Liu Hui 刘徽

The founder of Chinese traditional mathematical theory


Chinese Name: 刘徽

English Name: Liu Hui

Born: 225

Died: 295


Cleaning up the ancient Chinese mathematical system 清理中国古代数学体系

Put forward the methods of making a square cover, weight difference, circular cutting, etc 提出牟合方盖、重差术、割圆术等方法

Liu Hui 刘徽
Liu Hui 刘徽

Brief Biography of Liu Hui

Liu Hui, a great mathematician during the Wei and Jin Dynasties, was one of the founders of Chinese classical mathematical theory.

Liu Hui (about 225 to 295 years), a Han nationality, was born in Zouping City 邹平市, Binzhou 滨州, Shandong Province 山东省. He has made great contributions to the history of Chinese mathematics. His masterpieces “Nine Chapters Arithmetic Note 《九章算术注》” and “Island Arithmetic Sutra 《海岛算经》” are the most valuable mathematical heritage of China.

Liu Hui 刘徽
Zu Chongzhi 祖冲之

Liu Hui is quick in thought and flexible in method, advocating both reasoning and intuition. He was the first person in China who explicitly advocated the use of logical reasoning to demonstrate mathematical propositions. Liu Hui’s life is a life of hard exploration of mathematics. Although he has a low status, he has a noble personality. He is not a mediocre man fishing for fame, but a great man who never tires of learning. He has left us a precious treasure.

In May 2021, the International Astronomical Union (IAU) approved the naming of the lunar landforms near the Change-5 landing. Liu Hui is one of the eight topographical names.

Personal Life and Major Contributions

Nine Chapters of Arithmetic Annotation 《九章算术注》

His representative work “Nine Chapters of Arithmetic Annotation” is a note to the book “Nine Chapters of Arithmetic 九章算术”. Nine Chapters of Arithmetic is one of the oldest mathematical monographs in China, which was written in the Western Han Dynasty 西汉.

Nine Chapters of Arithmetic 九章算术” is the most important classical mathematical work in China. Its completion laid the foundation for the development of ancient Chinese mathematics and played an extremely important role in the history of Chinese mathematics. The current version of Nine Chapters of Arithmetic collects 246 application problems and solutions to various problems, which are respectively subordinate to nine chapters, namely, Fang Tian, Mi, Fa Fen, Shao Guang, Shang Gong, Yi Yi, Ying Insufficient, Equation and Pythagorean.

Liu Hui 刘徽
Nine Chapters of Arithmetic 九章算术

The production of Nine Chapters of Arithmetic is the result of social development and the long-term accumulation of mathematical knowledge. It brings together the achievements of mathematicians in different periods.

The algorithms contained in Nine Chapters of Arithmetic were supplemented and revised by mathematicians of the Han Dynasty on the basis of the mathematics handed down before the Qin Dynasty 秦朝 and adapted to the needs of the time.

Contribution in mathematics

Liu Hui made great contributions to mathematics. He put forward the idea of “finding Hui numbers 求徽数” in the endless problem of square root. This method is consistent with the later method of finding the approximate value of irrational roots. It is not only a necessary condition for the accurate calculation of pi but also promotes the generation of decimal decimals.

In the solution of linear equations, he created a method of mutual multiplication and elimination that is simpler than the direct division method, which is basically consistent with the current solution; It is the first time in the history of Chinese mathematics to put forward the “indefinite equation problem”; He also established the formula for the sum of the first n terms of the isochromatic series; Many mathematical concepts have been proposed and defined, such as power (area); Equations (linear equations); Positive and negative numbers and so on.

Liu Hui 刘徽
Circumcision and Pi 割圆术与圆周率

Liu Hui also put forward many recognized correct judgments as the premise of proof. Most of his reasoning and proof is logical and very rigorous so the Nine Chapters of Arithmetic and his own solutions and formulas are based on necessity. Although Liu Hui did not write a systematic work, the mathematical knowledge used in his annotation of Nine Chapters of Arithmetic has actually formed a theoretical system with unique characteristics, including concepts and judgments, and mathematical proof as its link.

Representative creation

“Mou He Fang Gai” 牟合方盖

In the note to “Nine Chapters of Arithmetic for the Opening of a Circle”, he pointed out the inaccuracy of the spherical volume formula V=9D3/16 (D is the diameter of the sphere), and introduced the famous geometric model of “Muhe Square Cover”. “Mou He Fang Gai” refers to the intersection of two inscribed cylinders whose axes are perpendicular to each other.

Liu Hui 刘徽
Mou He Fang Gai 牟合方盖

Circumcision and Pi 割圆术与圆周率

In the note of “Nine Chapters of Arithmetic: Round Field Technique”, the exact formula of circle area is proved by using circular cutting, and the scientific method for calculating pi is given. First, he cut a circle from a hexagon inscribed in the circle. Each time the number of sides multiplied, he calculated the area of 192 polygons to π=157/50=3.14, and then calculated the area of 3072 polygons to π=3927/1250=3.1416, which is called the “emblem ratio”.


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