Zu Chongzhi (429-500), Wen Yuan, was a famous mathematician and astronomer in the Northern and Southern Dynasties. Zu Chongzhi's ancestral home is Kuai County, Fanyang County (now Laishui, Hebei Province). In order to escape the war, Zu Chongzhi's grandfather, Zuchang, moved from Hebei to Jiangnan. Zuchang was once a "great craftsman" in Liu Song, in charge of civil engineering; Zu Chongzhi's father is also a DPRK official. Zu Chongzhi was born in Jiankang (now Nanjing, Jiangsu). Generations have been studying astronomical calendars, and Zu Chongzhi has been exposed to astronomical and mathematical knowledge since childhood. Zu Chongzhi gained a reputation as a learned man when he was young. When Emperor Xiaowu of Song heard about it, he sent him to "Hualin Xue Province" for research. 46 1 year, worked in the secretariat of southern Xuzhou (now Zhenjiang, Jiangsu), and successively served as a historian and government official in southern Xuzhou to join the army. In 464 AD, he was transferred to Lou County (now northeast of Kunshan, Jiangsu Province) as county magistrate. During this period, he compiled Da Li Ming and calculated pi. At the end of the Song Dynasty, Zu Chongzhi returned to Jiankang as a servant. After that, he spent a lot of energy studying mechanical manufacturing until the demise of the Song Dynasty. From 494 to 498, he served as a captain of Changshui in the Southern Qi Dynasty and received four salaries. In view of the constant war at that time, he wrote "On Security" and suggested that the imperial court reclaim wasteland, develop agriculture, stabilize people's livelihood and consolidate national defense. Zu Chongzhi died at the age of 72. Zu Chongzhi's major achievements are in mathematics, astronomical calendar and mechanical manufacturing. In addition, it is recorded in history that Zu Chongzhi is proficient in temperament and good at playing chess, and he also wrote the novel "A Record of Different Stories". Zu Chongzhi wrote a lot, but most of them have been lost. Zu Chongzhi's son Zu Xuan is also a mathematician. To commemorate this great ancient scientist, people named a crater on the back of the moon "Zu Chongzhi Crater" and the asteroid 1888 "Zu Chongzhi Asteroid". Mathematically, Zu Chongzhi studied Nine Chapters Arithmetic and Liu Hui's Annotation, and annotated Nine Chapters Arithmetic and Liu Hui's Heavy Difference. He is also the author of Composition, which brings together the mathematical research results of Zu Chongzhi and his son. This book is so profound that "scholars can't study its profundity, so they ignore it." Seal script was included in Ten Arithmetic Classics in the Tang Dynasty, and became a textbook of imperial academy in the Tang Dynasty. It took four years to learn seal script at that time, which shows the difficulty of seal script. Seal script was once spread to Korea, but it was lost in the Northern Song Dynasty. People can only know part of Zu Chongzhi's work through other documents: there is a brief record of Zu Chongzhi's study of pi in the Legal Records of Sui Shu; In the Tang Dynasty, Li recorded the method of Zu Chongzhi's father and son to find the volume of the ball in "Nine Chapters Arithmetic Notes". Zu Chongzhi also studied the problems of "open difference power" and "open difference station", which involved the problem of finding the roots of quadratic equation and cubic equation. Zu Chongzhi's mathematical contributions are mainly his calculation results of pi and the formula of sphere volume. [Editor] Calculating pi According to the records in the calendar of Sui calligraphy, Zu Chongzhi changed a ten-foot into a hundred-million-foot, and used this as the diameter to find pi, and the abundance (exceeding the approximate value) was 3.1415927; The approximate value of loss is 3. 14 15926, and the true value of pi is between profit and loss. Sui Shu did not specify how Zu Chongzhi calculated its surplus. It is generally believed that Zu Chongzhi adopted Liu Hui's secant technique, but there are many other speculations. Zu Chongzhi's result was accurate to the seventh place after the decimal point. It was not until more than a thousand years later that Al Cassie, a mathematician in15th century, and Veda, a French mathematician in16th century, broke this record. According to the habit of calculating and using fractions at that time, Zu Chongzhi also adopted pi of two fractional values: approximate ratio of 22/7 (or sparse ratio) and density ratio of 355/ 1 13. Among all integral fractions with denominator less than 1000, the ratio of density is the closest to pi, indicating that Zu Chongzhi may have obtained this ratio through some calculation. Mathematician Hua once thought that getting this secret ratio indicated that Zu Chongzhi might have mastered the concept of continued fraction. In Europe, it was not until16th century that German Otto and Dutchman Antuoni worked out the ratio of 355/13. Therefore, in order to commemorate this great mathematician in ancient China, Japanese mathematician Kazuo Sanshi suggested that 355/ 1 13 be called "ancestral rate". [Editor] Calculating the volume of a sphere Zu Chongzhi and his son Zuxuan solved the problem of calculating the volume of a sphere with ingenious methods. In Nine Chapters of Arithmetic, it is considered that the ratio of the volume of a circumscribed cylinder to the volume of a sphere is equal to the ratio of the area of a square to its inscribed circle. Liu Hui pointed out in the annotation for Nine Chapters Arithmetic that the statement in the original book is incorrect, only the ratio of the cover of a square (the volume of the same part where two cylinders intersect vertically) to the volume of a sphere is exactly equal to the ratio of the area of a square and its inscribed circle. However, Liu Hui did not give the volume formula of "Mouhe Square Cover", so he could not get the volume formula of the sphere. Zu Chongzhi and his son adopted "if the situation is the same, the products cannot be different." . (that is, "the volumes of two solids with the same cross-sectional area must be equal"), the volume of the square cover is calculated, and the volume of the sphere is equal to π/4 times that of the square cover, so that the final volume of the sphere is πd3/6(d is the diameter of the sphere). Zu Chongzhi and his son adopted the principle of "if the potentials are the same, the products cannot be different", which was rediscovered in Europe by Italian mathematician cavalieri (B. cavalieri, 1598- 1647) in the17th century, so the western literature generally called this principle cavalieri principle. In order to commemorate the great contribution of Zu Chongzhi and his son in discovering this principle, people also call it "Zuqiu principle". [Editor] Astronomical Calendar Contribution Zu Chongzhi's achievements in astronomical calendar are mostly contained in his Da Ming Calendar and his criticism of Da Ming Calendar. Before Zu Chongzhi, the calendar used by people was Li Yuanjia compiled by astronomer He Chengtian. After years of observation and calculation, Zu Chongzhi found that Li Yuanjia had great errors. So Zu Chongzhi set out to make a new calendar. In the sixth year of Song Xiaowu (AD 462), Da Ming Li was compiled. Daming Calendar was never adopted before Zu Chongzhi's death, and it was not officially promulgated until the 9th year of Tian Jian, Liang Wudi (AD 5 10). The main achievements of Daming Calendar are: distinguishing the tropic year from the sidereal year, introducing precession into the calendar for the first time, and measuring that the 45-year age difference is 1 1 month difference is one degree (about 70.7 years difference today). The introduction of precession is a great progress in the legal history of China. A tropical year is set at 365.24 148 1 (today's measurement is 365.2425438+09878), which is the most accurate data until Yang Zhongfu made a unified calendar in the fifth year of Qingyuan, Ningzong, Southern Song Dynasty (A.D. 1 199). The new leap week of 39 1 year (144 leap) is more accurate than the leap week of 19 year (7 leap) adopted in the previous calendar. The fixed intersection days are 27.2 1223 days (currently estimated as 27.2 1222 days). Accurate measurement of the number of months and days at the intersection makes it possible to accurately predict solar and lunar eclipses. Zu Chongzhi calculated the time of the four eclipses in the 23 years from the 13th year of Yuanjia (AD 436) to the 3rd year of Daming (AD 459) with Da Ming Li, and the results were completely in line with the reality. It is concluded that Jupiter overtakes the sun once every 84 years, that is, the period of revolution of Jupiter is 1 1.858 years (currently measured as 1 1.862 years). A more accurate five-star rendezvous period is given, in which the rendezvous period of mercury and Jupiter is also close to the modern value. A method of determining the winter solstice time by measuring the length of the noon sun shadow with a standard table is put forward. [Editor] Contribution of Machinery Manufacturing Zu Chongzhi also designed and manufactured many exquisite machines, which are recorded in the biographies of South Zu Chongzhi and Zu Chongzhi. He once designed and manufactured a water hammer mill that used water to grind rice and flour; Recasting the lost south guide car at that time, no matter how the car turns, the bronze man on the car always points south; A "Thousand-Li Ship" was built and put on trial on the Xinting River (now southwest of Nanjing), and it can sail 100 Li every day. He also designs and manufactures timing instruments, such as clepsydra and throwers. [Editor] The Annals of Sui Shu Classics recorded the 5 1 volume The Collection of Zu Chongzhi, a captain of Changshui, but it has been lost. Scattered in various historical records, there are the following works: "On Security", which has been lost. Ten volumes of Yi Shuoji have been lost. Yi Shi, Ilo Zhuang, has fallen. The annotation on filial piety in The Analects of Confucius has been lost. The six volumes of seal script have been lost. Nine volumes of Interpretation of Nine Chapters have been lost. The book "Notes on Heavy Difference" has been lost. Da Li Ming, Da Li Ming Biao, refute, open circle 2007-09-05 15:28:46 Supplement: Pi, generally expressed by π, is a common mathematical constant in mathematics and physics. It is defined as the ratio of the circumference to the diameter of a circle. It is also equal to the ratio of the area of a circle to the square of its radius. Accurate calculation of geometric shapes such as circle perimeter, circle area and sphere volume is the key value. In the analysis, π can be strictly defined as the smallest positive real number x satisfying sin(x) = 0, where sin is a sine function (defined by the analysis). The commonly used decimal approximation of π is 3. 14 15926, and the reduction ratio and density ratio given by Zu Chongzhi: 2007-09-05 15:29:56. Supplement: In the experimental period, China ancient book says: "The Road on Wednesday is one", which means "The Road on Wednesday is one". The Egyptian ancient book Ames papyrus (Ahmes, also known as "Ames papyrus document") in the 0/7th century BC; It was discovered by an Englishman Henry Rhind in 1858, so it is also called "Rhind Grass Piece Literature"), which is the earliest approximate value of pi in the world, and it is 256/81(= 3+1/9+1/27+. Before Archimedes, the measurement of π value depended on physical measurement.

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Zu Chongzhi was born in Jixian County, Fanyang in the Southern and Northern Dynasties (409-502 BC). He obtained the circumference of a hexagon inscribed in a circle by secant technique, and calculated the values of pi between 3. 14 15926 and 3. 14 15927. He used 22/7 as the approximate rate and 355/ 1 13 as the secret rate. These results predate the West by centuries. You know, at that time, there were only calculation tools, and the calculation work was very heavy. Because he is not afraid of hardship, he has strong perseverance to achieve this brilliant result. Zu Chongzhi calculated the side length of a regular hexagon to 28,672 after the decimal point in order to find the exact value of the seventh decimal place of pi, which is a great achievement. There are three points that deserve our attention. He did it himself, because you can't get the first to eighth decimal places. At the same time, another person got the ninth to sixteenth place ... The abacus used now only appeared in the twelfth century, and there was no abacus in the Zu Chongzhi era, which shows the hardships of prescribing. It is impossible for Zu Chongzhi to use * * * numbers, which were introduced to China in the 3rd century. You can imagine their troubles. Zu Chongzhi is not only a mathematician, but also an astronomer, writer and mechanical inventor. In astronomy, he put forward the best calendar at that time, Daming Calendar, and calculated that the time required for the earth to go around the sun was 365.38+04438+0 days. Now the data obtained by the instrument is 365.222 days, and his number is accurate to three decimal places. He also calculated that the moon's orbit around the earth is 27.2 1223 days, which is now recognized as 27.2 1222 days, with an error of 1 with the fifth decimal place. More than a thousand years ago, his achievements were worthy of our pride. He also invented the south guide car, the water hammer mill, the thousand-mile boat, and successfully manufactured a vehicle similar to Zhu Gekongming's "wooden ox and flowing horse", from which we can see how smart Zu Chongzhi is. Zu Chongzhi was not proud when he was alive. Not only was there no official to do it, but he didn't see the adoption of Daming Calendar before his death. The most regrettable thing is that the seal script, which records his and his son's mathematical achievements, was lost in the Song Dynasty. Today, there are many mountains named after great scientists on the moon. Zu Chongzhi is one of them and the only one in China. This shows how great he is!

Reference:. Geographical City /benny wong 16/ Juchong Pool