China was an outstanding mathematician and astronomer in the Southern and Northern Dynasties. The word Wen Yuan.
Born in Yuanjia, Song Wendi for six years (429), he died in Houyongyuan, Jidong for two years (500). His ancestral home was in Kuai County, Fanyang County (now Laiyuan County, Hebei Province), and he moved from Hebei to Jiangnan because of the war. Grandfather was a great craftsman in Liu and Song Dynasties and an official in charge of civil engineering. Father was invited to the court, knowledgeable and respected. Zu Chongzhi entered Hualin University in his youth to engage in academic research and activities. Before his death, he was an official in South Xuzhou (now Zhenjiang), engaged in history, joined the army in the government, made orders in Lou County (now northeast of Kunshan County), worshipped servants, and served as a captain in Changshui.
Zu Chongzhi's main contribution to mathematics is the calculation of pi. According to Sui Shu's law, he calculated that the true value of π□ is between 3. 14 15926(□ number) and 3. 14 15927 (abundance number). These two approximations are accurate to the seventh place after the decimal point, which is the most advanced achievement in the world at that time. It was not until the15th century that Arabian mathematician Cassie and French mathematician F. Veda got more accurate results. Zu Chongzhi determined the value of □ in two fractional forms: approximate ratio of 22/7(≈3. 14) and density ratio of 355/13 (≈ 3.1415929). These two values are asymptotic fractions of π, and the secret rate is 355/ 1 13, which was rediscovered by V. Otto of Germany and A. Antuoni of the Netherlands in the 6th century. Zu Chongzhi and his son Zu □ successfully solved the problem of calculating the volume of the ball, got the correct formula of the volume of the ball, and put forward the "Zu □ principle" called by later generations. Seal script, one of the ten famous classic books on calculation, was listed as an arithmetic textbook by imperial academy in the Tang Dynasty, and it was stipulated that it should be studied for four years, but it has been lost.
On the astronomical calendar, Zu Chongzhi created the Daming calendar, and introduced precession into the calendar at the earliest, which was a great progress of the ancient calendar in China. Adopt accurate new leap weeks of 39 1 year and 144 leap months. The data used by Da Liming are quite accurate, such as tropical years (365.2428), months and days of intersection (27.2 1223), the period of revolution of Jupiter and the rendezvous period of the five planets. It also invented a method to determine the time of winter solstice by measuring the noon shadow length of several days before and after the winter solstice with a standard table, which was also adopted by later generations for a long time. In the sixth year of Song Xiaowu (462), Zu Chongzhi wrote to the government of Liu Song, demanding the promulgation and implementation of Da Li Ming, but was attacked by Dai Faxing, the then minister. He thinks that Zu Chongzhi introduced precession and reformed leap week, which violates Confucian classics and blames Zu Chongzhi.
It is "fake chanting." Zu Chongzhi wrote a rebuttal paper tit for tat. He expressed a clear stand of "willing to listen to evidence and verify facts" and "talking nonsense and stealing without fear", and answered Dai Faxing's accusation with scientific reasons. He used observation facts to prove that due to precession, the astronomical phenomena he saw at that time were indeed different from those before the Spring and Autumn Period reflected by Confucian classics, and
The length of the tropic year is indeed less than the length of the four-year calendar. These astronomical facts are "tangible and verifiable", and people cannot "believe in the past and doubt the present".
Zu Chongzhi is also a well-read scientist, who also has research on all kinds of machinery. He has designed and manufactured a water hammer mill (a tool for processing grain by hydraulic power), a copper-driven compass, a "thousand-mile boat" that can travel hundreds of miles a day, and some land vehicles. He also designs and manufactures timepieces-leaky jars and ingenious devices.
In addition, Zu Chongzhi is also proficient in temperament, and even wrote a ten-volume novel "Tales of Different Stories".
He has written many books, among which Sui Shu Jing Ji Zhi recorded 51 volumes of Zu Chongzhi Collection, a captain of Changshui. Scattered in various historical records are: Zhuanshu, Notes on Nine Chapters of Arithmetic, Daming Calendar, Refuting Dai Faxing to Play Chapters, Bian Bian Lun, Yi Shuoji, Interpretation of the Analects of Confucius, Yijing, Laozi and Zhuangzi. But most of them
All the books are lost. Zu Chongzhi's son Jing Shuo was a famous mathematician and astronomer in the Southern Dynasties. At that time, Liang was a foreign assistant minister, a magistrate, a prefect of Nankang, a general of material officer, and was invited by the imperial court. Zu-has received a good family education since he was a child, and he made great achievements in astronomy and mathematics when he was young. He is the successor of Zu Chongzhi's scientific career, and Composition is a mathematical masterpiece jointly completed by his father and son. The "Zu Kai Yuan Method" cited in Li's note in Nine Chapters of Arithmetic Shaoguang records in detail the method that Grandfather solved the problem of sphere volume. Chapter 9 The old technique mistakenly thought that the ratio of the volume of the ball to the circumscribed cylinder was the ratio of the circle to the square, that is, □:4, so its formula for the volume of the ball was equivalent to □ (□ is the diameter of the ball), which was obviously incorrect. Liu Hui first discovered this mistake and pointed out that the ball and the circumscribed "square cover" (diameter □
* * * Part, Figure 1) The volume ratio is □:4, but he failed to find out the volume of the square cover. However, Grandfather solved this problem, and clearly put forward the axiom of "the same potential leads to different products" in the calculation process (that is, the cross-sectional areas of two solids at the same height are constant, so the volumes of the two solids are equal), which is the later "Zu □ principle". This principle was not rediscovered by Italian mathematician (F.) B. cavalieri until17th century. According to the Zu□ principle, the volume of the Mohamad square cover can be converted into the difference between the volumes of a cube and a quadrilateral (the Mohamad square cover with the dotted line of 1/8 on the left in Figure 2 is equal to the volume of a cube and a quadrilateral according to the Zu □ principle, so that the volume of the Mohamad square cover is equal to □, and the volume of the ball is obtained □ (. Zu □ wrote to the government of Liang for three times and suggested the use of Da Ming Li, which was finally adopted and promulgated in nine years (565,438+00), realizing Zu Chongzhi's unfinished wish. He also personally supervised the construction of an eight-foot copper watch, measured the length of the sun shadow, and found that Polaris was different from the fixed point of the northern celestial pole more than once, which corrected the wrong view that Polaris was the north pole of the celestial sphere. For the need of studying astronomy and accurate timing, he also studied and improved the common timer at that time-the broken kettle wine, and wrote a volume of "Missing Engraving Classics" (lost).
Zu's life is not smooth. In the 13th year of Liang Wudi Tian Jian (5 14), he was appointed as General Cai Guan and was ordered to build a floating weir. In the autumn of the 15th year of Tian Jian (May16), he was imprisoned because the newly-built dam was washed away by the flood. After he was released from prison, he stayed in the shogunate and King Liang for six years (525). Because of rebellion, he was detained by Wei and stayed at Yanming Hotel in Wei 'anfeng County, Xuzhou. During this period, he discussed astronomy and mathematics with Xin, a scientist in the north at that time. In the ordinary seven years, Zu was released to the Southern Dynasties. In his later years, he participated in Seven Records (a bibliography work) compiled by Liang, and was in charge of astronomy, astrology, map latitude and other ancient books. He also wrote 30 volumes of astronomical records, only some fragments, scattered in the Tang Dynasty's Kaiyuan Zhan Jing and other books.