He studied astrology, rhythm, arithmetic, poetry, bow, sword, and the science of construction. He served as the prefect of Qiongzhou and the minister of agriculture. Later, he was demoted and died in Meizhou. In 1247, he completed the book "Shu Shu Jiu Zhang", in which the great derivation method (the solution to the problem of the system of linear congruence equations, also known as the Chinese remainder theorem)Triclinal quadrature and Qin Jiushao algorithm (the numerical solution of positive roots of higher order equations) are important contributions in the world. They express an algorithm for solving the numerical solution of univariate higher order polynomial equations - positive and negative square root.
Qin Jiushao has an ancient word.His ancestral home is Lu County (now Fan County, Henan Province), and he was born in Puzhou (now Anyue County, Ziyang City).[3][8]Chinese ancient mathematician.Born in 1208, the first year of Jiading in the Southern Song Dynasty;aboutJingdingHe was demoted to Meizhou in the second year (1261), and died in Meizhou in February of the fourth year of Xianchun (1268) at the age of 61[2]。
Qin Jiushao's father, Qin Jiyan, was a scholar, and was an official doctor and secretaryJuvenile prison。Qin Jiushao was intelligent and diligent.Southern Song DynastySchaudin In the fourth year (1231), Qin Jiushao became a successful candidate in the imperial examination. He successively served as county magistrate, general judge, councillor, prefectural governor, Tongnong, and temple magistrate.He successively served as an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, was demoted to Meizhou around 1261, and soon died in office.In addition to government affairs, he extensively collected data on calendar, mathematics, astrology, music, construction, etc. for analysis and research.In the fourth to seventh year of Song Chunyou's reign (1244 to 1247), when he was dutiful to his mother, he edited the mathematical knowledge and research achievements he had accumulated for a long time, wrote the famous masterpiece "Counting Books and Nine Chapters", and created the "great derivation and seeking skill", known as the "Chinese Surplus Theorem".His "positive and negative prescription" is called "Qin Jiushao procedure".Almost all countries in the world are exposed to his theorems, laws and problem-solving principles in mathematics courses from primary school, middle school to university.
Famous American historian of scienceSuttonHe called Qin Jiushao: "He was one of the greatest mathematicians of his nation, his time, and indeed of all times".
Qin Jiushao isCrewe (Now HenanFan County）Man, father Qin Jihui, styled Hongfu, became a scholar in the fourth year of Shaoxi (1193), and was later appointedBazhou(Present SichuanBazhong）Keep.In March of 1219, the 12th year of Jiading, Xingyuan (today'sHanzhong, Shaanxi）SergeantZhang Fu, Mo Jian and others launched a mutiny and captured Lizhou after entering Sichuan (todayGuangyuan）Langzhou (todayLangzhong）, Guozhou (now Nanchong), Suining (now Suining)Puzhou(today's Anyue) and other places.When the mutinous army invaded Bazhou, Qin Jiyu abandoned the city and fled, and arrived in Lin'an (now Hangzhou), the capital of the Southern Song Dynasty, with his family.In Lin'an, Qin Jiyan once served as the minister, secretary and junior supervisor of the Ministry of Work.In June of the first year of Baoqing (1225), he was appointed prefect of Tongchuan and returned to Sichuan.
Qin Jiushao has lived in his hometown since he was young. At the age of 18, he was "the leader of the righteous army in the countryside", and later moved to Kyoto with his father.He is a very intelligent person, who is always attentive and studious.During his father's tenure as the doctor and secretary of the staff department, he worked hard to learn and accumulate knowledge.The minister of the Ministry of Works is in charge of construction, while the secretary province is in charge of books, and its subordinate organization has the Taishi Bureau.Therefore, he has the opportunity to read a large number of ancient books, visit experts in astronomical calendar and architecture, ask questions about astronomical calendar and civil engineering, and even go to the construction site to understand the construction situation.He once learned mathematics from a hermit who was proficient in mathematics.He also told the famous poetLi LiuLearn Pian Li poetry to reach a higher level.Through this stage of learning, Qin Jiushao became a knowledgeable and versatile young scholar. People said that he was "extremely skillful in nature, and he studied everything from astrology, music, arithmetic to construction". "Games, balls, horses, bows and swords are all unknowable."[4]
In 1225, Qin Jiushao followed his father to Tongchuan (now Santai County, Sichuan Province).The Mongolian army has invaded the area of Gansu and Shaanxi, and the fight against Mongolia (Yuan Dynasty) in the north is in full swing.The Southern Song Dynasty "recruited 5000 righteous soldiers, and made an agreement with the people, saying, 'When the enemy arrives, the officials will keep the original fort, the people will protect the mountain village, and the righteous soldiers will be guerrillas." Civilian armed forces were established in various places.Qin Jiushao, who knew the military, served as the "righteous leader" of civil armed forces to maintain local security.
Several years later, Li Liu invited him to collate books and documents in the Academy of National History of the Southern Song Dynasty, but he did not go.In the third year of Duanping (1236), Yuan soldiers invaded Sichuan, and the Jialing River basin was still in frequent wars. Qin Jiushao had to participate in military activities frequently.Later, he wrote in the preface of "Shu Shu Jiu Zhang": "When things were going wrong, we had a long way to go. We didn't want to be all in the middle of the rock. We were in danger and worried. After ten sacrifices, our heart was withered and angry", which truly reflected this turbulent life.Due to the advance of Yuan soldiers and the turmoil of routed soldiers,TongchuanIt was difficult for him to live in peace, so he went out of eastern Sichuan again and served as Qizhou (now HubeiQichun）Tongyi and Hezhou (now Hexian County, Anhui Province), and finally settled in Huzhou (now Zhejiang ProvinceWuxing)。During Qin Jiushao's term of office and state guard, he used his power to sell salt and forced it to the people for profit.After settling down in Huzhou, the houses built were "extremely spacious", and "after that, the houses were listed, with Xiuji and Orchestra as their location".It is reported that he lived a luxurious life in Huzhou, "the cost is not calculated".In August of the fourth year of Chunyou (1244), Qin Jiushao took Tong Zhilang as the sentence of Jiankang Mansion (now Nanjing, Jiangsu). In November, he left his post due to his mother's death and returned to Huzhou to observe filial piety.During this period, he devoted himself to the study of mathematics, and completed the famous mathematical book "Counting Books and Nine Chapters" in September of the seventh year of Chunyou (1247).As a result of his rich knowledge and achievements in astronomy and calendar, he was summoned by the emperor to explain his own views, and presented a draft and a "Outline of Mathematics" (that is, "Shu Shu Jiu Zhang").
In the second year of Baoyou (1254), Qin Jiushao returnedJiankang, he was re appointed as the Counsellor of the Yanjiang Institutional Envoy, and soon left his post.Since then, he has tried his best to attract and bribe the current dignitariesJia Shidao, was appointed in the sixth year of Baoyou (1258)QiongzhouShou was dismissed three months later.Liu Kezhuang, a contemporary, said that Qin Jiushao "arrived at the county (Qiongzhou) only a hundred days ago, and the people of the county were always greedy. They cried as soldiers to speed up his departure". Zhou Mi also said that he "went to the county for a few months, left home, and was very rich".It seems that because of his greed in Qiongzhou, the people are extremely dissatisfied.After returning to Huzhou from Qiongzhou, Qin Jiushao took refugeWu Qian, appreciated by Wu Qian, they are very close.Wu Qian has successivelyKaiqingIn the first year (1259), he was proposed to be the chief of the Si Nong Temple, and in the first year of Jingding (1260), he was proposed to be the Zhilinjiang Army (today's Qingjiang, Jiangxi). Both of them gave up because of fierce opposition.During this period, Qin Jiushao was keen on seeking official positions, fame and wealth, and had no significant achievements in science.In the fierce struggle within the ruling group of the Southern Song Dynasty, Wu Qian was dismissed and relegated, and Qin Jiushao was also implicated.In about the second year of Jingding (1261), he was demoted to Meizhou as a local official. "He did not stop governing in Meizhou", and soon died in office.
Qin Jiushao's main achievement in mathematics was to systematically summarize and develop the numerical solution of high-order equations and the solution of linear congruence group, and put forward a fairly complete "positive and negative square cutting" and "great derivation", reaching the highest level of mathematics in the world at that time.
Life Story
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Qin Jiushao (1208-1268), with ancient Chinese characters, was born in Puzhou (now Anyue County, Ziyang City, Sichuan Province).[8]
It was born in Puzhou in the spring of 1208, the first year of Jiading.
In October of the second year of Shaoding (1229), Qin Jiushao promoted the county captain of Qi County (now Qijiang Ancient Town, Santai County, Sichuan Province).
In August of the fourth year of Shaoding (1231), Qin Jiushao participatedWei LiaowengstabilizeLuzhouBarbarians repaired battlements in their towers.
In the fifth year of Shaoding (1232), in August, Yi Chou became a scholar. In the sixth year of Shaoding, Qin Jiushao led Wu Qian and other supervisors in Wei LiaowengTongchuanfu Road、Chengdu Fu RoadWhen we met Wu Qian, Wei Liaoweng and Wu Qian went with Qin Jiushao to visit Xu Yi who was ill.
In January of the third year of Duanping (1236), Qin Jiushao promoted Qizhou (now Hubei)Qichun County）General judgment.
In the autumn of the first year of Jiaxi (1237), Qin Jiushao knew Hezhou (now Hexian County, Anhui Province).
In the second year of Jiaxi (1238), Qin Jiushao returned to Lin'an and found thatXixiIt is inconvenient for people on both sides to cross the river. A bridge named "Xixi Bridge" was designed and built on the Xixi River. To commemorate Qin Jiushao, mathematician Zhu Shijie named the bridge "Daogu Bridge".
In the third year of the reign of Emperor Jiaxi (1239), after dealing with his father's affairs in Hangzhou, Qin Jiushao, his mother and wife returned to the house that his father had prepared in his early years outside the west gate of Huzhou to continue his father's worries.When Qin Jiushao was worried about his father in HuzhouQingyuan Mansion(Ningbo, Zhejiang) Wu Qian makes friends with You Ren and starts to rebuild the house prepared by his father.
In June of the third year of Chunyou, Wu Qian returned to Huzhou and Ding Muyou. Qin Jiushao had even closer contact with Wu Qian, who had been deprived of his official position.[5]
In the fourth year of Chunyou (1244), Qin Jiushao took the post of Tong ZhilangJiankang(Nanjing) Government pass judgment.In November, Qin Jiushao, Ding Muyou, dismissed his official post and went back to Huzhou to watch for his mother in her late eighties. He will devote himself to studying and applying mathematical achievements in practice, and write a book named "Mathematical Outline".At this time, Wu Qian is also in HuzhouDing Muyou, and they are very close.
In the eighth year of Chunyou's reign (1248), "Mathematical Outline" was recommended to the court.
Catalogist in the ninth year of Chunyou (1249)Chen ZhensunConsult Qin Jiushao when compiling the bibliography.
In the 10th year of Chunyou's reign (1250), Qin Jiushao stepped down as the general judge of Jiankang and became the governor of Suzhou.
In the second year of Baoyou (1254), Jiushao took officeJiangning(Nanjing, Jiangsu) Prefecture Magistrate, Counsellor of Yanjiang Zhizhi Department, managed the food routes of the ten prefectures in Jiangnan, and Baoyou left his post in the fourth year.
In the sixth year of Baoyou (1258), Qin Jiushao was recommended by Jia SidaoLi ZengboHe is the guardian of Qiongzhou. He goes there for several months.
In October of the first year of Kaiqing (1259), Wu Qian entered the prime minister for the second time, and Qin JiushaoJiangdong(Nanjing, Jiangsu) Deliberate the curtain.And went to the other side, except for Simong ChengPingjiang(The government is in today's Suzhou City) Take care of the rice straw, and let it go.
In the first year of Jingding (1260), Qin Jiushao knew Linjiang Army (west of Qingjiang County, Jiangxi Province)Linjiang TownThe Southern Song Dynasty was the Linjiang Army, which governed Qingjiang, Xinyu and other counties.[3]
In June of the second year of Jingding (1261), Qin JiushaoMeizhou, GuangdongKnow military and state affairs.
In February of the fourth year of Xianchun's reign (1268), Qin Jiushao had been in Meizhou for nearly six years. He learned that the imperial court had recovered the nobility for Wu Qian, but he had forgotten the grievances in his heart. He died in Meizhou at the age of 61.
Mathematical contribution
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Qin Jiushao's mathematical achievements are preserved in the book "Shu Shu Jiu Zhang".However, this book did not cause great influence at that time. Later, Yang HuiZhu ShijieNone of them cited the achievements of Qin Jiushao.The main content of "Shu Shu Jiu Zhang" focuses on the application of mathematics. The 81 topics in the book are all questions raised in combination with the actual needs at that time.
Epoch-making masterpiece
Count Nine Chapters
Qin Jiushao has devoted himself to studying mathematics for many years. After three years of filial piety in Huzhou, he wrote the world famous book of mathematics, "Shu Shu Jiu Zhang". "Gui Xin Miscellaneous Knowledge Continuation" is called "Mathematical Outline", and "Yongle Dadian" is called "Shu Shu Jiu Zhang".The book consists of nine chapters and eighteen volumes, nine chapters and nine categories: "Dayan Category", "Tianshi Category", "Tianyu Category", "Outlook Category", "Taxes and Duties Category", "Qiangu Category", "Construction Category", "Military Brigade Category", and "Market Objects Category". There are a total of 81 questions (9 questions) in each category. The book is rich in content, ranging from astronomy, astrology, calendar, weather measurement to river, water conservancy, architectureTransportation, various geometric figures and volumes, calculation and reciprocity of money and grain, taxes and levies, markets, and tooth margins.Many calculation methods and empirical constants still have high reference value and practical significance, and are known as "the treasure of calculation".
The writing method of the book is mostly composed of four parts: "asking", "answering", "technical" and "cursive": "asking" is to ask questions from real life;"Answer", give the answer;"Shu Yue", explaining the principle and steps of problem solving;"Cao Yue", giving a detailed solution process.This book has been recognized as a world famous mathematical book in the history of science at home and abroad.This book not only represents the advanced level of Chinese mathematics at that time, but also marks one of the achievements of mathematics in the medieval world.our countryHistory of mathematicsLiang Zongju, a famous scholar, said: "Qin Jiushao's" Counting the Nine Chapters of Books "(1247) is an epoch-making masterpiece with rich content and superb skills, especially Dayan Seeking a Skill（Indefinite equationChinese unique solution ofalgebraic equationThe numerical solution of the mathematical model has a high position in the history of world mathematics.At that time, the long dark night in Europe was still not over, but the creation of the Chinese people was like the rising sun shining in the east.
Dayan Seeks a Skill
The ancient Chinese method for solving a class of Dayan problems.Dayan problem originates from《Sunzi Suanjing》In“Things are unknown”Question: "There is something today, but I don't know its number. There is two left of three or three numbers, three left of five or five numbers, and two left of seven or seven numbers. Ask about the geometry of things?" This is a problem of solving the system of equations of linear congruence in modern number theory.Qin Jiushao, a mathematician in the Song Dynasty, systematically discussed the solution of this kind of problem in his "Shu Shu Jiu Zhang" (completed in 1247), and called it "Da Yan Qiu Yi Shu".Qin Jiushao's "Dayan Seeking a Skill" wascantor It is called "the luckiest genius".Qin Jiushao invented the "Dayan Seeking Method", that is, the first-order congruence method in modern algebra theory, which is one of the achievements in medieval world mathematics. Compared with the famous mathematicians in the West in 1801Gaussian(Gauss, 1777-1855) established the congruence theory 554 years earlier, which was called "China" by the WestRemainder theorem”。But his mathematical achievements in quadrature formula are more than those of ancient Greek mathematiciansHelenMore than a thousand years late.
Equation of arbitrary degree
Qin Jiushao also created a "positive negative square method", that is, the numerical solution of any equation of higher order, in addition to the "big derivation method" in his book "Shu Shu Jiu Zhang". This achievement invented by Qin Jiushao is 572 years earlier than the same solution of the British man W. G. Horner (1786-1837) in 1819.Qin Jiushao put forward the principle of "quotient is always positive, real is always negative, from constant to positive, and from constant to negative" when he listed the formula of "positive and negative formula", gave a unified operation rule by purely algebraic addition, and expanded it to any higher order equation.
Solution of linear equations
Qin Jiushao
In addition, Qin Jiushao also improved the solution of the system of linear equations, using mutual multiplication and subtraction to eliminate elements, which is completely consistent with the current addition and subtraction elimination method;At the same time, Qin Jiushao also gaveCalculationIt can be extended to the solution of general linear equations.The earliest year in Europe was 1559Cloth throw(Buteo, about 1490-1570, France) gave that he began to use the incomplete addition, subtraction and elimination method to solve the system of linear equations, 312 years later than Qin Jiushao, and the theoretical integrity is also inferior to Qin Jiushao.
The Triclinal Quadrature Formulas Listed in Volume 5 of His Book and Ancient Greek Mathematicians in the First Century A.DHelenThe formula given is the same in different ways;Volume 7 and Volume 8 also make the technique of prediction in the Island Suanjing carry forward and add luster.
Triclinic quadrature
Qin Jiushao also created and used“Triclinic quadrature”And so on, giving the solution of three sides of a known triangleTriangle area formula, and ancient Greek mathematiciansHelen(Heron, around 50 A.D.) The formula is exactly the same.Qin Jiushao also gave some empirical constants, such as the "three strong points pierce four soil and five weak points, the millet rate is 50, and the wall method is half" in the problem of soil construction, which is still of practical significance even at present.Qin Jiushao also gave the ingenious and general operation method of the mixed proposition of partition proportion and chain proportion in the "Inferring reciprocity" in Volume 77 of Volume 18, which is still of great significance.
Count Nine Chapters
Qin Jiushao is here《Count Nine Chapters》In the preface, it is said that mathematics "can communicate with the gods and conform to life in a big way, while in a small way, it can manage the affairs of the world and sort all things".The so-called "communicating with gods" means to travel between unpredictable things and investigate the mysteries;"Conforming to life" means conforming to the nature of things and their development laws.In Qin Jiushao's view, mathematics is not only a tool to solve practical problems, but also a lofty realm of "connecting with gods and obeying life".
Count Nine Chapters
There are nine chapters, nine categories and eighteen volumes in the book, with nine questions of each category totaling 81 arithmetic problems.In addition, there are also eulogies under each category, which are concise and comprehensive, and are used to describe the main content of this category of calculation, its relationship with the national economy and the people's livelihood, and its solution ideas.
The whole book is in the form of problem sets, not classified by mathematical methods.The essay not only talks about mathematics, but also involves natural phenomena and social life, which became an important reference for understanding the social, political and economic life at that time."Shu Shu Jiu Zhang" has a lot of innovations in mathematical content.The Chinese counting method and its calculus are completely preserved here;Natural numbers, fractions, decimals, and negative numbers are all specifically discussed, and it is the first time to use decimals to represent approximate values of irrational roots;In Volume 1, the greatest common divisor and the least common multiple are flexibly used in the major derivatives, and the serial calculation is initiated to obtain the least common multiple of several numbers;On the basis of the problem of "things don't know the number" in Sun Tzu Suan JingDayan Seeks a Skill, making the solution of linear congruence group standardized and programmed, more than 500 years earlier than the similar method created by Western Gauss, and recognized as "ChinaRemainder theorem”；Volume 17MarketplaceClass II gives a complete record of equation calculus. The book also follows Jia Xianzeng's method of multiplying and opening and then makes positive and negative square opening, so that it can solve the rational root or irrational root of equations of any degree, more than 500 years earlier than the same method of British Horner in the 19th century.
In addition, Qin Jiushao also proposed the Qin Jiushao algorithm.This algorithm is still a practical algorithm for polynomial evaluation.The algorithm seems simple, and its greatest significance lies in transforming the value of n-degree polynomials into the value of n-degree polynomials.In manual calculation, the Qin Jiushao algorithm and its coefficient table can greatly simplify the operation.
"Shushujiuzhang" is the inheritance and development of "Jiuzhang Arithmetic", which summarizes the main achievements of Chinese traditional mathematics in the Song and Yuan dynasties, and marks China'sAncient mathematicsThe peak of.When it was still a copy, it was included in Yongle Dadian and Sikuquanshu successively.In 1842, it was widely spread among the people after the first printing.Qin Jiushao's "positive and negative formula" and "Dayan Seeking One" have long influenced the research direction of Chinese mathematics.Focal circulation、Li Rui、Zhang Dunren、Luo TengfengThe works of mathematicians such as Shi Yuechun, Huang Zongxian, etc. were all written under the direct or indirect influence of Shushujiuzhang.Qin Jiushao's achievements also represented the mainstream and the highest level of mathematical development in the medieval worldHistory of mathematicsHe occupies a lofty position.
Correlation algorithm
Put a polynomial of degree n
It is rewritten as follows:
When calculating the value of a polynomial, first calculate the value of the first-order polynomial in the innermost bracket, that is
Then calculate the value of the polynomial level by level from the inside out, that is
In this way, finding the value of polynomial f (x) of degree n is transformed into finding the value of n polynomials of degree one.
The above method is calledHorner scheme 。This algorithm is still a practical algorithm for polynomial evaluation[6].
Remainder theorem
There is a story in folklore“Han XinPoint troops ".
Chinese Remainder Theorem
At the end of the Qin Dynasty, Chu and Han fought each other.Once, Han Xin fought 1500 soldiers against Li Feng, a senior general of the King of Chu.After a bitter battle, the Chu army was defeated and retreated to the camp. The Han army also killed or injured four or five hundred people. So Han Xin reorganized his troops and returned to the base camp.When we arrived at a hillside, a rear army suddenly reported that Chu cavalry was coming.I saw dust flying in the distance, and the sound of killing shook the sky.The Han army was already very tired. At this time, the troops were shouting.When Han Xin's troops arrived at the top of the slope, he saw that the enemy was less than 500 horses, so he quickly ordered troops to meet the enemy.He ordered three soldiers to stand in a row, and two more soldiers came out;Then he ordered five soldiers in a row, and three more soldiers came out;He ordered seven soldiers in a row, and two more soldiers were added.Han Xin immediately announced to the soldiers that there were 1073 warriors in our army, and the enemy was less than 500. We must defeat the enemy by standing high and attacking the few with the many.The Han Army had always believed in its commander, which made it even more convinced that Han Xin was "an immortal coming down to earth" and "an ingenious plan".So morale was boosted.For a moment, the banners waved and the drums roared. The Han army marched forward and the Chu army was in chaos.Soon after the battle, the Chu army was defeated and fled.
First, we first find the least common multiple 105 of 3, 5, and 7 (note: because 3, 5, and 7 are pairwise coprime integers, their least common multiple is the product of these numbers), multiply by 10, and then add 23 to get 1073 (people).
In the Sunzi Suanjing more than a thousand years ago, there was an arithmetic question: how many things are today?
The explanation means that a number divided by 3 and 2, divided by 5 and 3, divided by 7 and 2, is calculated.
Such a problem is also known as "Han Xin ordered troops".It forms a kind of problem, namelyElementary number theoryMiddle solution congruence.The method of conditional solution of such problems is called "Chinese surplus theorem", which was first proposed by the Chinese.
① There is a number. Divide by 3, then 2. Divide by 4, then 1. How much is this number divided by 12?
Solution: Divide by 3 and the number of 2 is:
2， 5， 8， 11，14， 17， 20， 23….
The remainder of dividing them by 12 is:
2，5，8，11，2，5，8，11，….
Divide by 4 and then leave 1:
1， 5， 9， 13， 17， 21， 25， 29，….
The remainder of dividing them by 12 is:
1， 5， 9， 1， 5， 9，….
The remainder of a number divided by 12 is unique. In the above two lines of remainder, only 5 is common. Therefore, the remainder of this number divided by 12 is 5.
If we change the question ①, we will not find the remainder divided by 12, but this number.It is obvious that there are many numbers that meet the conditions, which are 5+12 × integers,
Integers can take 0, 1, 2,..., endless.In fact, after we first found 5, we noticed that 12 is the least common multiple of 3 and 4, and the integral multiple of 12 is the number that meets the condition. This is to combine the two conditions of "dividing by 3 and remaining by 2, dividing by 4 and remaining by 1" into one condition of "dividing by 12 and remaining by 5".The question raised in Sun Tzu's Suanjing has three conditions. We can first combine the two conditions into one, and then combine with the third condition to find the answer.
② Divide a number by 3 and 2, divide it by 5 and 3, divide it by 7 and 2, and find the minimum number that meets the conditions.
Solution: First, list the numbers divided by 3 and then 2:
2， 5， 8， 11， 14， 17， 20， 23， 26，…，
Then list the number of 3 after dividing by 5:
3， 8， 13， 18， 23， 28，….
In these two columns, the first common number is 8.3 and the least common multiple of 5 is 15. The two conditions are combined to form an 8+15 × integer. List the numbers in this column as 8, 23, 38,..., and then list the numbers 2, 9, 16, 23, 30,
The minimum number that meets the requirements of the question is 23.
In fact, we have combined the three conditions in the topic into one: dividing 105 by 23
The number of soldiers in Han Xin Point is between 1000 and 1500, which should be 105 × 10+23=1073
An ancient mathematical book in China, Sun Tzu Suanjing, also has a similar problem: there is something today, but I don't know its number. How about three or three, two, five or five, three, seven or seven, and two?
Answer: 23
The saying goes: two out of three, one hundred forty, three out of five, sixty-three, two out of seven, three out of seven, and three out of three. If you combine them, you can get two hundred and thirty. If you subtract two hundred and ten, you can get two hundred and thirty.If there is one left in three or three numbers, it will be 70; if there is one left in five or five numbers, it will be 21; if there is one left in seven or seven numbers, it will be 15.
The author of Sun Tzu Suan Jing and the exact age of his works cannot be examined. However, according to the textual research, the age of his works will not be after the Jin Dynasty. With this textual research, the Chinese people found the solution to the above problem earlier than the West. Therefore, the promotion of this problem and its solution are known as the "Chinese Surplus Theorem".The Chinese Remainder Theorem occupies a very important position in modern abstract algebra.
In the fourth to seventh year of Song Chunyou (1244-1247 AD), Qin Jiushao spent three years in Huzhou as a dutiful son to his mother. He sorted out his accumulated mathematical knowledge and research results, and wrote the world-famous mathematical masterpiece Shu Shu Jiu Zhang.After the book was completed, it was not published.The manuscript is almost lost, and the title of the book is not exact.After going through the Song and Yuan Dynasties to the founding of the Ming Dynasty, no one wrote this bookAppetite, until Ming DynastyYongle Reign, onJiejinWhen editing Yongle Dadian, he wrote that the book was called Nine Chapters of Mathematics.After more than 100 yearsWang YinglinAfter copying, it was revised by Wang into "Counting Nine Chapters".
The book is not only rich in quantity, but also top in quality.Historically, Qin Jiushao's "Shu Shu Jiu Zhang" is comparable to "Jiu Zhang Shu Shu Shu Shu Shu Jiu Zhang";From a worldwide perspective, Qin Jiushao's "Counting Books and Nine Chapters" is also worthy of being a world famous mathematical book.Qin Jiushao not only won the supreme honor for China, but also made outstanding contributions to world mathematics.
Evaluation of later generations
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Statue of Yuanjue Cave in Anyue, Sichuan
Qin Jiushao is a world famous mathematician who attaches importance to both theory and practice, is good at inheritance and innovation, cares about the national economy and the people's livelihood, observes the sufferings of the people, advocates the implementation of benevolent policies, and actively supports and participates in the war against gold and Mongolia.His famous book "Shu Shu Jiu Zhang" is the history of Chinese mathematics, and evenHistory of World MathematicsThe brilliant page had a wide impact on the development of mathematics in later generations.Qin Jiushao independently introduced the formula of triclinic quadrature, which filled a gap in China's traditional mathematics, from which we can see that China's ancient mathematics has a very high level.Famous mathematician in Qing DynastyLu Xinyuan(1834-1894) praised that "Qin Jiushao was not a hero when he was able to lay stress on his unique knowledge when the world did not talk about algorithms." The famous German mathematical historian M. Cantor (1829-1920) spoke highly of the art of great derivation, and praised the Chinese mathematician who discovered the algorithm as "the luckiest genius".Famous American historian of scienceSutton(G. Sarton, 1884-1956) said that Qin Jiushao was "one of the greatest mathematicians of his nation, his time, and indeed that time".
Memorial Hall
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Qin Jiushao Memorial Hall
The Memorial Hall of Qin Jiushao in Anyue County was named the first batch of patriotism education bases in Ziyang by the municipal party committee and government.
Qin Jiushao Memorial Hall is located in Yuanjue Cave. It covers an area of 81 meters in length and width, with a building area of 1538 square meters. It is an ancient building modeled after the Song Dynasty. There are several books and nine chapters, Jiushao's hometown, observatory and other scenic spots in the museum.
Historical influence
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In June 2020, the leading group of Sichuan Historical Celebrities Cultural Inheritance and Innovation Project was selected as the "Second Batch of Sichuan Historical Celebrities".[7]
