Liu Hui (a famous mathematician in ancient times) has a complete and detailed data collection.

Liu Hui (about 225-295), a native of Zouping, Binzhou, Shandong Province, was a great mathematician in Wei and Jin Dynasties and one of the founders of China's classical mathematical theory. He is a very great mathematician in the history of Chinese mathematics. His representative works "Nine Arithmetic Notes" and "Arithmetic on the Island" are China's most precious mathematical heritage. Liu Hui has quick thinking and flexible methods. He advocates reasoning and intuition. He was the first person in China who explicitly advocated using logical reasoning to demonstrate mathematical propositions. Liu Hui's life is a life of hard exploration of mathematics. Although his position is low, his personality is noble. He is not a mediocre man who seeks fame and fame, but a great man who never tires of learning. He left us a valuable fortune.

Basic Introduction Chinese Name: Liu Hui Nationality: China Nationality: Birthplace of Han Nationality: Zouping, Shandong Province? Date of birth: ca. 225 AD Date of death: ca. 295 AD Occupation: Mathematician's main achievement: Cleaning up the ancient mathematical system in China.

This paper puts forward some representative works, such as Harmonious Housing Reform, The Skill of Double Difference, Nine Chapters of Arithmetic Notes, Calculation on the Island, Personal Achievements, Representative Works, Historical Records and Tales of People. Nine Chapters of Arithmetic was written in the early Eastern Han Dynasty, with a total of 246 solutions. In solving simultaneous equations, calculating four fractions, calculating positive and negative numbers, calculating the volume and area of geometric figures and many other aspects, it is among the advanced in the world. Cao Wei Zhenguan four years, Liu Hui notes "Nine Chapters Arithmetic". However, due to the primitive solution and the lack of necessary proof, Liu Hui made supplementary proof. In these proofs, his creative contributions in many aspects are shown. He was the first person in the world to put forward the concept of decimal, and used decimal to represent the cube root of irrational numbers. In algebra, he correctly put forward the concept of positive and negative numbers and the principle of addition and subtraction, and improved the solution of linear equations. In geometry, "secant" is put forward, that is, the method of finding the area and perimeter of a circle by using inscribed or circumscribed regular polygons to exhaust the circumference. He scientifically obtained the result that pi = 3. 14 16 by using secant technology. He cut a circle from a circle with a diameter of 2 feet by connecting a regular hexagon, and then he got a regular hexagon 12 and a regular hexagon 24 ... The thinner he cut, the smaller the difference between the area of a regular polygon and the area of a circle. In his original words, it is "cut carefully, and the loss is not big. If you cut again, there will be no loss." He calculated the area of 3072 polygons and verified this value. The scientific method of calculating pi put forward by Liu Hui has established China's leading position in the world for more than 1000 years. Liu Hui has made great contributions to mathematics, and put forward the idea of "seeking the number of emblems" among endless problems. This method is consistent with the later method of finding the approximate value of irrational roots. It is not only a necessary condition for accurate calculation of pi, but also promotes the generation of decimals. In the solution of linear equations, he created a simpler method of mutual multiplication and elimination than direct division, which is basically consistent with the current solution; And put forward the problem of indefinite equation for the first time in the history of Chinese mathematics; He also established the summation formula of arithmetic progression's first n terms; Many mathematical concepts are put forward and defined, such as power (area); Equation (linear equation); Positive and negative numbers and so on. Liu Hui also put forward many recognized correct judgments as the premise of proof. Most of his reasoning and proof are logical and rigorous, so he bases the nine-chapter arithmetic and his own solutions and formulas on inevitability. Although Liu Hui didn't write his own works, the mathematical knowledge he used in Nine Chapters Arithmetic has actually formed a unique theoretical system, including concepts and judgments, with mathematical proof as the link. Liu Hui put forward in "Circular Excision" that "cut carefully, lose less, cut hard, can't cut off, and be in tune with the circle without losing", which is a masterpiece of China's ancient limit concept. In the book Island Calculation, Liu Hui carefully selected nine survey questions. The creativity, complexity and representativeness of these topics attracted the attention of the west at that time. Liu Hui has quick thinking and flexible methods. He advocates reasoning and intuition. He was the first person in China who explicitly advocated using logical reasoning to demonstrate mathematical propositions. Personal Achievements Liu Hui's mathematical achievements can be roughly divided into two aspects: one is to sort out China's ancient mathematical system and lay its theoretical foundation, which is embodied in Nine Chapters of Arithmetic Notes. In fact, it has formed a relatively complete theoretical system: number system theory ① expounds the general division, reduction, four operations and simplification rules of complex fractions of the same number and different number; In the annotation of prescription, he discussed the existence of irrational roots from the infinite meaning of prescription, introduced new numbers, and created a method of infinitely approaching irrational roots with decimals. (2) In calculus theory, he first gave a clear definition of rate, and based on three basic operations of multiplication and division, he established a unified theoretical basis for the operation of numbers and formulas. He also defined the "equation" in China's ancient mathematics by rate, that is, the augmented matrix of linear equations in modern mathematics. Liu Hui comments ③ In Pythagorean theory, the Pythagorean theorem and the calculation principle of Pythagorean solution are demonstrated one by one, the theory of similar Pythagorean form is established, and Pythagorean measurement is developed. Through the analysis of typical figures such as "transverse to the hook" and "straight to the stock", a similar theory with China characteristics is formed. The theory of area and volume puts forward Liu Hui's principle by using the principle of complement, the deficiency of complement and the limit method of "cyclotomy", which solves the problem of calculating the area and volume of various geometric shapes and geometries. The theoretical value of these aspects is still shining. Second, on the basis of inheritance, put forward your own ideas. This aspect is mainly reflected in the following representative innovations: ① Circumcision and Pi he wrote in Nine Chapters of Arithmetic? In the annotation of roundness field, the exact formula of circle area is proved by secant technique, and the scientific method of calculating pi is given. He first cuts a circle from the hexagon inscribed in the circle, and every time the number of sides is doubled, he calculates the area of 192 polygon, π= 157/50=3. 14, and then calculates the area of 3072 polygon, π = 3927/1. (2) Liu Hui's principle in Nine Chapters of Arithmetic? Yang Equestrian Notes, when he solved the volume of cone by infinite division, he put forward Liu Hui's principle of calculating the volume of polyhedron. Mouhe Square Cover said that in the annotation of Nine Chapters of Arithmetic Circle Opening, he pointed out the inaccuracy of the formula V=9D3/ 16(D is the diameter of the ball) and introduced the famous geometric model Mouhe Square Cover. "Mouhe Square Cover" refers to the intersection of inscribed cylinders with two perpendicular axes. In the annotation of "Nine Chapters of Arithmetic Equation Skills", he proposed a new method to understand linear equations, and applied the idea of ratio algorithm. He put forward the gravity difference technique in the book Calculation of Island, and used the methods of weight table, cable connection and accumulated torque to measure the height and distance. He also developed gravity difference technology from two observations to three observations and four observations by analogy. In the 7th century, India and Europe only began to study the problem of two observations in15 ~16th century. Liu Hui's work not only had a far-reaching impact on the development of ancient mathematics in China, but also laid a lofty historical position in the history of mathematics in the world. In view of Liu Hui's great contribution, many books call him "Newton in the history of Chinese mathematics". The representative work introduces his representative work "Notes on Nine Chapters Arithmetic", which is an annotation to the book "Nine Chapters Arithmetic". Nine Chapters Arithmetic is one of the oldest mathematical monographs in China, which was written in the Western Han Dynasty. The completion of this book has gone through a historical process. Some of the mathematical problems collected in the book were handed down in the pre-Qin period, and were edited by many people for a long time, and finally sorted out by mathematicians in the Western Han Dynasty. The content of the final version circulated today was formed before the Eastern Han Dynasty. Nine Chapters Arithmetic is China's most important classic mathematical work. Its completion laid the foundation for the development of ancient mathematics in China and played an extremely important role in the history of Chinese mathematics. The current edition of "Nine Chapters Arithmetic" contains 246 applied problems and answers to various questions, which belong to Tian Fang, Su Mi, Descent, Shao Guang, Shanggong, Average Loss, Profit and Loss, Equation and Pythagoras. The appearance of nine chapters arithmetic is the result of social development and long-term accumulation of mathematical knowledge, which brings together the labor achievements of mathematicians in different periods. Liu Hui, a mathematician in the Three Kingdoms period, said: "Duke Zhou used the nine-number system, and nine chapters were enough. Zhang Cang, Hou Peiping of Han Dynasty, Cheng Gengshouchang and the old farmer are all good fortune tellers. Cang et al. are called deletion and supplement because of the remnants of old texts. Therefore, the purpose of the school is different from the ancient or different, and the theory is closer. " According to Liu Hui's research results, Nine Chapters Arithmetic originated from Nine Numbers in Duke Zhou. The Nine Chapters Arithmetic he saw was edited by Zhang Cang and Geng Shouchang in the Western Han Dynasty on the basis of inheriting the legacy of the pre-Qin Dynasty, which contained a lot of supplementary contents in the Western Han Dynasty. According to historical documents and unearthed cultural relics, what Liu Hui said is credible. All kinds of algorithms contained in Nine Chapters Arithmetic were supplemented and revised to meet the needs of the time on the basis of mathematics handed down by mathematicians in the pre-Qin and Han Dynasties. According to Liu Hui's textual research, Zhang Cang and Geng Shouchang are both major mathematicians involved in the revision. According to Records of the Historian Biography of Prime Minister Zhang Lie, Zhang Cang (about 250 BC-0/52 BC) experienced the Qin Dynasty and the Han Dynasty. In the sixth year of Emperor Gaudi (2065438 BC+0 BC), he was named Emperor Peiping for his meritorious service in attacking Tibetan tea. "Since the history of Qin Wei, the book tomorrow. And make good use of the arithmetic calendar. " He also "wrote 18 books to explain the law of yin and yang." Geng Shouchang's date of birth is unknown. When Emperor Gaozu Xuan Di became an official, he became a senior farmer, and he was favored by the emperor (see Record of Eating Goods in Hanshu). He advocated the theory of Huntian in astronomy, and in the second year of Ganlu (the first 52 years), he played "To spend the moon with a round instrument and measure the astronomical phenomena" (see the Book of the Later Han Dynasty). Zhang Cang and Geng Shouchang are both famous mathematicians and hold high positions. Naturally, they will preside over the revision of arithmetic handed down from the pre-Qin period. According to Liu Hui's records, his annotation Nine Chapters Arithmetic was finally edited by Geng Shouchang. We believe that the time when Geng Shouchang edited Nine Chapters of Arithmetic can be set as the time when this book was completed. The influence of works Nine Chapters Arithmetic is an official mathematics textbook compiled by the state, which has a great influence on the development of mathematics in Han Dynasty. There are four chapters in Guang Yun, namely Nine Chapters of Shu, which were practiced by Xu Shang, Du Zhi, Wu and RoyceWong in the Han Dynasty. In the Biography of Ma Yuan in the later Han Dynasty (about 70 ~ 14 1), it is recorded as "knowledgeable and versatile, good at nine chapters of arithmetic". In addition, Zheng Xuan (127 ~ 200), Liu Hong and others recorded the Nine Chapters of Arithmetic. It can be seen that this book was an important teaching material for learning mathematics at that time. The inscription on a bronze plate in the second year of Guanghe in the Eastern Han Dynasty (179) stipulates: "Big Sinon takes five seals (138? ) letters, ... multi-state copper bucket, oblique name. According to Huang Zhong's calendar, "Nine Chapters Arithmetic" is equal in length, weight and size, which is consistent throughout the country. " This shows that the book was not only widely circulated in the Eastern Han Dynasty, but also the mathematical problems involved in the development of weights and measures should be based on the algorithm in the book. Xu Shang and Du Zhi may be the first mathematicians to study the Nine Chapters Classic after it was written. Both Xu Shang and Du Zhi were mathematicians in the late Western Han Dynasty. Han Shu's Records of Literature and Art recorded 26 volumes of Xu Shang Arithmetic and 16 volumes of Du Zhi Arithmetic. These two books were written by Yin Xian before correcting his mathematical works in the third year (the first 26 years) of Emperor Han Cheng. The completion date of Xu Shang's and Du Zhi's works is not far from the time when Geng Shouchang deleted and supplemented Nine Chapters of Arithmetic. Their mathematical works should be completed on the basis of studying nine chapters of arithmetic. Liu Hui's Nine Chapters Arithmetic not only occupies an important position in the history of Chinese mathematics, but also makes an important contribution to the development of world mathematics. Fraction theory and its complete algorithm, proportion and proportion distribution algorithm, area and volume algorithm, and solutions to various application problems are described in detail in the chapters of square field, millet, decay, quotient work and even loss. The opening method, profit and loss (double hypothesis method), the concept of positive and negative numbers, the solution of linear simultaneous equations and the general formula of integer pythagorean string in Shaoguang, Profit and Loss, Equation and Pythagorean are all outstanding achievements in the history of mathematics in the world. There are Liu Hui's notes and Tang Li's notes in Nine Chapters of Arithmetic Biography. Liu Hui was an outstanding mathematician in ancient China. During the Three Kingdoms period, he lived in Wei. Regarding the system of weights and measures in past dynasties, the Chronicle of Sui Shu Law and Discipline quoted the comments of the merchants as saying that "Chen Wei was stationed for four years (263) and Liu Hui had nine chapters." His life cannot be examined in detail. Liu Hui's Notes on Nine Chapters not only made important achievements in sorting out the ancient mathematical system and perfecting the ancient calculation theory, but also put forward rich and colorful ideas and inventions. Liu Hui has made outstanding contributions in arithmetic, algebra and geometry. For example, he used the ratio theory to establish a unified theoretical basis for the sum of numbers and formulas, applied the principle of complementarity in and out and the limit method to solve many problems of area and volume, and established a unique theory of area and volume. He used nine chapters to strictly prove many conclusions, and some of his methods have great inspiration for later generations and even today's mathematics. According to the historical book "Sixteen Records of the Book of Jin", the sixth record: Wei Jingyuan is four years old, and Liu Hui notes the "Nine Chapters" cloud: When Wang Mang was young, Liu Xin's foot was weaker than today's foot, nine inches and five centimeters deeper than Wei's foot; That is, Xun Xu said that this foot is four and a half feet long. Chen Wei stayed in Wang Jingyuan for four years, and Liu Hui commented on "Nine Chapters of Business Merit", saying: "Today, large companies are welcomed by farmers, with a circular diameter of one foot, three inches and five minutes, and a depth of one foot, with a total area of 1,441 inches and three tenths of an inch. Wang Mang's copper hoof is nine inches, five minutes and five centimeters deep and one foot, three inches, six minutes, eight centimeters and seven millimeters in diameter. Based on the emblem technique, it is very strange to welcome nine fights, seven liters and four combinations today. " Song Shu Juan Shi San Zhi San: Hu Ming and Liu Xin in the Han Dynasty paradoxically misunderstood his figures, which is considered as a drama defect. The string of the "dry elephant" is fixed. At the turn of the "opening scene" on Sunday, the bandits said that the weather was not allowed, and the family was ruined and the people died. And Zheng Xuan, Kan Ze, Wang Fan, Liu Hui, and comprehensive liberal arts, and each is more sparse.