Today, people will disdain such a trivial matter as counting from 1 to 1. However, thousands of years ago, this matter made people take great pains. Before 7, years ago, they couldn't even count more than two. If they were asked how many four wild animals they caught, they would answer, "Many". If anyone could count to 1 at that time, it would be considered an outstanding genius. Later, people will slowly associate numbers with their hands. Take one thing in each hand, which is 2. When I counted to three, I was stumped again, so I put the third thing at my feet and the "problem" was solved.
in this way, the ancestors of the Chinese nation came out of the chaotic world through gradual exploration.
First, tying a rope to count numbers, and then it developed into "calligraphy". Five or six thousand years ago, people could write numbers from 1 to 3. By the Spring and Autumn Period more than 2, years ago, ancestors could not only write more than 3, mathematics, but also had the consciousness of addition and multiplication. In Jin Wenzhou <: Ding > There is such a passage in the book: "The East Palace says: ※ Pay 1 grain, and leave 1 grain as a grain. If you pay for it next year, you will pay it." This passage contains a question of rolling interest. It is said that if you borrow 1 bundles of millet and return them later, it will be changed from 1 bundles when you borrow them to 2 bundles. If it is returned every other year, it will have to be increased from 1 bundles borrowed to 4 bundles. Expressed by the mathematical formula:
1+1=2
2×2=4
In addition to great progress in counting and algorithm, the ancestors of the Chinese nation began to record some digital knowledge in books. One of the classical books revised by Confucius in the Spring and Autumn Period (551-479 BC) <: Zhouyi > In the middle, there was gossip. This magical gossip is still the research object of people in China and abroad, and it plays an important role in mathematics, astronomy, physics and so on.
by the warring States period, mathematical knowledge had far exceeded the level of 1~3. At this stage, they began to cultivate and sow in arithmetic, geometry and even in the field of modern applied mathematics. In the field of arithmetic, the four arithmetic operations were established during this period, and the formula in multiplication was already in <: Tube > 、< Xunzi > 、< Zhou Yishu >; And other works appear sporadically, and score calculation has also been applied to planting land and distributing food. In the field of geometry, Pythagorean theorem appeared. In the field of algebra, the concept of negative number has sprouted. What surprised future generations most was that during this period, the bud of "game theory" appeared, which is a problem in the field of modern applied mathematics. It is a branch of operational research, which mainly uses mathematical methods to study whether two parties with conflicts of interest have their own optimal strategies to win the other party in competitive activities and how to find out these strategies. This branch of mathematics was formed as a discipline during or after the Second World War in this century, but as early as more than 2, years ago, Sun Bin, a famous strategist in the Warring States Period (36-33 BC), put forward the problem of "fighting equestrian", and the content of this problem reflects the mathematical thought of striving for overall optimization in game theory. The problem of "fighting equestrian" is that Qi Weiwang wants to compete with the general Tian Ji, and each of them has an upper, middle and lower horse. The three horses in Tian Ji are slightly inferior to those in Qi Weiwang. If the corresponding contest method of the same level is used, Tian Ji will undoubtedly lose, and Tian Ji is so anxious that he doesn't know what to do. At this time, Sun Bin nudged from the side, and Tian Ji used Sun Bin's method to win Qi Weiwang 2-1.
what method did Sun Bin use? Please take a look at the following schematic diagram:
Tian Ji Qi Weiwang
inferior horse superior horse
superior horse moderate horse
moderate horse inferior horse
Don't you think our ancestors were really smart when they saw this?
when history advanced to the Qin and Han dynasties, ancestors stopped carving words on bones. They write everything they need to remember on bamboo chips and wood chips with a brush. This kind of written bamboo and wood chips is called "Jane" or "Xie". This kind of bamboo slips or slips was handed down most in the Western Han Dynasty.
From those Han bamboo slips, we found that the number of examples of multiplication and division in arithmetic increased obviously in Qin and Han dynasties, and there were also multi-step multiplication and division methods and the middle formula of the 99-99 multiplication method. In geometry, I have a good knowledge of the calculation of rectangular area and volume.
the most noteworthy things in this period are the calculation and decimal system. With them, ancestors will no longer worry about the lack of suitable means of calculation. In ancient China, until the Tang Dynasty, this set of computing system was used all the time.
The exact origin time of calculation and preparation is still unclear, except that the system of calculation and preparation was formed around the Qin and Han Dynasties.
to understand what financing is all about, you must first know what financing is. Chips are small sticks with a diameter of 1 minute and a length of 6 minutes. The materials of these sticks are bamboo, wood, bone, iron and copper. Their functions are similar to abacus beads. At present, many batches of raised objects have been unearthed. In 1971, it was found in a rectangular male-female tomb unearthed in Qianyang County, Shaanxi Province that the man's body was tied with a silk belt bag in the crotch, which contained a bone raised. A batch of early bone chips unearthed in the southern suburbs of Shijiazhuang in 198 were also hung on the waist of the deceased. From the quotation, it can be seen that calculation and financing have been universal among intellectuals in Han Dynasty. As for how to use the chips, according to the records, it is like this: when calculating, put the chips on a special case or put them casually. For numbers below 5, put a few chips, while for the four numbers from 6 to 9, you need to use a horizontal or vertical chip as 5, and the rest of the numbers are still put a few chips.
for the convenience of calculation, the ancients stipulated the vertical and horizontal representation. Vertical representation is used for single, hundred and ten thousand digits; Horizontal representation is used for ten or thousand digits, and when zero is encountered, one digit is empty.
Decimal system is exactly what we commonly use in our daily life today. That is to say, for positive integers or positive decimals, based on ten, every ten goes into one, every hundred goes into two, every thousand goes into three and so on. The emergence of decimal system has created good conditions for the development of four operations.
Development and Prosperity Period
Editor
The development and prosperity period of mathematics in China was from the end of the Western Han Dynasty to the middle of the Sui Dynasty. This is the first peak of China's mathematical theory. The symbol of this peak is the mathematical monograph <: Chapter 9 Arithmetic > The birth of. There are at least 18 years of Nine Chapters of Arithmetic. Who is its author? Who compiled it? So far, there is no research. Historians only know that it is the crystallization of mathematical knowledge in China during the Qin and Han Dynasties, and it began to spread and use in the 1st century.
This book is divided into nine chapters:
① Square field (algorithm of four fractions and method of finding area by plane shape).
② Millet (calculation method of grain trade).
③ Decay (calculation method of distribution ratio).
④ Less-extensive (square root and open method)
⑤ quotient work (solid volume method)
⑤ average loss (calculation method for managing the even burden of grain transportation).
⑦ surplus and deficiency (the solution of profit and loss problems also involves other types of problems that can be handled by this solution).
⑧ equation (linear equation group solution and positive and negative operation).
⑨ pythagorean (the application of pythagorean theorem and the solution of simple measurement problems).
The book contains 246 mathematical application problems, each of which is divided into question, answer and technique (solution). Some have one topic and one skill, and some have three parts, and the content of each chapter is closely related to social production.
The birth of this book not only shows that a complete mathematical system has been formed in ancient China, but also it is difficult to find another mathematical monograph with comparable performance in the world at that time.
at the peak of the development of this mathematical theory, in addition to the masterpiece Nine Chapters Arithmetic, Liu Hui's Nine Chapters Arithmetic and his < Island calculation classics > 、< Sun Tzu's calculations > (The author is unknown), <; Xiahou Yang's Calculation Classics > 、< Zhang Qiu's Calculations > And Zu Chongzhi's < Composing > Mathematics monograph, etc.
During this period, the outstanding figures who made new achievements in mathematics were Zhao Shuang from Three Kingdoms, Liu Hui from Wei Jin and Zu Chongzhi from Southern Dynasties.
heyday
Editor
The heyday of China's mathematics was from the middle Sui Dynasty to the late Yuan Dynasty.
the scientific development of any country can not be separated from a clean and enlightened social environment and a solid economic foundation. From the middle of Sui Dynasty to the end of Yuan Dynasty, because the rulers summed up the lessons from the overthrow of dynasties and adopted a series of enlightened policies, the economy developed rapidly and science and technology were greatly improved, and mathematics, as a part of science and technology, also entered its heyday at this time.
during this period, the regularization of mathematics education and the emergence of mathematics talents are the most important characteristics.
Before Sui Dynasty, education in schools did not attach importance to mathematics, so there was no mathematics major. In the Sui Dynasty, this situation was broken, and in the school equivalent to a university, the major of arithmetic began to be set up. In the Tang Dynasty, imperial academy, the highest institution of learning, also set up a mathematical museum, in which doctors and teaching assistants were readily available to train mathematical talents. At this time, the importance of mathematics education is also reflected in the issue of selecting officials. According to ancient books <: History of Tang Que >; According to records, there is such a story: there was a great official in the Tang Dynasty, whose name was Yang Shang. He asked his staff to recommend an excellent clerk for promotion. After a thousand selections, when there are two people left, I can't decide which one to remove. Because these two clerks have the same conditions in all aspects: the same position, the same "length of service" and similar comments ... Who should I choose? I have no choice but to hand in the contradiction. After learning the news, Yang Yang also spent a lot of time and thought about it again and again, and finally decided to test them with a math problem. He said to the two candidates, "As clerks, your career determines that you should have the ability to calculate quickly. If I give a question, whoever answers it correctly first will be promoted." Later, the person who got the right answer first was naturally promoted, and the other person returned to his original position with conviction. This shows that the Tang Dynasty attached importance to mathematics.
with the math major. Good teaching materials are indispensable. During this period, there was Li Chunfeng (? ~ AD 714) and others were ordered by the government, and after studying and screening, they stipulated the special textbook for imperial academy Computer Museum. This textbook is called <: Ten books of calculating classics > , a full set of * * * ten: <; Zhou Kuaisuanjing > , "Nine Chapters of Calculations > 、< Sun Tzu's calculations > 、< Five Cao suan Jing > 、< Xiahou Yang's Calculation Classics > 、< Zhang Qiu's Calculations > 、< Island calculation classics > 、< Five classics arithmetic > 、< Composing > And <: Ancient calculation classics > .
For this set of professional textbooks, imperial academy has also stipulated the study period and established a system of one exam per month. Since then, mathematics education has gradually improved.
Under the increasingly perfect mathematical education system, a generation of famous mathematical masters have emerged, namely: Wang Xiaotong, Liu Zhuo, Yi Tuan, Shen Kuo, Li Ye, Jia Xian, Yang Hui, Qin Jiushao, Guo Shoujing, Zhu Shijie ...
Science has always been the wealth of all mankind, and the mathematical level of China at that time quickly attracted North Korea and. After a period of study, knowledge about field, rent and grain exchange is introduced into the algorithm. Imperial academy's curriculum and examination system have been absorbed in running a school. From this point of view, at this stage, China has been at the forefront of the development of mathematics in the world.
Slow development period
Editor
Next, from the late Yuan Dynasty to the middle Qing Dynasty, the development of mathematics in China was slow, which was almost eclipsed by the flourishing period of mathematics mentioned above.
from the end of the song dynasty to the establishment of centralized system in the yuan dynasty, the land of China was ravaged for years, science and technology were ignored, and a large number of valuable mathematical heritages suffered losses.
after the establishment of the Ming dynasty, production developed for a short time, but it immediately declined due to the corruption of feudal rule, and it was not until the early years of the Qing dynasty that it was relieved.
In such an environment of political corruption, economic backwardness and peasant uprisings, it is reasonable for mathematics to fall into the trough.
However, the trend of world development has always waited for no one. Taking advantage of the decline of China's mathematics, western mathematics has quietly caught up and infiltrated into China in turn.
When western capitalism began to sprout, Catholic missionaries, pirates and businessmen flocked to China in order to seek development. In addition to taking away raw materials, markets and cheap labor from China, they also brought some cultural knowledge.
among the missionaries who came to China from 16th century to 18th century, Matteo Ricci (1552-161), an Italian, had the greatest influence. From 1583 to 1599, when he was living in Zhaoqing, Shaozhou, Nanchang and Nanjing, China, he met many famous scholars in China, such as Li Zhi, Xu Guangqi and Li Zhizao. These people are in a state of mind that they are dissatisfied with empty talk about Neo-Confucianism and eager to enrich Qiang Bing. Therefore, they are eager for the latest scientific and technological achievements in the world. The arrival of Matteo Ricci undoubtedly played a hit-it-off role.
Matteo Ricci, Xu Guangqi and Li Zhizao respectively translated two mathematical works: <; Geometric elements > 、< Homonym refers to > .
Among them, The Elements of Geometry is popular with few omissions. Although there was no ready-made China vocabulary in the original Latin at that time, Xu Guangqi overcame difficulties and created many appropriate translations, which made the book reach the level of faithfulness, expressiveness and elegance.
Since Matteo Ricci and China scholars jointly translated monographs, the spread of western learning to the East has gained momentum.
So what is China's own "specialty" of mathematics in this period? It's abacus
During the Sui and Tang Dynasties, people began to make plans for improvement. They try to simplify the calculation method and make up the formula ... However, in the rapidly developing field of mathematics, the calculation algorithm will inevitably be replaced by other algorithms.
at the end of the yuan dynasty, a small and handy abacus appeared. People are overjoyed at this new tool, which is simple in calculation and easy to carry. Some people even put it into proverbs, poems and lyrics.
The appearance of abacus soon led to books on abacus formula and abacus algorithm. In the 16th and 17th centuries, among a large number of books on abacus calculation in China, the most famous one was Cheng Dawei's "Directing the Arithmetic to Unify Zong". After the popularity of abacus calculation, the calculation disappeared automatically.
Not long after China invented abacus, in 1642, 19-year-old French mathematician Pascal (AD 1623-1662) introduced the world's earliest computer. At present, although the world has entered the computer age, abacus still has its place. It has been tried that it is even faster than a small calculator in addition and subtraction operations.
the confluence of Chinese and western mathematics
Editor
When the development of mathematics in China was slow, western mathematics had made great strides ahead, so there was a confluence of Chinese and western mathematics development in the history of mathematics development in China, which was about 184-1911.
As mentioned earlier, around the 16th century, western missionaries brought some new mathematical knowledge. Despite