the beginning of the Ming Dynasty, the Chinese abacus was spread to Japan, then to Russia, and from Russia to Western European countries, which had a great influence on modern civilization. in the middle of the 15th century, there were specifications for the manufacture of the abacus in the Luban Wooden Scriptures. Nowadays, we can see the abacus materials are wood, bamboo, copper, iron, jade, cloisonné, ivory, bone and so on. The small ones can be hidden in pockets and the big ones have to be carried by people.

With the use of the abacus, people summarized many calculation mnemonics to make the calculation faster. This method of calculating with the abacus is called bead calculation. In the Ming Dynasty, bead calculations have been quite popular, and published a lot of books about bead calculations, among which the most influential one is Cheng Dawit's (1533~1606) Direct Algorithm Unification of Zong (1592).

The Algorithms of the Tuzong is an arithmetic book that focuses on the application of bead calculations. The book ****17 volumes, with 595 application problems, most of which were extracted from other books of arithmetic, but all calculations were converted to bead calculations. The book contains abacus schemas and bead calculations, with examples of how to perform calculations on the abacus according to the mnemonics. Among them, the bead algorithm of open square and open cube was firstly proposed by Cheng Da-wei. At the end of the book, an appendix entitled "The Origin and Flow of Mathematical Scriptures" records the names of 51 mathematical books since the Song and Yuan dynasties, most of which have been lost, and this appendix becomes a valuable historical material of mathematics.

Types of Abacus

It is worth noting that the term abacus does not exclusively refer to the Chinese abacus. From the existing literature, many ancient civilizations have had their own abacus. The various types of abacuses, both ancient and modern, can be broadly divided into three categories: sand table, abacus, bead piercing abacus.

① sand plate is on the desktop, slate and other flat panels, covered with fine sand, people use wooden sticks, etc. in the fine sand writing, drawing and calculation. ② later gradually not sand, but in the plate engraved on a number of parallel lines, placed on the top of a small stone (called "calculator") to keep track of the number and calculations, this is the abacus. 19th century in Greece, Salamis found in the mid-19th century, a 1-meter-long marble abacus, is the Ancient Greek abacus, which is now in the Museum of Athens. Abacus has been an important calculation tool in medieval Europe, but the form varies greatly, the line has a straight horizontal, rounded and flat, sometimes resulting in a conical (similar to the current checkers), the top is also labeled with digital. The Chinese abacus, the Japanese abacus, and the Russian abacus are referred to as the Chinese abacus, the Japanese abacus, and the Russian abacus. Japanese abacus is called "ten Lu plate", and the Chinese abacus is different from the longitudinal section of the bead is not flat round but rhombus, smaller size and more files. Russian abacus has a number of curved wooden bars, set in a wooden frame, each wearing 10 beads. Among the various ancient abacuses in the world, the Chinese abacus is the most advanced bead counting tool.

Was there an accountant in the Yellow Emperor's time, or was there an "accountant" who could do the math? Today's people do not know.

Legend has it that the abacus and math were invented by a man named Li Shou under the Yellow Emperor. The Chinese style "Arabic" alphabet was invented in the first time of counting, which is still circulating in the countryside. 80 years old and above can still write and use it. These ten letters are written as follows: |, ‖, ? |, ‖, ? |, ‖, ×, ? |, ‖, ×, ? The letters are: |, ‖, ×, ×, ? , eve, and ten. For example, three pounds and eight taels is written as "?" Two buckets and four liters are written as "‖×" Eighteen zhang of cloth is written as "ten?" ; three feet and four inches of wood is written as "? ×".

After the Yellow Emperor united the tribes, the pioneers fished and hunted all day long, made clothes and crowns, and built boats and carts, and production was booming. More and more material, accounting, accounting has become every family and every person often encountered things. At the beginning, had to use a rope to keep track of things, carved wood for the number of ways to deal with the daily accounting problems. Once, the hunter Yu Zai, returned 7 goats, the stone of keeping the prey only admitted to return 1, Yu Zai a check in kind, just or 7. Why only 1? It turned out that the stone heard seven as 1, in the grass rope only tied a knot. Another time, the Yellow Emperor's granddaughter Heiying for Rayon received 9 tiger skin, stone in the grass rope only 6 knots, short of 3. So the number of in-kind goods is getting more and more chaotic, false claims often happen. The Yellow Emperor was greatly annoyed by this.

One day, the head of the Yellow Emperor's palace went up the mountain to pick wild fruits and found a tree of ripe peaches. He climbed up the tree while picking and eating, I do not know how much to eat, only to feel the mouth flow sour water, belly bloating, and then did not dare to eat more, jumped down the tree, sitting on the ground to rest.

Suddenly he realized that the peach kernels thrown on the ground were very beautiful. He picked them up one by one from the ground and counted them, exactly 20. He thought: these ten peach kernels are like 10 tiger skins, and the other ten are like 10 goat skins. In the future, whoever returns how many trophies, will send them how many peach kernels. Who led away how many prey, will give who a few mountain peach kernels. In this way no one will be able to renege. The chief returned to the Yellow Emperor's palace and told the Yellow Emperor his idea. The Yellow Emperor thought about it and found it very reasonable. He ordered the chief to manage all the accounts of the palace. After the head of the Li acted as the yellow emperor's palace general "accountant", he ordered people to collect a variety of wild fruits, separate categories. For example, the mountain residue fruit on behalf of the goat; chestnut fruit on behalf of the wild boar; peach fruit on behalf of the birds of prey; papaya fruit on behalf of the tiger, the leopard ...... regardless of which hunting team back to what prey, the Li capital according to the different fruits of the account. Who expected, the good times do not last long. All kinds of wild fruits stored for a long time, all discoloration and decay, a moment to distinguish between a variety of wild fruits color, the accounts all confused. For this matter under the head of the gas straight stomping feet. Finally, he finally came up with a way. He went to the beach to pick back a lot of different colors of stone pieces, respectively, put into the ceramic plate. This bookkeeping is no longer afraid of discoloration and decay. Due to the head of a moment of happiness did not strictly custody. One day, he went out to do something, his children attracted a group of children playing, a see the head of the family put a lot of plate plate, the inside of the different colors of the beautiful stone tablets, the children feel curious, you fight me to see accidentally, the plate fell to the ground to break, the stone tablets all scattered. The account of the head of the subordinate was in disarray again. He squatted on the ground alone and had to pick up the stones one by one. The wife of the head of the family, Flower Lady, came over and pointed her finger at the head of the family, saying, "What a fool! You put an eye in the stone piece and string it up with a rope." Smart people are afraid of people pointing out the trick. The head of the Department was suddenly enlightened, he gave each piece of different colors of stone pieces are punched on the eye, with a thin rope one by one to wear up. Every wear enough ten numbers or 100 numbers, in the middle of a different color stone piece. In this way, it is much less complicated to count. The head of the Clerks themselves often have a number in mind. From then on, the palace outside the palace, up and down, no more false claims. With the continuous development of production, the acquisition of a variety of game, hides, figures are getting bigger and bigger, more and more varieties, can not always wear stone tablets to keep accounts. It seemed that the head of the clan could no longer think of any good solutions. Once, he went up the mountain to look for children, and found a mountain full of ripe red European corn. There were only ten of them on each plant, all bright red and very pretty. He folded a few branches and held them in his hand, looking at them from left to right; he also wanted to use them as a tool for calculating accounts, but then he thought, "No, I've already failed in the past. The chief sat alone on the ground, the more he thought, the more he lost his mind. At that time, three people, Qibo, Feng Hou and Li Mu, went up the mountain to collect herbs, and found a few bunches of red Osmanthus seeds in the hands of Li Shou. He was sitting on the ground, staring blankly. Feng Hou asked Li Shou what he was thinking about. The head of the department turned his head to see that it was the three old ministers. He hurriedly stood up and told the three old ministers what he had been thinking about just now when he was keeping the accounts and counting the money. The Wind Empress was one of the founders of the Guide Car. After listening to the idea of the chief, he took over the chief's words and said, "I don't think we should use so many stone tablets in the future for bookkeeping and accounting. With only 100 stone tablets, you can top one hundred thousand eight hundred thousand numbers." The chief asked, "How?" The wind queen told the chief to pick all the red corn, and folded back under ten thin bamboo sticks, each stick on ten, a series of ten strings, and inserted on the ground. The wind queen said: "For example, today the hunting team returned 5 deer, you will push 5 red corn seeds upward from the bamboo sticks. Tomorrow, if you return 6 deer, you push 6 more upwards." The head of the clan said, "That won't do! There are only ten on a stick, and you have already pushed up 5, so if you want to push up 6 more, then there will be no more red osiers to push." The wind queen said, "I ask you, what is five plus six?" The head of the clan said, "Of course it's 11!" The Wind Queen said, "That's right! You should just move one place forward. From the number of balls, it looks like there are only two. It's actually a count of eleven. Then again, if the hunting party hands back nine deer, how do you keep track of the math? One more place forward; what is nine plus eleven? Twenty, of course. Looking at the number of balls on the bamboo stick; there are only two red osiers, which actually tops 20 numbers. That is to say, every enough ten numbers, every enough 100 numbers, one place forward. For example, if a hunting party returns 80 deer, how do you memorize the algorithm? 20 plus 80, the whole 100 numbers, and then one more digit, and the number of sticks becomes one red ossuary. Actually it tops 100 numbers." The head of the clan asked again, "After rounding, how can you remember!" Rimu went on to say, "That's good, after rounding, a mark should be scratched. For example, ten numbers are followed by a circle (10); 100 numbers are followed by two circles (100); 1,000 numbers are followed by three circles (1,000); 10,000 numbers are followed by four circles (10,000). This is called one, ten, one hundred, one thousand, and ten thousand. When the head of the class understood the reasoning behind the rounding, his confidence increased a hundredfold. He went home and made a big clay plate, picked up the white pearls from the turtle's stomach, and made eyes for each one. Every 10 a wear, wear into 100 number of "abacus". Then write the number of digits on the top; such as ten, hundred, thousand, ten thousand. From now on, remembering the number, accounting no longer need so many pieces of stone. Abacus, Chinese contemporary "computer" predecessor, 5000 years ago was born. As the times move forward, the abacus is constantly being improved, becoming today's "bead calculator". Especially in the folk, when not many people recognize words, but, as long as you know the basic principles of the abacus, and operating procedures, everyone will apply.

So, the abacus was soon widely spread and used in ancient China.

So, the abacus quickly spread and was widely used in ancient Chinese folklore.