Around the Song and Yuan Dynasties, abacus beads became popular. At the end of the Yuan Dynasty, there was a book called "The Record of Dropping out of Farming in Nancun Village", which recorded a saying in the south of the Yangtze River that new slaves were like "balls" and did not dial automatically; After a while, it looks like an abacus bead. You can dial it. Finally, like a "fixed bead", it can't be dialed. There has been a metaphor of "abacus beads" in the saying that pearl abacus has been used in Jiangnan area for a period of time and has been popularized to a certain extent. But at that time, calculation was not abolished, and calculation and abacus were used at the same time.
The popularization of abacus and the final elimination of abacus were completed in the Ming Dynasty. At that time, due to the development of practical mathematics and business mathematics, simple and fast calculation was urgently needed, which provided an opportunity for abacus, a calculation tool, to show its talents. In addition, the traditional calculation method has been gradually simplified since the Tang and Song Dynasties, forming a set of operational formulas. These formulas use few words, but their meanings are complete. When calculating with a formula, the result is often worked out in your mind as soon as you read the formula, but the formula in your hand is still slowly being sorted out, which leads to the contradiction of whether your hand can answer it or not. Comparatively speaking, the speed of manually moving abacus beads is much faster than that of arranging abacus beads, and abacus beads have the advantage of "randomly dialing beads to get answers". Therefore, abacus was once popular in the world, and soon replaced abacus in all aspects, and finally was sent to the history museum. The abacus calculation in Ming Dynasty is exactly the same as that in modern times. For example, 1578, Ke Shangyou's book "General Trajectory of Mathematics" once drew a "abacus schema". This is a thirteen-file abacus diagram, with two beads on top and five beads on the bottom, separated by a wooden beam, which is exactly the same as the current abacus. This kind of abacus is slightly different from the abacus that was popular in Japan later. The popular abacus in Japan only puts an abacus bead on the beam. There are two calculation beads on the beam. On the one hand, it is convenient to suspend the calculation temporarily, and on the other hand, it is convenient to add and subtract the old weight (1 kg = 16). Therefore, in practical calculation, it is more convenient to place only one calculation bead on the beam.
As for the calculation formula of abacus in Ming dynasty, it is also roughly the same as today's abacus formula.
For example, the formula for addition is:
"One-on-one, five divided by four, nine into ten.
Two up, two down, five divided by three, two back 80%.
..................................................................................................................................................................................
The subtraction formula is:
"Once, once ten plus nine, once four plus five.
Two returns two, two returns ten returns eight, two returns three returns five.
............ "and so on.
The multiplication formula is the "99 formula", such as "99 81, 89 72", and so on. The division formula follows the formula of "nine returns" compiled in the Yuan Dynasty, such as "two plus five, every two gets ten, 3131" and so on. These songs are quite perfect and easy to use, and they are still in use until now.
Because abacus was very popular in Ming Dynasty, many books about abacus were published at that time. Among them, Cheng Dawei's algorithm unified team has the greatest influence and the widest spread. Cheng Dawei was one of the most important mathematicians in Ming Dynasty. He read widely since he was a child, and after he was twenty, he did business in the middle and lower reaches of the Yangtze River, while constantly studying mathematics. He visited famous teachers all over the world and extensively searched for computational classics. After years of accumulation and compilation, he finally finished his masterpiece "Arithmetic Unity" at the age of 60. After the book was published, it quickly became popular in China and spread to Japan. At that time, almost everyone who studied algorithms had one. Until the end of the Qing Dynasty, abacus books published in various places were either manuscripts or adaptations, which were widely circulated for a long time and were rare in the history of Chinese mathematics.
Since the15th century, China's abacus calculation has gradually spread to Japan, Korea, Vietnam, Thailand and other places, which has had an important impact on the development of mathematics in these countries. Later, it was spread to the west by some European business travelers. Now, the academic circles all over the world agree that the abacus was invented by China and China is the hometown of the abacus. Moreover, today, when the world has entered the era of electronic computers, abacus is still a widely used computing tool in the world. Even in highly modernized countries, such as the United States and Japan, more and more people are learning to use abacus. The United States, Britain, France and other countries have incorporated abacus into the primary school curriculum. The United States has also sent people to Japan to study abacus, and the number of people who should take the abacus technical level certificate is increasing every year. As Araki Schoenberg, president of the Japan Abacus Education Union, said, "Abacus, which was born in China and spread to Asian countries, is becoming popular all over the world through the cooperation of experts from Japan and China.