Qin was born in Luxian County (now Fanxian County, Henan Province) and lived in his hometown since childhood. /kloc-was "the first soldier in the village" when he was 0/8 years old, and later moved to Beijing with his father. He is a very clever man, paying attention everywhere and studying tirelessly. When my father was a doctor and minister of industry, it was the time for him to study hard and accumulate knowledge.
The Ministry of Industry is in charge of construction, the Secretariat is in charge of books, and its subordinate institutions are Taishi Bureau. Therefore, he had the opportunity to read a lot of classics, visit experts in astronomical calendar and architecture, ask questions about astronomical calendar and civil engineering, and even get to know the construction situation in depth.
He once studied mathematics from a hermit. He also studied the poem of lovers by the famous poet Li Liu, and reached a higher level. Through this stage of study, Qin became an erudite young scholar. At that time, people said that he was "born extremely clever, learning everything from astrology, temperament and arithmetic to creation" and "knowing everything about games, balls, horses, bows and swords."
1225, Qin went to Tongchuan with his father and worked as a county captain for a period of time. A few years later, Li Liu invited him to the National History Museum of Southern Song Dynasty to inspect books and documents, but he didn't make it. In the third year of Duanping (1236), Yuan soldiers invaded Sichuan, and there were frequent wars in Jialing River basin, so Qin had to participate in military activities frequently. Later, he wrote in the preface of "Nine Chapters of Counting Books": "I am in trouble in the current situation and in trouble in the years. I didn't care about myself, but I was worried about danger. I wasted ten years and was exhausted. "This truly reflects this turbulent life. Due to the advance and defeat of Yuan soldiers, Tongchuan was difficult to be peaceful, so he went out of East Sichuan again, served as a judge (now Qichun, Hubei) and a garrison commander in Hezhou (now Hexian, Anhui), and finally settled in Huzhou (now Xing Wu, Zhejiang).
During Qin's tenure and national defense, he used his power to forcibly sell salt to the people for profit. After settling in Huzhou, the houses built were "extremely spacious" and "the houses were put on the market late to show off the beautiful scenery and orchestra". It is reported that he lives a luxurious life in Huzhou, "the expenses are not counted."
In the fourth year of Chunyou (1244), in August, Qin passed the sentence of Tongzhilang as Jiankang House (now Nanjing, Jiangsu), and left his job in November because of his mother's funeral and returned to Huzhou to observe filial piety. During this period, he devoted himself to the study of mathematics, and in September of the seventh year of Chunyou (1247), he completed the mathematical masterpiece Shu Shu Jiu Zhang. Because of his rich knowledge and achievements in astronomical calendar, he was summoned by the emperor to explain his views and presented a draft and a "mathematical outline" (that is, "counting books and nine chapters").
In the second year of Baoyu (1254), Qin returned to Jiankang, was appointed as the representative of the system along the river, and left his post soon. Later, he strongly attached to and bribed Jia Sidao, a powerful official of the dynasty. In the sixth year of Baoyu (1258), he was appointed as the secretariat of Qiongzhou, but he was dismissed three months later. Contemporary Liu Kezhuang said that Qin "arrived in the county (Qiongzhou) for only a hundred days, and the county people were tired of their greed and violence, and they sang a song of death and crying to get away quickly", but also said that he "went to the county for several months and came home with a lot of money". It seems that because of his insatiable greed in Qiongzhou, the people are extremely dissatisfied.
After Qin returned to Huzhou from Qiongzhou, he took refuge and was appreciated. They are closely related. Janice was appointed as the founder of Sinong Temple in the year of Kaiqingyuan (1259), and was appointed as Linjiang Army (now Qingjiang, Jiangxi) in the first year of Ding Jing (1260), but all of them were abandoned because of fierce opposition. During this period, Qin was keen on being an official and pursuing fame and fortune, and made no remarkable achievements in science. In the fierce struggle within the ruling group of the Southern Song Dynasty, Qin was dismissed from office and demoted, and Qin was also implicated. In the second year (126 1), Ding Jing was demoted as a local official of Meizhou and "continued to govern Meizhou", and died in his post soon.
Qin devoted himself to studying mathematics for many years and lived in mourning in Huzhou for three years. He wrote the world-famous mathematical book Nine Chapters of Mathematics, the sequel of Gui Xin's Miscellaneous Knowledge is called Mathematical Outline, and the Yongle Grand Ceremony is called Nine Chapters of Mathematics. The book has nine chapters and eighteen volumes, including nine categories: Dayan, Shi Tian, Tianjing, Prospecting, Forwarding, Grain, Architecture, Military and Municipal Objects. 9 questions in each category (9 questions) * * 865438. Many calculation methods and empirical constants still have high reference value and practical significance until now, and are known as "calculation classics". The writing style of this book is mostly composed of four parts: question, answer, skill and scolding: "question" is to ask questions from real life; "Answer", give the answer; "Shu Yue", explaining the principle and steps of solving problems; Cao Yue gives a detailed process of solving problems. This book is recognized as a world-famous mathematical work in the history of science at home and abroad. This book not only represents the advanced level of mathematics in China at that time, but also marks the highest level of mathematics in the Middle Ages.
Liang Zongju, a Chinese historian of mathematics, commented: "Qin's Book of Nine Chapters (1247) is an epoch-making masterpiece with rich content and superb level. In particular, the technique of solving by the method of large derivative (the only indefinite equation solution in China) and the numerical solution of higher algebraic equations occupy a lofty position in the history of mathematics in the world. At that time, the long night in Europe was not over yet, but the creation of China people shone like the rising sun in the east. "
Qin's "Great Development and Skills" was 554 years earlier than Gauss's, and he was called "the luckiest genius" by Cantor.
Qin invented the method of "large extension", that is, the first congruence group solution in modern number theory, which is the highest achievement of medieval mathematics. It is 554 years earlier than the congruence theory established by the famous western mathematician Gauss (180 1), and it is called "China remainder theorem" by the west. Qin not only won great honor for China, but also made outstanding contributions to world mathematics.
In "Nine Chapters", Qin not only created the positive and negative balance method, that is, the numerical solution of arbitrary high-order equations, which was also the highest achievement of medieval mathematics. Qin's achievement in this invention is better than Horner's (181837) achievement in 2009. Qin's positive and negative balance method puts forward the principle that "quotient is always positive, real is often negative, from positive to negative, and profit is often negative", and gives a unified operation rule by pure algebraic addition, which is extended to any high-order equation.
In addition, Qin also improved the solution of linear equations, using mutual multiplication and subtraction to eliminate, which is completely consistent with the current addition and subtraction elimination method; At the same time, Qin gave a rough calculation formula, which can be extended to the solution of general linear equations. In Europe, it was first given by prerre bourdaud in 1559 (about 1490 ~ 1570, France). He began to solve equations with incomplete addition, subtraction and elimination methods, which was 3 12 years later than Qin, and was not as complete as Qin in theory.
Qin also initiated the "triclinic quadrature technique" and gave a formula for calculating the area of three sides of a known triangle, which was completely consistent with Helen's formula (about 50 AD). Qin also gave some empirical constants, such as "the three strong points are divided into four soils and five five, the millet rate is fifty, and the wall method is half", which is still of practical significance even now. Qin also gave a clever combination of the mixed proposition of distribution ratio and chain ratio in question 77 of volume 18 of Deduction and Reciprocity.
Qin's philosophy and mathematics thought have obvious consistency with Taoism and Confucianism in Song Dynasty. He clearly pointed out that "number and Tao are not two books", and his personal experience in mathematics practice made him have a clearer understanding of the importance of mathematics. He said that mathematical research is "big enough to understand the gods and follow life; If you are small, you can handle the affairs of the world. Like everything, you can look at it from a very shallow distance! " However, he also admitted that his understanding of "knowing God's will" was not profound, so he focused on finding mathematical problems in astronomical calendars, production and life, business and trade, and military activities, trying to meet the needs of social practice and warning people to learn mathematics well and be good at calculation, so as to avoid "financial damage" and other adverse consequences due to calculation errors. To this end, he worked hard and wrote a mathematical masterpiece of more than 200,000 words. His thoughts and practices are commendable and should be fully affirmed.
Qin is a mathematician who pays equal attention to theory and practice and is good at inheritance and innovation. His method of seeking greatness and broadening, positive and negative cholesky decomposition and his masterpiece "Shu Shu Jiu Zhang" are a dazzling page in the history of Chinese mathematics, which has a wide influence on the development of mathematics in later generations. Sutton (1884 ~ 1956), a famous American historian of science, said that Qin was "one of the greatest mathematicians in his country, his time and even all times".
Qin's China's remainder theorem comes from a story in folklore-"Han Xin ordered soldiers". At the end of Qin Dynasty, Chu and Han contended. Han Xin was once at war with Li Feng, the general of Chu State 1500 soldiers.
The Chu army was defeated and retreated back to camp. The Han army also killed and injured 400 people, so Han Xin reorganized the military forces and returned to the base camp. When we were on a hillside, a rear unit reported that Chu cavalry were chasing us. I saw the dust flying in the distance and the sound of ShaSheng was deafening. The Han army was very tired, and then the team was in an uproar. Han Xin's military forces reached the top of the slope and saw that the enemy was less than 500. They quickly ordered the troops to meet them. He ordered three soldiers in a row and ended up with two more; Then he ordered the soldiers to line up five times, and as a result, there were three more; He ordered a platoon of seven soldiers, only to get two more. Han Xin immediately announced to the soldiers: Our army 1073 Warriors, with less than 500 enemy troops. If we are condescending, we will surely defeat the enemy in numbers. The Han army believed in its commander-in-chief, and now believed that Han Xin was a "fairy" and a "SJ". So morale is greatly boosted. At that time, flags shook, drums roared, the Han army advanced step by step, and the Chu army was in a mess. Shortly after the battle, the Chu army was defeated and fled.
First, find the least common multiple of 3,5,7, 105 (note: because 3,5,7 are pairwise coprime integers, the least common multiple is the product of these numbers), multiply it by 10, and then add 23 to get 1073 (person).
In Sun Tzu's Art of War more than a thousand years ago, there was such an arithmetic problem: "Today's events are unknown, and the number of three and three leaves two, the number of five and five leaves three, and the number of seven and seven leaves two. What is the geometry of things? " According to today's words: divide a number by 3 and 2, by 5 and 3, by 7 and 2, and find this number.
This kind of problem is also called "Han Xin points soldiers". A kind of problem is formed, that is, the solution congruence in elementary number theory. The conditional solution of this kind of problem is called "China's Remainder Theorem", which was first put forward by Qin.
① There is a number, divided by 3 and 2, divided by 4 and 1. What is this number divided by 12?
Solution: The number of 2 divided by 3 is: 2, 5, 8, 1 1, 14, 17, 20, 23. ...
The remainder when they are divided by 12 is: 2, 5, 8, 1 1, 2, 5, 8, 1 1 ...
Divided by 4, 1 is: 1, 5,9, 13,17,21,25,29. ...
The remainder when they are divided by 12 is: 1, 5,9, 1, 5,9. ...
The remainder of a number divided by 12 is unique. There are only 5 and * * * in the remainder of the above two lines, so the remainder of this number divided by 12 is 5.
If you change the problem of ①, you will not find the remainder divided by 12, but this number. Obviously, there are many qualified figures. It is an integer of 5+ 12, and the integer can take 0, 1, 2 ... endlessly. In fact, after we find out 5 first, we notice that 12 is the least common multiple of 3 and 4, plus the integer multiple of 12, all numbers meet the conditions. In this way, the two conditions of "divide by 3 and 2, divide by 4 and 1" are merged into one condition of "divide by 12 and 5". There are three conditions for the question raised in Sun Tzu's calculation. We can combine the two conditions into one first. Then merge with the third condition to find the answer.
② Divide a number by 3 and 2, by 5 and 3, and by 7 and 2 to find the minimum number that meets the conditions.
Answer: List the remaining 2: 2, 5, 8, 1 1, 14, 17, 20, 23, 26 divided by 3. ...
List the remaining 3: 3, 8, 13, 18, 23, 28 after division by 5. ...
In these two columns, the first common number is 8? The least common multiple of 3 and 5 is 15. These two conditions are combined into an integer 8+ 15. List the numbers of this string as 8, 23, 38 ... and then list this number divided by 7 and 2, 2, 9, 16, 23, 30. ...
The minimum number to meet the requirements of the topic is 23.
In fact, we have combined the three conditions in the title into one: divided by 105 plus 23. Then Han Xindian's soldiers are between 1000 and 1500, which should be 1050+23= 1073.
Qin's main achievement in mathematics is to systematically sum up and develop the numerical solution of higher-order equations and the first congruence group solution, and put forward quite complete "extraction of positive and negative squares" and "seeking one skill by taking great derivative", which reached the highest level of mathematics in the world at that time.