Mathematics is one of the most developed basic science subjects in ancient China，And "bet365 champions league Junshu" is the most important mathematical classic in ancient China。

The biography of "bet365 champions league Junshu" contains the text of "bet365 champions league Junshu" of the Western Han Dynasty、Three kinds of contents are the annotations of Liu Hui of the Three Kingdoms Wei Dynasty and Li Chunfeng of the Tang Dynasty。It has both narrow and broad meanings。In a narrow sense，Only refers to Zhang Cang of the Western Han Dynasty (？—First 152)、This text of "bet365 champions league Jun Shu" compiled by Geng Shouchang (1st century BC) and others。Broadly speaking，Also includes annotations by Liu Hui and Li Chunfeng。Liu Hui calculated pi in the "Jiu Zhang Zhuan Zhu" Yuan Tian Shu Zhu ■ = 3.14，This is why March 14 is designated as "International Mathematics Day"。

　　The content and style of "bet365 champions league"

《bet365 champions league Junshu》Fan Jiujuan，Juan Fangtian，There are various area formulas and the world’s earliest and most complete four arithmetic rules for fractions。Roll of two corns，It is a proportional algorithm based on Kon's technique (Kon's three-rate method)。Volume three points，is the proportional allocation algorithm，There are also some proportion issues that can be attributed to today's techniques。Volume 4 Shaoguang，It is the inverse operation of area and volume problems，The most important thing is that he proposed the world's earliest square root and cube root procedures。Volume Five Business Gong，is a distribution algorithm for various volume formulas and earthwork workload。Loss in all six volumes，It is a reasonable burden algorithm for taxation，There are also various arithmetic problems。Insufficient volume，It is an algorithm for profit and loss problems and its application in other calculation problems。Volume 8 Equations，is the current solution method for linear equations，There are also rules for adding and subtracting positive and negative numbers and methods for formulating equations。Volume 9 Pythagorean，It is the Pythagorean Theorem、Solution to the Pythagorean Form、Pythagorean Rongfang、Pythagorean circle and simple measurement problems。It establishes the basic framework of Chinese classical mathematics。

"bet365 champions league Junshu" contains nearly a hundred very abstract technical texts or formulas、Solutions and 246 examples。Four arithmetic rules for fractions、Proportional and proportional allocation algorithm、Profit and deficiency algorithm、Opening method、Solution method of linear equations、The rules for adding and subtracting positive and negative numbers and the partial solution to the Pythagorean pattern are hundreds or even thousands of years ahead of other cultural traditions，It is a major achievement of world significance。

It is generally accepted in academic circles that "bet365 champions league Art" is a collection of applied problems。This generalization is not accurate，Actually the main part is not a question、One answer、A collection of questions about Yishu，It is in the form of an algorithmic summary example。

About the relationship between the text and the title of "bet365 champions league Jun Shu"，Generally speaking, there are the following situations。

　　1.Abstract technical literature on a type of problem summarizes one or several examples。This type of content is often one question per skill or multiple questions per skill，Even math problems。bet365 champions league are different situations here。

(1) Give one or several example questions first，Then give one or several abstract articles。There are only questions and answers in the examples，No technical text。For example, Fang Tianzhang listed three examples of fraction addition and then gave the "synthesis technique", which is the rule of fraction addition。All Fang Tianzhang，Mill Chapter 2 Meridian Rate Technique、His rate and counter-rate skills，Shao Guangzhang’s Prescription Technique、Opening the Circle、Opening Cube and Opening Circles，All contents of Shang Gongzhang except for the techniques of city walls and other techniques and the techniques of Chutong and their examples，Both lose bet365 champions league and lose 4 spells，The Surplus and Deficiency Chapter Two Surplus and Two Deficiency Techniques and One Technique、Three techniques including the operation of sufficient enough and insufficient sufficient enough，Pythagorean Pythagorean Technique、Pythagorean Rongfang、Pythagorean Rongyuan and 5 techniques for measuring Yi, etc.，All belong to this situation，Total 71 techniques、102 example questions。

(2) Give the abstract technical text first，List a few more examples。Example questions only have questions and answers，No technical literature。Shang Gong Zhang Cheng Yuan and other techniques、Cudi Tong and other techniques and their examples，The Insufficiency of Insufficiency Chapter and its first technique fall into bet365 champions league situation，Total 4 techniques、14 example questions。

(3) First give the abstract general technique，Give some more examples。Examples include questions、Answers and application of general techniques。Cumi Chapter Jin Youshu and its 31 examples，Decaying Chapter Declining Technique、Regression technique and its 9 examples，Shao Guang Zhang Shao Guang Shu and his 11 examples，11 General Calculation Problems Solved by the Insufficiency and Insufficiency Technique，And Equation Chapter Equation Technique、Position and Negative Technique、Profit and Loss Technique and its 18 Examples，A total of 7 techniques (the surplus and insufficient techniques are not included bet365 champions league calculation)，80 example questions。

These three situations total 82 techniques、196 questions，About 80% bet365 champions league book。Here，Articles are the center，is the subject，They are all very abstract and rigorous，And it is universal，Replaced with modern symbols, it is a formula or calculation program。The title appears as an example question and is attached to the technical text。We call it the form bet365 champions league academic summary question。

2. bet365 champions league application problem set

bet365 champions league kind of content is often one question and one skill。The degree of abstraction of their technical texts also varies。

(1) An abstract technical article about a problem。For example, if both lose the chapter "髇雁"]，Although his writing does not leave the subject of days，But there is no specific number operation，Adapted to the same problem。All lost Zhang Changan to Qi、Male and female tiles、Correction、Fake field、Cheng Geng、Articles on Five Canals and Common Ponds，The same is true for the writings on bet365 champions league Chapter, holding a pole and leaving the house, etc.。

(2) Calculation of specific issues。Non-deprecating questions for failing bet365 champions league，Most of the questions in the non-even loss category with equal loss of seals，Most of Pythagorean Chapter’s technical texts on solving the Pythagorean problem and “setting up four tables to look into the distance” and other topics are calculated with specific figures，It cannot exist independently from the topic。

There are 50 questions in this part，All are non-decline classification problems with decay bet365 champions league、Atypical uniform loss problem of uniform loss，As well as problems such as solving the Pythagorean form and establishing four tables to see into the distance。They are all topic-centered，The technical text is just the solution or calculation of the attached problem。

Self-evident，"bet365 champions league Jun Shu" cannot be summarized as "one question、One answer、A collection of application problems of "Yishu"。We think，There are at least three different styles of works in the history of mathematics，One is to form an axiomatic system like Euclid's "Elements"；The second is a set of applied problems like Diophantus's "Arithmetic"，The same is true for Chinese works such as "Sun Zi Suan Jing"；The main part of "bet365 champions league Junshu" is different from these two，But the third type，That is, the form of algorithmic statistics example。

It’s not difficult to see，The techniques in "bet365 champions league Jue" are not at the same level。It can be divided into at least three levels: one is a very abstract type of problem、Strict and universal algorithm。The second is a relatively abstract algorithm for a problem。The third is the calculation of specific issues。

　　Compilation of "bet365 champions league Junshu"

The compilation of "bet365 champions league Junshu" not only involves the "bet365 champions league Junshu" itself，It also involves the positioning of certain historical figures such as Zhang Cang，It is also related to the understanding of pre-Qin mathematics，Is a major issue in the study of the history of Chinese mathematics。The name of "bet365 champions league Junshu" was first seen in the existing historical materials in Da Sinong Dendrobium in the second year of Guanghe (179) of the Eastern Han Dynasty、In the inscription of Quan，It became a classic of the official standard of weights and measures in the 2nd century，Indicates that it was compiled into a book much earlier。

(1) Compilation of "bet365 champions league Junshu"。There are mainly the following opinions about the compilation of "bet365 champions league Junshu"。Liu Hui's "Nine Chapters Preface" says: "The Duke of Zhou established the rituals with nine numbers，Nine numbers and others，Then "Nine Chapters" is it。The past violently attacked the Qin Dynasty and burned books，Mingshu dispersion。Since then，Zhang Cang, Marquis of Beiping in Han Dynasty、The great ministers, farmers, and prime ministers Geng Shouchang all use good fortune-telling to tell the world。Cang et al. due to the remains of old texts，Deletion and addition of each name。The purpose of the original school may be different from the ancient one，And the people discussed are mostly close to each other。"This is to say，"Nine Numbers" has developed into "Nine Chapters" in the pre-Qin Dynasty，Dispersed due to violent Qin burning books，Zhang Cang of the Western Han Dynasty、Geng Shouchang’s collection of posthumous documents，It was made by successive deletions and additions。This is the earliest record of the compilation of "Nine Chapters" in existing historical materials。

Tang Fake Edition of "Xiahou Yang Jing Jing"、Northern Song Dynasty Jia Xian、Southern Song Dynasty Rongqi、Yuan Moruo and others believe that "bet365 champions league Jun Shu" was written by the Yellow Emperor or Li Shou。Dai Zhen of the Qing Dynasty said "There is Chang'an in the book、The name of Shanglin”，And "Shanglin Garden was during the reign of Emperor Wu"，Negative of Zhang Cang's deletions and additions to "bet365 champions league Jue"，It is believed that the compilation of "Nine Chapters" was after the middle of the Western Han Dynasty。Qian Baocong even pushed it to the second half of the 1st century AD。

Dai Zhen、Qian Baocong and others have different levels of research，But there is no historical data sufficient to overturn Liu Hui’s conclusion，For example, Shanglinyuan，It existed during the time of Qin Shihuang。Liu Hui’s death is not far away，Not only can I learn from the reliable opinions of previous sages on the compilation of "bet365 champions league"，And you can see much more information than Dai Zhen and others。

(2) "Nine Numbers" and "Nine Chapters"。No matter how different people’s opinions are on the compilation of "Nine Chapters"，However, we do not deny that "bet365 champions league Junshu" is related to "Nine Numbers"。"Zhou Li: Local Officials and Situ" records that Nine Numbers is one of the six basic educations received by noble children。At the end of the Eastern Han Dynasty, Zheng Xuan quoted Zheng Zhong at the beginning of the Eastern Han Dynasty and said: "Nine numbers: square field、corn、Difference、Shaoguang、Shang Gong、Loss all、Equation、Not enough wins、Pang Yao。There is a big difference now、Xijie、Pythagorean。""Xijie" is a derivative text。Zheng Zhong believes that "Fangtian" to "Pangyao" are inherent mathematical categories in the Pre-Qin Dynasty，“Chongdian” and “Pythagorean” were developed in the Han Dynasty。

The "bet365 champions league numbers" in the early Western Zhou Dynasty developed into the Spring and Autumn Period and the Warring States Period，Become the bet365 champions league branches mentioned by Er Zheng。Most of its algorithms are relatively abstract，It is a reflection of the strong abstract thinking ability of pre-Qin people。actually，There are several clues of the bet365 champions league Numbers in Pre-Qin classics and unearthed cultural relics。"Shang Jun Shu" says that "the ruler of the world must "examine the numbers" if he wants to expand the land and govern the people"。"Guanzi" contains Guan Zhong's proposition that "the relationship between the earth and the earth weakens the government"。It is most intuitive to measure the area of ​​​​fields in squares，When the land is not square，"Mozi" and "Mencius" both have records of "extremely strong points make up for weak points"，This is the content of Shao Guangshu。When "Guanzi" talks about water and soil engineering, it is necessary to distinguish the "Cheng Gong" of the four seasons, that is, the standard workload。"Guanzi" also said that "the superiors and the inferiors give orders to each other，John’s Table，The evil one can be known”，Should be an important method。

Comparison between the "Nine Numbers" in Pre-Qin Dynasty and the chapter names in "bet365 champions league"，Difference only、Not enough wins、There are differences in the next three items。The first two have the same meaning。There is a big difference between "Pangyao" and "Pythagorean"，But according to the tips of Jia Xian of the Northern Song Dynasty，Also include Pythagorean Technique、Pythagorean Rongfang、Pythagorean circles and simple surveying questions (mainly questions about measuring city directions), etc.。

Previous analysis and explanation of the style of "Nine Chapters"，Among them, three situations in the form of examples of technical literature and generalization cover Fangtian、corn、Shaoguang、Shang Gong、Insufficient surplus、All six chapters including equations and decay problems in the decay chapter、Jianshu problem of Junshu chapter and Pythagorean technique of Pythagorean chapter、Pythagorean Rongfang、Pythagorean Rongyuan、Problems such as measuring cities。The content in the form of application problem sets is the non-degraded classification problems of the remaining chapters、Uneven loss problems in the chapter on equal loss，As well as problems such as solving the Pythagorean form and establishing four tables to see into the distance。This part of the content is not only about style、The style is completely different from the part of the technical summary example，And it’s divided into chapters、The nature of these questions in the chapter is inconsistent with the title，There are also big differences in editing ideas，is an obvious patch。Then if these contents are eliminated from these three chapters，And restore the title of Volume 9 to "Nang Yao"，The remaining content of "bet365 champions league Junshu" is not only completely consistent with the title，They are all in the form of technical essay summary examples，And it is surprisingly consistent with the "nine numbers" mentioned by Er Zheng。This is irrefutably proven，The "nine numbers" mentioned by Zheng Zhong did exist during the Spring and Autumn Period and the Warring States Period，What Liu Hui said is "Nine Numbers"，Then "Nine Chapters" are right" is well-founded。In other words，In Pre-Qin，There is indeed a book developed from the "Nine Numbers" and based on the main part of the biography "Nine Chapters"，"bet365 champions league Jun Shu" which mainly takes the form of technical text and examples。

(3) The era reflected by the prices in "Nine Chapters"。The article "An Examination of Prices in the Qin and Han Dynasties" in the "Research on the Legal History of the Qin and Han Dynasties" by Horiki Japan examines the era reflected by the prices in "Nine Chapters"。He thinks，""bet365 champions league Junshu" basically reflects the Warring States period、Price in Qin Dynasty”。In particular, the similarity in labor income is of great significance to confirm the above conclusion。Therefore，"bet365 champions league Junshu" reflects the price level of the Warring States and Qin Dynasties as a whole，Instead of the price level of the Han Dynasty。This provides new evidence for Liu Hui’s statement。It’s just that Horiki still followed the theory that "bet365 champions league Junshu" was written in the 1st century AD，Make the discussion difficult to be self-consistent。

(4) Liu Hui’s discussion on the compilation of "bet365 champions league Junshu" is correct。The most important argument that denies Liu Hui’s argument about Zhang Cang’s deletions and additions to “Nine Chapters” is that the method of equalization was only implemented during Emperor Wu of the Han Dynasty。In fact，Both of the two mentioned in "Salt and Iron Theory" lost，The ancient method of equalizing loss is similar to the equalizing method of "Nine Chapters"，The modern equal loss implemented during the reign of Emperor Wu of the Han Dynasty is different from this。The Bamboo Slips unearthed at the same time as "筭书书" contains the Law of Uniform Loss。A fragment of a mathematical work unearthed from a tomb in Shuanggudui, Fuyang during the reign of Emperor Wen of the Western Han Dynasty，There is a question that is the fragment of the first question in the "bet365 champions league Jun Shu".。This fundamentally overturns the arguments of Dai Zhen and others who deny Liu Hui’s argument。

In addition，Liu Hui has a rigorous academic style of seeking truth from facts，If he hadn’t seen the conclusive records of Zhang Cang and others’ deletions and additions to “bet365 champions league Jun Shu”，Serious issues such as the compilation of "Nine Chapters"，It is absolutely impossible to talk nonsense。

The guiding ideology of Zhang Cang and others in compiling "bet365 champions league Junshu" is Xun School Confucianism。Xunzi、Zhang Cang、Jia Yi is a direct teacher-student relationship。Jia Yi is the main representative of Xun School Confucianism in the early Western Han Dynasty，It can be seen that Zhang Cang believes in Xun School Confucianism。"Xunzi·Ruxiao" divides knowledge into knowledge、See、know、Four levels of rows，And "learning stops when you practice it"。And "bet365 champions league Junshu" is good at calculation，Algorithm-centric，The algorithm has the characteristics of solving practical problems as its fundamental purpose，Exhibits the style of “seeking truth from facts”，It is the acceptance of Xunzi’s materialist thoughts。

　　(The author is a researcher at the Institute of History of Natural Sciences, bet365 champions league Academy of Sciences)