Chinese math has those famous formulas and theorems

Calculation is an ancient Chinese calculation tool, the real meaning of the ancient Chinese mathematical system was formed in the period of three or four hundred years from the Western Han Dynasty to the Northern and Southern Dynasties. The Book of Arithmetic, written in the early years of the Western Han Dynasty, is the earliest surviving Chinese mathematical monograph, which was discovered by archaeologists in 1984 in the Han Dynasty bamboo slips unearthed at Zhangjiashan in Jiangling, Hubei Province. The Zhou Thigh Calculating Scripture, compiled in the late Western Han Dynasty, is an astronomical work on the theory of "Covering the Sky," but it includes two mathematical achievements - (1) a special or universal form of the collinearity theorem ("If one seeks the evil to the sun, the sun is lower than the sun, and the sun is higher than the sun, the sun is higher than the sun. If one seeks the evil to the sun, take the sun's lower part as the sentence, the sun's higher part as the stock, multiply the sentence and the stock by each, and divide it by the square, then one gets the evil to the sun." --This is the earliest written record of the collinearity theorem in China); (2) "Chen Zi's method of measuring the sun's height or distance".

The Nine Chapters of Arithmetic occupies a very important place in the development of ancient Chinese mathematics. It has been organized by many people and was written around the time of the Eastern Han Dynasty. The book ****collects 246 mathematical problems and provides their solutions. The main contents include the four rules of fractions and the proportionality algorithm, calculations of various areas and volumes, calculations on the measurement of hooks and strands, and so on. In terms of algebra, Nine Chapters on Arithmetic was the first book in the history of world mathematics to introduce the concept of negative numbers and the rules for adding and subtracting positive and negative numbers; the solutions to systems of linear equations taught in secondary schools nowadays are more or less the same as those introduced in Nine Chapters on Arithmetic. The focus on practical application is a distinctive feature of The Nine Chapters on Mathematics. Some of the book's knowledge also spread to India and Arabia, and even through these regions as far as Europe.

The Nine Chapters of the Art of Arithmetic marks the formalization of the ancient Chinese mathematical system based on the calculation of chips.

Ancient Chinese mathematics focused on theoretical research during the Three Kingdoms and the Two Jin dynasties, with Zhao Shuang and Liu Hui as the main representatives.

Zhao Shuang's academic achievements were reflected in his interpretation of the Zhou Thigh Calculating Classic. He also used geometric methods to prove the collinearity theorem in his Notes on the Circle and Square Diagrams, which in fact embodied the method of the Principle of Cutting and Patching. Solving quadratic equations by geometrical methods was also one of Zhao Shuang's major contributions to ancient Chinese mathematics. During the Three Kingdoms period, Liu Hui of Wei annotated the Nine Chapters of the Mathematical Art, and his work Nine Chapters of the Mathematical Art not only explains and deduces the methods, formulas, and theorems of the Nine Chapters of the Mathematical Art, but also systematically elaborates the theoretical system and mathematical principles of traditional Chinese mathematics, and has many creations. His invention of "Circle Cutting" (the area of a square polygon inside a circle is infinitely close to the area of a circle) laid the foundation for the calculation of pi, and Liu Hui also calculated the approximate value of pi - "3927/1250 ( 3.1416)". He designed the geometric model of "Mouhe square cover", which laid an important foundation for later generations to seek the formula for the volume of the ball. In the process of studying the volume of polyhedra, Liu Hui used the limit method to prove the "Yangmaji". In addition, the Hai Dao Shu Jing is also a mathematical treatise compiled by Liu Hui.

The North and South Dynasties were a period of vigorous development of mathematics in ancient China, and there were mathematical works such as Sun Zi Shu Jing, Xiahou Yang Shu Jing, and Zhang Qiu Jian Shu Jing.

The work of Zu Chongzhi and Zu Yi was the most representative of this period. They focused on mathematical thinking and mathematical reasoning, and took a step forward on the basis of their predecessor Liu Hui's Nine Chapters of Arithmetic. According to historical records, their work "Suffixing Art" (which has been lost) made the following achievements: ① Circumference was accurate to the sixth decimal place, obtaining 3.1415926<π<3.1415927, and the approximate rate of π was found to be 22/7, and the dense rate was found to be 355/113, of which the dense rate was the optimal value for numerator and denominator within 1,000; in Europe, it was not until the 16th century that the Germans Ordnance (Otto) and the Dutch Antoine (Holland) made the mathematical reasoning and the mathematical reasoning. Otto) and the Dutch Anthonisz (Anthonisz) until the 16th century in Europe to reach the same result. ② Zu Yi derived the formula for the volume of a sphere on the basis of Liu Hui's work, and put forward the theorem that if the cross-sectional areas of two three-dimensional bodies at equal heights are equal, then the volumes of the two bodies are equal ("if the power potentials are the same, then the products cannot be different"); in Europe, it was the Italian mathematician Cavalieri who put forward the same theorem in the 17th century... ...Zu's father and son meanwhile contributed to astronomy.

The main achievement of the Sui and Tang dynasties was the establishment of the Chinese mathematical education system, which was probably mainly related to the establishment of the Arithmetic Hall in the State Academy and the imperial examination system. At that time, the Ten Books of Arithmetic became a specialized textbook for students. The Ten Books of Arithmetic collected 10 mathematical works, such as Zhou Thigh Arithmetic, Nine Chapters of Arithmetic, and Sea Island Arithmetic. So the system of mathematics education at that time had a positive significance in inheriting the ancient mathematical classics.

In 600 A.D., Liu Zhuo of the Sui Dynasty was the first in the world to put forward the equidistant quadratic interpolation formula when he formulated the "Imperial Calendar"; and the monk line of the Tang Dynasty developed it into the unequal spacing quadratic interpolation formula in his "Dayan Calendar".

From the 11th century to the 14th century Song, Yuan period, is to calculate the main content of the ancient Chinese mathematics of the heyday of the performance of this period is the emergence of many outstanding mathematicians and mathematical works. Ancient Chinese mathematics takes Song and Yuan mathematics as the highest level. In the world, Song and Yuan mathematics is also almost in the leading group together with Arabic mathematics.

Jia Xian in the "Huang Di nine chapter algorithm fine grass" proposed to open any higher power of the "multiplication of the open method", the same method until 1819 by the British Horner found; Jia Xian's binomial theorem coefficients table and 17th-century Europe appeared in the "Barsga triangle" is similar. The table of coefficients of Jia Xian's binomial theorem is similar to "Basga's triangle" which appeared in Europe in the 17th century. Unfortunately, Jia Xian's book manuscript of "The Nine Chapters of the Yellow Emperor's Algorithm" has been lost. Qin Jiushao was an outstanding mathematician in the Southern Song Dynasty, and in 1247 he popularized the "method of multiplying and opening" in his "Nine Chapters of the Book of Numbers", discussed the numerical solution of higher equations, and cited more than 20 solutions of higher equations (up to ten equations) drawn from his practice, while in the 16th century the Italian Fierro proposed the solution of cubic equations. The solution of cubic equations was only proposed by the Italian Philo in the 16th century. In addition, Qin Jiushao also studied the theory of one congruent equation.

Li Ye published "Measuring the Circle and Sea Mirror" in 1248, which was the first work to systematically discuss "Tianyuan jutsu" (higher quadratic equations of one element), and is a milestone in the history of mathematics. What is particularly rare is that in the preface of this book, Li Ye openly criticized the long-standing fallacies of the cab winds, such as belittling the practical activities of science and reducing mathematics to "cheap skills" and "playthings".

In 1261 A.D., Yang Hui of the Southern Song Dynasty (birth and death dates unknown) used the "stacking technique" to find the sums of several types of higher-order arithmetic series in "The Algorithm of the Nine Chapters". In 1274 A.D., he also described the "Jiu Gui Jie Fa" in the "Multiplication and Division Tong Chang Ben Mou" (The End of Multiplication and Division), which introduced various algorithms of multiplication and division in calculations. In 1280 A.D., when the Yuan Dynasty's Wang Xun and Guo Shoujing formulated the "Calendar of the Time", they listed the interpolation formula of the third difference. Guo Shoujing also used geometric methods to find two formulas equivalent to the present spherical triangle.

In 1303 A.D., Zhu Shijie of the Yuan Dynasty (date of birth and death unknown) wrote Four Elements of Yujian, in which he popularized the technique of Tianyuan into the technique of Quaternary (four elements of the higher quadratic equations) and proposed the solution of elimination of elements. In Europe, it was not until 1775 AD that the Frenchman Bezout proposed the same solution. Zhu Shijie also carried out research on the sum of each finite term level problem, on the basis of which the interpolation formula of the higher difference was derived, Europe to the Englishman Gregory (Gregory) in 1670 AD and Newton (Newton) between 1676 and 1678 AD to put forward the general formula of interpolation.

After the establishment of the Ming Dynasty in the mid- to late 14th century, the rulers practiced the imperial examination system characterized by the eight-legged essay, and drastically reduced the mathematical content of the national imperial examination, so that since then the ancient Chinese mathematics began to show a total decline.

Bead counting became popular in China during the Ming Dynasty, and in 1592, Cheng Dawit compiled the "Direct Algorithm of Unification of the Zong," a work that combined the best of the theory of counting. However, it has been argued that the popularization of bead counting was one of the main reasons that inhibited the further development of ancient Chinese mathematics, which was built on the foundation of arithmetic.

Because of the need to calculate the astronomical calendar, some Western mathematical knowledge was introduced to China by Western missionaries from the late 16th century. Mathematician Xu Guangqi learned Western mathematics from Italian missionary Matteo Ricci, and they also jointly translated the first six volumes of the Original Geometry (completed in 1607). Xu Guangqi applied Western logical reasoning to justify the Chinese art of hook and strand surveying, and thus wrote two works, Measuring Differences and Similarities and The Meaning of Hook and Strand. Deng Yu-hsin compiled The Great Measurement [2 volumes], The Table of Eight Lines of the Cutting Circle [6 volumes], and Luo Ya-gu's Measurement of the Whole Meanings [10 volumes], which are works that introduce Western trigonometry.