A brief introduction to ancient mathematicians in China, whichever one is good.

Liu Hui (a famous mathematician in ancient times)

Liu Hui (about AD 225-295), a native of zouping county, 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, and advocates both reasoning and intuition. He is the first person who China explicitly advocated to demonstrate mathematical propositions by logical reasoning. Liu Hui's life is a life of hard exploration of mathematics. Although the status is low, but the 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 a precious wealth to our Chinese nation.

Liu Hui's mathematical achievements are roughly in two aspects:

The first is to sort out China's ancient mathematical system and lay its theoretical foundation, which is embodied in Nine Chapters of Arithmetic Notes. It has actually formed a relatively complete theoretical system:

Number system theory

(1) Expounds the arithmetic rules of general division, reduction, four operations and simplification of complex numbers with the same number and different numbers; 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.

Comments on Liu Hui

(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.

③ In pythagorean theory, the pythagorean theorem and the calculation principle of pythagorean solution are demonstrated one by one, and a theory similar to pythagorean form is established and pythagorean measurement is developed. Through the analysis of typical figures such as "crossing in the hook" and "straight in the stock", a similar theory with China characteristics was formed.

Area and volume theory

Liu Hui's principle is put forward 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) Pi and Pi, where is the Nine Chapters 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.

Theory of "seeking housing reform"

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.

New technology of equation

In the annotation of "Nine Chapters of Arithmetic Equations", he put forward a new method to understand linear equations, using the idea of ratio algorithm.

Gravity difference technology

In his "Island Calculation", he put forward the repeated difference technique, and used repeated tables, continuous cables, cumulative moments and other methods 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".

representative works

Introduction of works

His masterpiece Notes on Nine Chapters Arithmetic is the annotation of 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 solutions to various problems, which belong to nine chapters: Tian Fang, Su, Decline, Shao Guang, Shang Gong, 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, the Nine Chapters of Arithmetic he annotated 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.