China is one of the ancient civilizations in the world, located in the east of Asia, near the west coast of the Pacific Ocean. Mathematics has a long history and brilliant achievements in China. Let's describe it in sections according to historical development.
1. Pre-Qin embryonic period
The Yellow River Basin and the Yangtze River Basin are the cradles of China culture. Around 2000 BC, the first slave country, the Xia Dynasty, appeared in the middle and lower reaches of the Yellow River. Then came the Shang and Yin Dynasties (about BC 1500-BC 1027 b.c) and the Zhou Dynasty (BC 1027 b.c- 22 BC1year). Historically, it is also called the Spring and Autumn Period and the Warring States Period from the 8th century BC to the establishment of the Qin Dynasty [[221b.c]].
The Book of Changes records that "in ancient times, there was a rule of tying ropes, and later sages changed it into a book contract". There are many numerals in Oracle Bone Inscriptions unearthed in Yin Ruins. From one to ten, as well as hundred, thousand and ten thousand, are special symbolic characters. * * * There are 13 independent symbols, and the notation is written in a combined document, including decimal notation, with a maximum of 30,000.
Calculation is a calculation tool in ancient China, and this calculation method is called calculation. The age of calculation cannot be verified, but it is certain that calculation has been very common in the Spring and Autumn Period.
There are two ways to calculate numbers by counting chips, vertical and horizontal:
1 2 3 4 5 6 7 8 9
When representing multi-digits, the decimal numerical system is adopted, and the digits of each digit are arranged from left to right, criss-crossing (the rule is: one is vertical and ten is horizontal, one hundred stands upright, one thousand is relative to ten, and ten thousand is equal to one hundred), and zero is represented by spaces. Calculation and financing establish good conditions for addition, subtraction, multiplication and division.
Calculation was not gradually replaced by abacus until the end of Yuan Dynasty in15th century. It was on the basis of calculation that China ancient mathematics made brilliant achievements.
In geometry, "Historical Records Xia Benji" said that ruler, moment, mark, rope and other drawing and measuring tools were used. And a special case of Pythagorean Theorem (called Pythagorean Theorem in the West) has been discovered. During the Warring States Period, the Work Inspection Book written by Qi people summed up the technical specifications of handicrafts at that time, including some measurement contents and some geometric knowledge, such as the concept of angle.
A hundred schools of thought contended during the Warring States period also promoted the development of mathematics, and some schools also summarized many abstract concepts related to mathematics. As we all know, Mo Jing's definitions and propositions of some geometric terms, such as "a circle, an equal length", "flat, the same height" and so on. Mohist school also gave the definitions of finite and infinite. Zhuangzi records the famous theories of Hui Shi and others, and the topics put forward by debaters such as Huan Tuan and Gong Sunlong, emphasizing abstract mathematical ideas, such as "the greatest is the greatest, the smallest is the smallest", "one foot pestle, half a day, inexhaustible" and so on. Many mathematical propositions such as these definitions and limit ideas of geometric concepts are quite valuable mathematical ideas, but this new idea of attaching importance to abstraction and logical rigor has not been well inherited and developed.
In addition, the Book of Changes, which tells the gossip of Yin and Yang and predicts good and bad luck, has sprouted from combinatorial mathematics, reflecting the idea of binary system.
2. Early years of Han and Tang Dynasties
This period includes the mathematical development from Qin and Han Dynasties to Sui and Tang Dynasties 1000 years, and the successive dynasties were Qin and Han Dynasties, Wei, Jin, Southern and Northern Dynasties, Sui and Tang Dynasties. The Qin and Han Dynasties was the formation period of China's ancient mathematical system. In order to systematize and theorize the increasing mathematics knowledge, specialized mathematics books have appeared one after another.
There are two main achievements in mathematics in Zhou Bi suan Jing, an astronomical work compiled at the end of the Western Han Dynasty [the first century BC]: (1) put forward the special case and universal form of Pythagorean theorem; (2) Chen Zi's method of measuring the height and distance of the sun was a pioneer of gravity difference. In addition, there are more complicated root-finding problems and fractional operations.
Nine Chapters Arithmetic is an ancient mathematical classic that has been compiled and revised by several generations. Written in the early years of the Eastern Han Dynasty [1st century BC]. This book is written in the form of problem sets, and * * * collects 246 questions and their answers, which belong to nine chapters: Tian Fang, Xiaomi, Decline, Shaoguang, Work, Average Loss, Profit and Loss, Equation and Pythagoras. The main contents include four fractional and proportional algorithms, the calculation of various areas and volumes, and the calculation of pythagorean measurement. In algebra, the concept of negative number and the law of addition and subtraction of positive and negative numbers introduced in the chapter of equation are the earliest records in the history of mathematics in the world. The solution of linear equations in the book is basically the same as that taught in middle schools now. As far as the characteristics of Nine Chapters Arithmetic are concerned, it pays attention to the application and integration of theory with practice, and forms a mathematical system centered on calculation, which has had a far-reaching impact on the ancient calculation in China. Some of its achievements, such as decimal numerical system, modern skills and surplus skills, have also spread to India and Arabia, and through these countries to Europe, which has promoted the development of world mathematics. During the Wei and Jin Dynasties, China's mathematics developed greatly in theory. Among them, the work of Zhao Shuang and Liu Hui is regarded as the beginning of China's ancient mathematical theory system. Zhao Shuang was one of the earliest mathematicians who proved mathematical theorems and formulas in ancient China, and made detailed comments on Zhou Kuai Shu Jing. The Nine Chapters Arithmetic annotated by Liu Hui not only explains and deduces the methods, formulas and theorems of the original book as a whole, but also makes many innovations in the process of discussion, and even writes the island calculation method, which uses gravity difference technology to solve the problems related to measurement. One of Liu Hui's important tasks is to create secant, which lays a theoretical foundation for the study of pi and provides a scientific algorithm.
The society in the Southern and Northern Dynasties was in a state of war and division for a long time, but the development of mathematics was still vigorous. Sun Tzu's Art of War, Xiahou Yang's Art of War and Zhang Qiu's Art of War are all works of this period. Sun Tzu's mathematical classics give the problem that "things are unknown", which leads to the solution of a congruence group problem; The "Hundred Chickens Problem" in Zhang Qiujian suan Jing leads to three unknown indefinite equations.
The most representative works in this period are the works of Zu Chongzhi and Zu Rihuan. On the basis of Liu Hui's annotation of Nine Chapters Arithmetic, they greatly promoted traditional mathematics and became a model of attaching importance to mathematical thinking and reasoning. They also made outstanding contributions to astronomy. Their book seal script has been lost. According to historical records, they have made three great achievements in mathematics: (1) Calculate pi to the sixth place after the decimal point and get 3. 14 15926.
Large-scale architecture in Sui Dynasty objectively promoted the development of mathematics. In the early years of the Tang Dynasty, Wang Xiaotong wrote the Sutra of Ji Gu, which mainly discussed the calculation of earthwork in civil engineering, the division of labor and acceptance of engineering, and the calculation of warehouses and cellars.
The Tang Dynasty made great progress in mathematics education. In 656, imperial academy established a Mathematics Museum with doctors and teaching assistants in mathematics. Taishi ordered Li and others to compile and annotate ten calculation books (including Zhou Pi Ai Shu, Jiu Zhang Shu Shu, Dao Shu, Sun Zi Shu, Zhang Qiu Shu, Xiahou Yang Shu, Ji Gu Shu and Sun Zi Shu). It has played an important role in preserving ancient mathematical classics.
In addition, due to the need of calendar in Sui and Tang Dynasties, the quadratic interpolation method was established, which laid the foundation for the higher-order interpolation method in Song and Yuan Dynasties. In the late Tang Dynasty, computing technology was further improved and popularized, and many practical arithmetic books appeared, trying to simplify the multiplication and division algorithm.
3. Song and Yuan Dynasties
After the demise of the Tang Dynasty, the Five Dynasties and Ten Kingdoms remained the continuation of the warlord melee. Until the Northern Song Dynasty unified China, agriculture, handicrafts and commerce flourished rapidly, and science and technology advanced by leaps and bounds. 1 1 century to14th century (Song and Yuan Dynasties), computational mathematics reached its peak, which was the heyday of unprecedented prosperity and fruitful achievements in ancient Chinese mathematics. During this period, a number of famous mathematicians and mathematical works appeared, which are listed as follows: Jia Xian's Nine Chapters of the Yellow Emperor (165438+mid-20th century), Gu Gen Lun (65438+mid-2nd century), Shu Jiu Chapters (1247) and. Yang Hui's nine-chapter algorithm [126 1], daily algorithm [1262], Yang Hui's algorithm [1274- 1275] and Zhu Shijie's arithmetic enlightenment [65438] were numerous in the Song and Yuan Dynasties. The main tasks are:
The numerical solution of 1. higher order equation;
2. The celestial sphere method and quaternary method, that is, the legislation and solution of higher-order equations, are the first time in the history of Chinese mathematics to introduce symbols and use symbolic operations to solve the problem of establishing higher-order equations;
3. Find a technique that is greatly extended, that is, the solution of a set of congruences, now called China remainder theorem;
4. Recruitment superposition, that is, high-order interpolation and high-order arithmetic progression summation. In addition, other achievements include the new development of Pythagorean method, the research of solving spherical right triangle, the research of vertical and horizontal diagram [magic square], the concrete application of decimal, the appearance of abacus and so on. During this period, folk mathematics education also developed, and the exchange of mathematics knowledge between China and Islamic countries also developed.
4. Western learning input period
This period lasted more than 500 years from the establishment of the Ming Dynasty in the middle of14th century to the end of the Qing Dynasty in the 20th century. In addition to abacus, mathematics is in a weak state as a whole, involving the limitations of abacus, the deletion of mathematics content in the examination system of13rd century, the eight-stage examination system of Daxing in Ming Dynasty and other complex issues. Many Chinese and foreign historians of mathematics are still discussing the reasons involved. /kloc-At the end of the 6th century, western elementary mathematics began to be introduced into China, which led to the integration of Chinese and western mathematics research in China. After the Opium War, modern advanced mathematics began to be introduced into China, and China's mathematics turned into a period of mainly studying western mathematics. Until the end of19th century, China's research on modern mathematics really began.
The greatest achievement of the Ming Dynasty was the popularization of abacus, and many abacus readers appeared. It was not until the publication of Cheng Dawei's Command Arithmetic [1592] that the abacus theory became a system, marking the completion of the transition from compilation to abacus calculation. However, due to the popularity of abacus calculation, calculation almost disappeared, and ancient mathematics based on calculation gradually disappeared, and mathematics stagnated for a long time.
During the Sui Dynasty and the early Tang Dynasty, Indian knowledge of mathematics and astronomy was introduced to China, but it had little influence. By the end of16th century, western missionaries began to enter China and cooperated with China scholars to translate many western mathematical monographs. Among them, the first and most influential one is the first six volumes of Geometrical Elements translated by Italian missionaries Matteo Ricci and Xu Guangqi [1607], whose rigorous logical system and translation methods are highly praised by Xu Guangqi. Xu Guangqi's "Measuring Similarities and Differences" and "The Meaning of Pythagoras" applied the logical reasoning method of "Elements of Geometry" and demonstrated China's Pythagorean observation. In addition, most of the nouns in the textbook "Elements of Geometry" are the first and still in use today. In the imported western mathematics, trigonometry is second only to geometry. Before that, trigonometry had only sporadic knowledge, and then it developed rapidly. The works that introduce western trigonometry include Deiss [2 volumes, 163 1], the secant circle and eight-line table compiled by Deng [6 volumes], and giacomo Rowe's "Measuring Meaning" [10 volumes, 163 1]. In Xu Guangqi's almanac of Chongzhen (volumes 137, 1629- 1633), the mathematical knowledge about the curve of circular vertebra was introduced.
After entering the Qing Dynasty, Mei Wending, an outstanding representative of Chinese and Western mathematics, firmly believed that China's traditional mathematics must be refined, made in-depth research on ancient classics, and treated western mathematics correctly, which made it take root in China and had a positive impact on the climax of mathematics research in the middle of Qing Dynasty. Contemporary mathematicians include Wang Xizhi and Xirao Nian. Emperor Kangxi of the Qing Dynasty loved scientific research, and his Essentials of Mathematics [53 volumes, 1723] was a comprehensive elementary mathematics work, which had a certain influence on mathematical research at that time.
During the reign of Ganjia, the school of Ganjia, which was mainly based on textual research, compiled Sikuquanshu, in which the mathematical works included Ten Books of Calculating Classics and the works of Song and Yuan Dynasties, which made important contributions to the preservation of endangered mathematical classics.
In the research of traditional mathematics, many mathematicians have made inventions. For example, Jiao Xun, Wang Lai and Li Rui, who are called "three friends who talk about the sky", have done a lot of important work. Li obtained the summation formula of triangular self-riding crib in the Class of Stack Ratio [about 1859], which is now called "Lie identity". Compared with mathematics in Song and Yuan Dynasties, these works are an improvement. Ruan Yuan, Li Rui and others compiled a 46-volume Biography of Astronomers and Mathematicians [1795-1810], which initiated the study of the history of mathematics.
After the crow war of 1840, the closed-door policy was forced to stop. The second climax of translation and introduction began with the addition of "Arithmetic" in Wentong Pavilion and the addition of a translation pavilion in Shanghai Jiangnan Manufacturing Bureau. The main translators and works are: the last nine volumes of The Elements of Geometry [1857] jointly translated by Li and the English missionary William, giving China a complete Chinese translation of The Elements of Geometry; Algebra (13); The generation of micro products, volume 18 [1859]. Li and the English missionary Ai He translated 3 volumes of the Theory of Conic Curves, and Hua and the English missionary John Flair translated 25 volumes of Algebra [1872], 8 volumes of Tracing the Source of Differential Products [1874] and Doubts 10 [/kloc-]. In these translations, many mathematical terms and terms were created, which are still used today. 1898, Shi Jing University Hall was established and Wentong Museum was merged. 1905, the imperial examination was abolished and western-style school education was established. The textbooks used were similar to those of other western countries.
5. The development period of modern mathematics
This period is a period from the beginning of the 20th century to the present, which is often divided into two stages marked by the establishment of 1949 New China.
Modern mathematics in China started from studying abroad in the late Qing Dynasty and the early Republic of China. 1903 Feng Zuxun who studied mathematics earlier, 1908 Zheng who studied in America, 19 10 Hu Mingfu who studied in America,191/kloc-0. 19 13 Chen who studied in Japan and Xiong qinglai who studied in Belgium [19 15], Su et al. who studied in Japan 19 19. Most of them became famous mathematicians and mathematicians after returning to China, and made important contributions to the development of modern mathematics in China. Among them, Hu Mingfu received his doctorate from Harvard University in the United States on 19 17, becoming the first mathematician in China to receive his doctorate. With the return of foreign students, mathematics education in universities all over the world has improved. At first, there was only the Mathematics Department of Peking University1912; 1920, Jiang Lifu established the Department of Mathematics in Nankai University, Tianjin; 192 1 and 1926, Xiong Qinglai established mathematics departments in Southeast University [now Nanjing University] and Tsinghua University respectively, and soon established Wuhan University, cheeloo university University and Zhejiang University. 1930, Xiong Qinglai initiated the establishment of the Mathematics Research Department in Tsinghua University, and began to recruit graduate students. Chen Shengshen and Wu Daren became the earliest mathematics graduate students in China. In 1930s, [1927], [1934], Hua [1936] and Xu [1936] went abroad to study mathematics, and they all became the backbone of modern mathematics development in China. At the same time, foreign mathematicians also came to China to give lectures, such as Russell in Britain [1920], boekhoff in the United States [1934], osgood [1934], Wiener [1935] and Adama in France [/kloc-]. 1935 the inaugural meeting of chinese mathematical society was held in Shanghai, attended by 33 delegates. The publication of 1936 annals of chinese mathematical society and Journal of Mathematics marks the further development of modern mathematics research in China. Before liberation, mathematical research focused on the field of pure mathematics, and more than 600 theories were published at home and abroad. In terms of analysis, Chen's trigonometric series theory and Xiong Qinglai's research on meromorphic functions and whole functions are representative works, as well as functional analysis, variational methods, differential equations and integral equations; In the field of number theory and algebra, Hua's analytical number theory, geometric number theory, algebraic number theory and modern algebra have achieved remarkable results; In geometry and topology, Su's differential geometry, his algebraic topology, his fiber bundle theory and indicator theory have all done pioneering work: in probability theory and mathematical statistics, Xu obtained many basic theorems and strict proofs in univariate and multivariate analysis. In addition, Li Yan and Qian Baoyu initiated the study of the history of Chinese mathematics, and they did a lot of basic work in the annotation and textual research of ancient historical materials, which made our national cultural heritage shine again.
China Academy of Sciences was established in June 1949 1 1. March 195 1 reissue of China Mathematics Journal [1952 changed to Mathematics Journal], March 195 10 reissue of China Mathematics Journal [1953]. 1951August, the Chinese Mathematical Society held its first national congress after the founding of the People's Republic of China to discuss the development direction of mathematics and the reform of mathematics teaching in various schools.
Since the founding of People's Republic of China (PRC), great progress has been made in mathematical research. In the early 1950s, Hua's theory of heap primes [1953], Su's introduction to projective curves [1954], Chen's sum of series of rectangular functions [1954], and Li Yan's series on the history of middle arithmetic [65438] were published. In addition to continuing to make new achievements in number theory, algebra, geometry, topology, function theory, probability theory and mathematical statistics, history of mathematics and other disciplines, they have also made breakthroughs in differential equations, computing technology, operational research, mathematical logic, mathematical foundation and so on. Many of them have reached the world advanced level, and at the same time, they have trained and grown a large number of outstanding mathematicians.
At the end of 1960s, China's mathematics research basically stopped, education was paralyzed, personnel were drained, and foreign exchanges were interrupted. After many efforts, the situation has changed slightly. 1970, Mathematics Magazine was reissued, and Practice and Understanding of Mathematics was founded. 1973, Chen Jingrun published a paper "A big even number is expressed as the sum of the products of a prime number and no more than two prime numbers" in China Science, which made outstanding achievements in the research of Goldbach conjecture. In addition, mathematicians in China have some original opinions on function theory, Markov process, probability application, operational research and optimization methods.
1978 165438+ the third congress was held in the Chinese mathematical society on 10, which marked the revival of mathematics in China. 1978 National Mathematics Competition resumed, 1985 China began to participate in the International Mathematical Olympiad. 198 1 year, Chen Jingrun and other mathematicians won the National Natural Science Award. 1983, the state awarded the first batch of 18 young and middle-aged scholars with doctorates, among which mathematicians accounted for 2/3. 1986, China sent representatives to the international congress of mathematicians for the first time and joined the international mathematical union. Wu Wenjun was invited to give a 45-minute lecture on the history of ancient mathematics in China. In the past ten years, mathematical research has achieved fruitful results, and the number of published papers and monographs has doubled and the quality has been rising. At the annual meeting of 1985 to celebrate the 50th anniversary of the founding of chinese mathematical society, the long-term goal of mathematics development in China was determined. The delegates are determined to make unremitting efforts to make China a new mathematical power in the world at an early date.
Ancient Egyptian mathematics (ancient Egyptian mathematics)
The Nile valley in northeast Africa gave birth to Egyptian culture. From 3500 to 3000 BC, a unified empire was established here.
At present, our understanding of ancient Egyptian mathematics mainly comes from two papyrus written in the language of monks, one is Moscow papyrus written around 1850 BC, and the other is Rhine papyrus written around 1650 BC, also known as Ames papyrus. Ames's papyrus is rich in content. The Egyptian method of multiplication and division, the usage of unit fraction, the method of trial and error, the solution of the problem of circular area and the application of mathematics in many practical problems are described.
The ancient Egyptians used hieroglyphics, and their numbers were expressed in decimal system instead of value system, and there was a special fractional representation. The arithmetic established by the Egyptian number system has the characteristics of addition, and the multiplication and division operation can only be completed by constant doubling. The ancient Egyptians expressed all the scores in Huasong unit scores (the sum of scores with numerator 1). In Ames' cursive script, there is a big score table, and the score of 2/(2n+ 1) is expressed as the sum of unit scores, such as 2/5 = 1/3+ 1/60.
1/776 and so on.
The ancient Egyptians have been able to solve some problems that belong to the first equation and the simplest quadratic equation, as well as some preliminary knowledge about arithmetic progression and geometric series.
If Babylonians developed excellent arithmetic and algebra, on the other hand, it is generally believed that Egyptians were better at geometry than Babylonians. One view is that the Nile regularly floods once a year, flooding the valleys on both sides of the river. After the flood, Lao Wang wanted to redistribute the land, and the long-accumulated knowledge of land survey gradually developed into geometry.
Egyptians can calculate the area of a simple plane figure, and the calculated pi is 3.16049; They also know how to calculate the volumes of prisms, circles, cylinders and hemispheres. Among them, the most amazing achievement is to calculate the volume of the truncated pyramid, and the calculation process they gave is consistent with the modern formula.
As for the use of a lot of mathematical knowledge in the process of building pyramids and temples, Egyptians have accumulated a lot of practical knowledge, which needs to be upgraded to systematic theory.
Indian mathematics (Indian mathematics)
India is one of the earliest culturally developed regions in the world, and the origin of Indian mathematics, like other ancient peoples, is based on the actual needs of production. However, there is a special factor in the development of Indian mathematics, that is, its mathematics, like the calendar, has been fully developed under the influence of Brahman rituals. Coupled with the exchange of Buddhism and trade, Indian mathematics and mathematics in the Near East, especially in China, are advancing in mutual integration and promotion. In addition, the development of mathematics in India has always been closely related to astronomy, and most mathematical works have been published in some chapters of astronomical works.
Rope Sutra is a classic of ancient Brahmanism, probably written in the 6th century BC, and it is a religious work of great significance in the history of mathematics. It is about the geometric law embodied in the design of the altar by pulling the rope, and the Pythagorean theorem is widely used.
Since then, about 1000 years, due to the lack of reliable historical materials, little is known about the development of mathematics.
The 5th-12nd century witnessed the rapid development of mathematics in India, and its achievements played an important role in the history of mathematics in the world. During this period, some famous scholars appeared, such as Riyabuta in the 6th century, who wrote Arie Bo Li Shu. In the 7th century, Brahma Gupta wrote Brahma-Huta-Sidenta, which contained mathematics chapters such as Lecture Notes on Arithmetic and Lecture Notes on Indefinite Equations. Mahvera in the 9th century; /kloc-Bhaskara (the second one) in the 20th century wrote Siddh nta iromani, and the important parts of mathematics are Lil vati and V jaganita.
In India, the decimal notation of integers appeared before the 6th century. With nine numbers and a small circle representing zero, any number can be written with the help of a numerical system. They therefore established arithmetic operations, including four arithmetic rules of integers and fractions; Square root and publisher's rules, etc. For "zero", they not only regard it as "nothing" or vacancy, but also take it as a number to participate in the operation, which is a great contribution of Indian arithmetic.
This set of numbers and position symbols created by Indians was introduced into the Islamic world in the 8th century, and was adopted and improved by Arabs. At the beginning of the 3rd century, 65438 spread to Europe through Fibonacci's abacus book, and gradually evolved into 1, 2, 3, 4, … etc., which is still in use today and is called Indo-Arabic numerals.
India has made great contributions to algebra. They use symbols to represent algebraic operations and abbreviations to represent unknowns. They recognized negative numbers and irrational numbers, described four algorithms of negative numbers in detail, and realized that quadratic equations with real solutions have two forms of roots. Indians have shown outstanding ability in indefinite analysis. They are not satisfied with understanding only one indefinite equation, but are committed to finding all possible integer solutions. Indians have also calculated the sum of arithmetic series and geometric series, and solved business problems such as simple interest and compound interest, discount and partnership.
Indian geometry is based on experience. They don't pursue logical rigorous proof, but only focus on developing practical methods, which are generally related to measurement and pay attention to the calculation of area and volume. Their contribution is far less than their contribution in arithmetic and algebra. In trigonometry, Indians use half-chords (sine) instead of Greek full chords, make sine tables, prove some simple trigonometric identities and so on. Their research in trigonometry is very important.
Arabic mathematics
Since the ninth century, the center of mathematics development has shifted to Arabia and Central Asia.
Since the establishment of Islam in the early 7th century, it has rapidly formed a powerful force, and rapidly expanded to a vast area outside the Arabian Peninsula, spanning three continents: Europe, Asia and Africa. In this vast area, Arabic is the common official language, and Arabic mathematics here refers to mathematics learned in Arabic.
Since the eighth century, it takes about one to one and a half centuries to translate Arabic mathematics. Baghdad has become an academic center with a science palace, an observatory, a library and a college. Scholars from all over the world have translated a large number of classical works from Greece, India and Persia into Arabic. In the process of translation, many documents have been revised, verified and supplemented, and a large number of ancient mathematical heritages have been reborn. On the basis of accepting foreign cultures, Arab civilization and culture developed rapidly, and remained vigorous until the15th century.
〔Al-khowarizmi〕 was the most important mathematician in early Arabia. He wrote the first book introducing Indian numerals and Arabic symbols in the Islamic world. After12nd century, Indian numerals and decimal notation began to be introduced into Europe. After hundreds of years of reform, these numerals became the Indian Arabic numerals we use today. Another masterpiece by Hua Lazimi, The Algebra of ILM· al-Jabrwa 'lmugabalah, systematically discusses the solution of the quadratic equation in one variable, and the formula for finding the root of the equation first appeared in this book. The modern word "algebra" [algebra] also comes from "al jabr" in the title of the book.
Trigonometry plays an important role in Arabic mathematics, and its emergence and development are closely related to astronomy. Arabs developed trigonometry on the basis of the work of Indians and Greeks. They introduced several new trigonometric quantities, revealed their properties and relationships, and established some important trigonometric identities. All the solutions of spherical triangle and plane triangle are given, and many accurate trigonometric function tables are made. Among them, famous mathematicians are: Al-[Al-〔Al-Battani〕], Abu 'l-Wefa, [〔Al-Beruni〕] and so on. /kloc-Nasir-Ud-deen, a scholar in the 3rd century, wrote a systematic and complete treatise on trigonometry, which made trigonometry break away from astronomy and become an independent branch of mathematics, which had a great influence on the development of trigonometry in Europe.
In terms of approximate calculation, [〔Al-kashi〕] in15th century described the calculation method of pi in his Theory of Circles, and got that pi was accurate to16th place after the decimal point, thus breaking the record kept by Zu Chongzhi for 1000 years. In addition, Al Cassie has done important work on decimals, and he is also the first Arab scholar we know to deal with binomial theorem in Pascal's triangle form.
Arabic geometry is lower than algebra and trigonometry. Arabs do not accept the strict logical argument of Greek geometry.
Generally speaking, Arabic mathematics lacked creativity, but at that time, most parts of the world were in a period of scientific poverty and made great achievements. What is commendable is that they have served as the preservers of a great deal of spiritual wealth in the world, which returned to Europe only after the dark ages passed. Europeans mainly know the mathematical achievements of ancient Greece, India and China through their translations.
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