Liu Hui (about 225~295 years), Han nationality, ShandongBinzhouZou Pingcity[1]Human, a great mathematician during the Wei and Jin Dynasties, is one of the founders of Chinese classical mathematical theory.stayHistory of Chinese MathematicsHas made great contributions to his masterpiece《Notes to Chapter Nine Arithmetic》And《Island Sutra Calculation》Is China's most valuable mathematical heritage.
Liu Hui is quick in thought and flexible in method, advocating both reasoning and intuition.He was the first person in China to explicitly advocate the use oflogical reasoningTo demonstrateMathematical propositionPeople.Liu Hui's life is a life of hard exploration for mathematics.Although his position is low, his personality is noble.He is not a mediocre man fishing for fame, but a great man who never tires of learningChinese nationLeft behind valuable wealth.In May 2021,International Astronomical Union(IAU) approved China'sChang'e VNear the landing siteMoonLiu Hui is one of the eight geomorphological names.[4]
However, due to the primitive solution and the lack of necessary proof, Liu Hui made supplementary proof for this.In these proofs, he showed his creative contributions in many aspects.He was the first person in the world to proposeDecimalConceptual people, and use decimal numbers to express irrational numbersCube root。In algebra, he correctly proposedPositive and negative numberThe concept ofLinear equationsSolution of.In terms of geometry“Cyclotomy", to be used for the circumferenceInscribedorCircumscribeRegular polygonExhaustion is a method for finding the area and perimeter of a circle.He scientifically calculated the result of pi ≈ 3.1416 by using cyclotomy.He used cyclotomy, from a diameter of 2 feetCircle inscribed regular hexagonStart to cut a circle, and then get the regular 12 sided shapeRegular 24 sided......, the thinner the cut, the sum of the regular polygon area andCircular areaThe smaller the difference is, in his original words, it is "the more you cut it, the less you lose it, and the more you cut it, so that it cannot be cut, then it will fit into the circumference without losing anything." He calculated the area of 3072 sides and verified this value.Liu Hui'sscientific method, which has established China's leading position in calculating pi in the world for more than 1000 years.
Liu Hui
Liu Hui made great contributions to mathematics. He put forward the idea of "seeking Hui's number" in the endless problem, which was similar to the laterIrrational rootOfApproximate valueIt is not only accurate calculation of pinecessary condition, and promoted the generation of decimal numbers;In the solution of linear equations, he createdDirect divisionSimplerMutual multiplication and cancellation method, basically consistent with the current solution;And onHistory of Chinese MathematicsIt was first proposed last time“Indefinite equationProblems ";He also established the formula for the sum of the first n terms of the isochromatic series;Proposed and defined manyMathematical concept: such as power (area);Equations (linear equations);Positive and negative numbers, and so on. Liu Hui also proposed many recognized correct judgments as the premise of proof. Most of his reasoning and proof are logical and very rigorous, thus establishing the Nine Chapters of Arithmetic and his own solutions and formulas onInevitabilityBased on.Although Liu Hui did not write his own worksHis noteThe mathematical knowledge used in Nine Chapters of Arithmetic has actually formed a unique feature, including concepts and judgments, andMathematical proofIt is the theoretical system linking them.
Liu Hui is inCyclotomyIt can be regarded as a masterpiece of the ancient Chinese concept of limit.《Island Sutra Calculation》In the book, Liu Hui carefully selected nineMeasurement problems, the creativity, complexity and richness of these topicsRepresentativeness, were all noticed by the West at that time.Liu Hui is quick in thought and flexible in method, advocating both reasoning and intuition.He was the first person in China to explicitly advocate the use oflogical reasoningTo demonstrateMathematical propositionPeople.
Personal achievements
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Liu Hui's achievements in mathematics can be roughly divided into two aspects:
③ In terms of Pythagorean theoryOne by onePythagorean theoremAnd solutionPythagoreanIt established the theory of similar Pythagorean, developed the Pythagorean measurement, and formed the Chinese characteristicsimilarity theory 。
Area and volume theory
Principle and“Cyclotomy”The limit method ofLiu Hui Principle, and solved a variety of geometricGeometryThe area and volume calculation problem.The theoretical value of these aspects is still shining.
Second, on the basis of inheritance, he put forward his own ideas.This is mainly reflected in the followingRepresentativeness's original ideas:
① Circle cutting and Pi, he used circle cutting to prove thatCircular areaThe exact formula for calculating pi is givenscientific method。He firstCircle inscribed hexagonStart cutting a circle, multiply the number of sides each time, calculate the area of 192 sides, and get π=157/50=3.14, and then calculate the area of 3072 sides, and get π=3927/1250=3.1416, called“Emblem rate”。
② Liu Hui PrincipleIn the note of Nine Chapters of Arithmetic Yang Equestrian, when he solved the volume of the cone with the method of infinite division, he proposedpolyhedronLiu Hui principle of volume calculation.
He pointed out the ball in the note of "Nine Chapters of Arithmetic to Open a Circle"Volume formulaV=9D3/16 (D isBall diameter）OfAccuracyAnd introduced the famousgeometric model 。"Mouhe Fanggai" refers tocubeThe two axes of are perpendicular to each otherInscribedcylinderThe intersecting part of.
New technique of equation
In the note of "Nine Chapters of Arithmetic Equations", he proposed a new method to understand linear equations, and used the idea of ratio algorithm.
Weightotherapy
At self writing《Island Sutra Calculation》In, he proposed the technique of weight difference, and used the methods of height measurement and distance measurement such as weight meter, cable and cumulative moment.He also used the method of "analogy and evolution" to develop the technique of heavy difference from two surveys to "three surveys" and "four surveys".However, India began to study the problem of two forecasts in the 7th century and Europe in the 15th to 16th century.Liu Hui's work not only had a profound impact on the development of ancient Chinese mathematics, but alsoHistory of mathematicsIt also established a lofty historical position.In view of Liu Hui's great contribution, many books call him“History of Chinese MathematicsNewton on.
Representative works
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Introduction
His representative work "Nine Chapters of Arithmetic Notes" is a note to the book "Nine Chapters of Arithmetic".Nine Chapters of Arithmetic is one of the oldest mathematical monographs in Chinabe published in book formIn the Western Han Dynasty.The completion of this book has gone through a historical process. Some of the various mathematical problems collected in the book were handed down before the Qin Dynasty, which had been deleted, supplemented and revised by many people for a long time, and finally were sorted out by mathematicians in the Western Han Dynasty.CurrentFixed costThe content of was formed before the Eastern Han Dynasty.
Nine Chapters of Arithmetic is one of the most important classical mathematical works in China. Its completion laid the foundation for the development of ancient mathematics in China and played an extremely important role in the history of mathematics in China.The current edition of Nine Chapters of Arithmetic has collected 246 application problems and solutions to various problems, which belong to Fang Tian, Mi Mi, Fai Fen, Shao GuangCommercial meritChapter 9: Average Output, Surplus and Deficiency, Equation, Pythagorean Equities.
《Chapter Nine Arithmetic》The generation ofsocial developmentAnd the result of long-term accumulation of mathematical knowledge, which brings together theLabor achievements。three countriesLiu Hui, a mathematician at that time, believed that:“Duke Zhou made ritualThere are nine numbers, nine numbers and so on, then the Nine Chapters is rightHan Beiping Marquis Zhang Cang, Da Si NongZhongchengGeng ShouchangThey all live by good fortune telling.Cang and others are called "deletion and supplement" because of the remnants of the old text.Therefore, the purpose of the proofreading is different from that of the ancient times, and most of them talk about the recent language. "According to Liu Hui's research results, "Nine Chapters of Arithmetic" originated from the "Nine Numbers" in the era of the Duke of Zhou, and the "Nine Chapters of Arithmetic" he saw was in the Western Han DynastyZhang CangGeng Shouchang, on the basis of the posthumous writings of the Pre Qin Dynasty, made up of a large number of additions in the Western Han Dynasty.According to historyAccording to the analysis of literature and unearthed cultural relics, what Liu Hui said is credible.
The algorithms contained in Nine Chapters of Arithmetic were handed down by mathematicians in the Han Dynasty before the Qin DynastyFundamentals of MathematicsOn the one hand, it was supplemented and revised to meet the needs of the time.According to Liu Hui's textual research, Zhang Cang and Geng Shouchang were both major mathematicians who participated in the revision work.According to Records of the Historian, Biographies of Prime Minister Zhang, Zhang Cang (about 250-152 BC) experienced the Qin and Han dynasties, and he attacked in the sixth year of Emperor Gao (201 BC)Tibetan teaHe was granted the title of Marquis of Beiping for meritorious service."Since the Qin Dynasty, it has been a pillar of history, and it will be a book tomorrowNaturalization。He is also good at using the calendar. "He also "wrote 18 books on the law of Yin and Yang." The birth date of Geng Shouchang is unknown,Emperor Xuan of the Han DynastyThe official of the time was the most senior minister, Nong Zhongcheng, who was favored by the emperor (see《Hanshu · Food and Goods Record》）。He advocated in astronomyHuntian saidIn the second year of Ganlu (52 BC), he played "measuring the sun and the moon with a round instrument to test the movement of the sky" (see the Book of the Later Han Dynasty - Chronicles of Law and Calendar).Zhang Cang and Geng Shouchang are both famous mathematicians, and they are in high positions《arithmetic》It is very natural.According to Liu Hui's records, the Nine Chapters of Arithmetic he annotated was finally deleted by Geng Shouchang.We believe that the time when Geng Shouchang deleted and supplemented Nine Chapters of Arithmetic can be defined as the time when this book was completed.
Influence of works
Liu Hui
《Chapter Nine Arithmetic》It was an official mathematics textbook compiled by the national organization, which had a great impact on the development of mathematics in the Han Dynasty.《Song rhyming dictionary》Volume IV "Nine chapter art, Han Dynasty"Xushang, Du Zhi, Wu ChenchiWang CanAnd good ", The History of the Later Han Dynasty, Biography of Ma YuanMa Xu(About 70~141 years) Negative record of "erudite and good at nine chapter arithmetic".In addition, there areZheng Xuan(127~200 years)Liu HongAnd others' "Nine Chapters of Arithmetic".It can be seen that this book was an important teaching material for learning mathematics at that timeCopperplateThe inscription on it stipulates: "The great minister of agricultureWu Yin(138?) The imperial edict...... Especially made copper bucket, oblique and appellation for various states.According to the yellow clock calendar, "Nine Chapters of Arithmetic" unifies the seven policies in terms of length, weight, and size, making the whole world the same. "This shows that the book was not only widely spread in the Eastern Han Dynasty, but alsoWeights and measuresThe mathematical problems involved in the development should also be based on the algorithm in the book.Xu Shang and Du Zhi may be the first mathematicians who studied Jiuzhang Suanshu after its completion.Xu Shang and Du Zhi were mathematicians in the late Western Han Dynasty.《Hanshu · Yiwenzhi》It has 26 volumes of Xu Shang Arithmetic and 16 volumes of Du Zhi Arithmetic.Both books areEmperor Cheng of the Han DynastyThree years (first 26 years)Yin XianIt was written before proofreading mathematical works.The time when Xu Shang and Du Zhi finished their 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.
"Nine Chapters of Arithmetic" not only occupies an important position in the history of Chinese mathematics, but also has an important contribution to the development of world mathematics.Fraction theory and its complete algorithm, proportion and proportionallocation algorithm The area and volume algorithms, as well as the solutions of various application problems, have been described in detail in the chapters of the book, such as Fang Tian, Millet, Decay, Quotient Work, Average Transmission, etc.However, the opening methods in the chapters of "Shaoguang", "Surplus Deficiency", "Equation", "Pythagorean", etcSurplus deficiency technique(Double dummy method), positive and negativeNumber conceptLinear simultaneousEquationsThe solution and the general formula of integer Pythagorean chord are outstanding achievements in the history of world mathematics.The biographical version of Nine Chapters of Arithmetic has Liu Hui's notes and Tang Dynasty's notesLi ChunfengComments for, etc.
Liu Hui was an outstanding mathematician in ancient China. He lived in the Three Kingdoms periodWei 。Sui Shu · Lv Li ZhiMeasurement systemQuoting Shang Gongzhang's annotation, he said that "Liu Hui annotated Nine Chapters in the fourth year of Wei Chen's stay in Wang Jingyuan (263)." His life could not be examined in detail.Liu Hui's Annotation of Nine Chapters is not only in sorting outAncient mathematicsImportant achievements have been made in the system and improvement of ancient calculation theory, andRich and colorfulAnd inventions.Liu Hui has made outstanding contributions to arithmetic, algebra, geometry and so on.For example, he used the ratio theory to establish the theoretical basis for the unity of number and formula, and he appliedPrinciple of input and output phase compensationAnd the limit method solves many problems of area and volume, and establishes a unique theory of area and volume.He gave strict proofs to many conclusions in Nine Chapters, and some of his methods have great inspiration for later generations, even for today's mathematics.
Historical records
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The Book of Jin, Vol. 16, Zhi No. 6:In the fourth year of Wei Jingyuan, Liu Hui noted that：usurper who founded the Xin dynastyAt that time, Liu Xin's dendrobium was four minutes and five centimeters weaker than today's, and nine inches and five minutes deeper than Wei's dendrobium;I.eXun XuThe so-called four and a half feet long today is also true.
In the fourth year of Wei Chen staying in Wang Jingyuan, Liu Hui annotated "Nine Chapters of Commercial Merit"Said: "TodayBig Si NongThe round diameter of the dendrobium is one foot three inches five fifths of a centimeter, the depth is one foot, and the volume is 1441 inches three tenths of an inch.Wang Mang's copper dendrobium is now nine inches deep and five cents and seven cents and six cents and seven cents in diameter.In terms of emblem technique, it is strange that today's dendrobium can hold nine buckets, seven liters and four combinations. "[2]
The Third of the Thirteen Annals of the Song Dynasty: In the Han Dynasty, Hu Ming and Liu Xin were deceptively wrong. This is the fault of their drama.The string of Ganxiang is fixed《Beginning of scene》On Sunday at the turn of the day, the bandits said that the weather measurement was not accurate, so they took advantage of and removed the fallacy, which was very wrong for Si Youli.andZheng Xuan、Kan Ze、Wang Fan, Liu Hui, and a comprehensive number of arts, but each more sparse.[3]
