Zu Chongzhi's biography of Zu Chongzhi was born in Jiankang (now Nanjing) in 429 (the sixth year of Yuanjia in the Southern Song Dynasty), and his ancestral home was in Qixian County (now Laishui County, Hebei Province). At the end of the Western Jin Dynasty, a large-scale war broke out in the north, and Zu Chongzhi's ancestors migrated from Hebei to the south of the Yangtze River to settle down. Zu Chongzhi was born in Jiangnan. His grandfather Zuchang was a great craftsman of Liu in Song Dynasty. He is an official in charge of civil engineering in the imperial court. His father, Zushuo, is knowledgeable and often invited to attend royal ceremonies and banquets.
Zu Chongzhi received a good family education from an early age. Grandpa told him "The Stars Move", his father led him to read the classics, his family's edification and his own diligence made him interested in natural science, literature, philosophy, especially astronomy, and he gained a reputation for erudition in his youth.
Early experience
Zu Chongzhi once said in his works that he began to "specialize in mathematics and search for the past and the present" from a very young age. He collected almost all documents, records and materials from ancient times to the present. At the same time, it is advocated that we should never "falsely push the ancients", never tie ourselves to the outdated wrong conclusions of the ancients, and make accurate measurements and careful calculations in person. As he himself said, he often "looks at the ruler, looks at the instrument and tries his best to make plans."
Because of Zu Chongzhi's well-read reputation, he was sent to Hualin University, an academic research institution of the imperial court at that time, by Emperor Xiaowu of the Southern Song Dynasty to do research work, and later worked in Zongmingguan. At that time, Zongmingguan was the highest scientific research academic institution in China, equivalent to the current China Academy of Sciences. There are five disciplines: literature, history, Confucianism, Taoism and Yin and Yang, which are taught in different categories. Zu Chongzhi is one of them. Here, Zu Chongzhi came into contact with a large number of ethnic books, including astronomy, calendars, arithmetic and other books, which provided a prerequisite for reference and expansion.
Focus on science
46 1 year (the fifth year of the Southern Song Dynasty and the early Ming Dynasty), Zu Chongzhi worked in the secretariat office in the south of Xuzhou (now Zhenjiang, Jiangsu Province), and served as an official and a government official to join the army. During this period, although Zu Chongzhi's life was very unstable, he still persisted in academic research and made great achievements.
In 462 (the sixth year of the Southern Song Dynasty and the Ming Dynasty), Zu Chongzhi presented the carefully compiled Daming Calendar to Emperor Xiaowu of Song Dynasty for promulgation and implementation. Emperor Xiaowu of Song ordered officials familiar with the calendar to discuss the advantages and disadvantages of this calendar. Finally, Emperor Xiaowu decided to adopt a new calendar in the ninth year of the Ming Dynasty (465).
In 464 (the sixth year of the Southern Song Dynasty and the early Ming Dynasty), Zu Chongzhi was transferred to Lou County (now the northeast of Kunshan County, Jiangsu Province) as county magistrate. Later, he went to Jiankang (now Nanjing, Jiangsu) and served as a servant shooting officer. From then on, until the early years of the Southern Dynasties, he spent a lot of energy on the research of mechanical manufacturing, recreated a compass driven by copper pieces, invented a "thousand-mile boat" and a "wooden ox and flowing horse" that could run for hundreds of miles a day, and designed and manufactured a clepsydra (ancient timer) and ingenious devices.
Old age life
Zu Chongzhi's later years coincided with the late Southern Qi Dynasty, with sharp contradictions within the ruling class, political darkness and social unrest. In this case, Zu Chongzhi's research direction has changed greatly. He focuses on literature and social sciences, but he also cares about politics.
From 494 (the first year of Longchang in the Southern Dynasty) to 498 (the fifth year of Jianwu in the Southern Dynasty), he served as a captain of Changshui. At that time, he wrote "On Security", suggesting that the government reclaim wasteland, develop agriculture, enhance national strength, stabilize people's livelihood and consolidate national defense. When Emperor Qi Ming saw it, he asked him to "travel around the world, make great achievements and benefit the people", but Nanqi's rule could no longer be maintained. The crumbling state power, coupled with years of wars in the Northern and Southern Dynasties, made it impossible for Zu Chongzhi's good political ideas to be implemented within the country, let alone realized.
In 500 (the second year of Qi Yongyuan in the Southern Dynasty), this outstanding great scientist died at the age of 72. His painstaking astronomical calendar book Da was published in the name of Jia in the ninth year (5 10).
A pioneering work in the history of mathematics-"ancestral rate"
Zu Chongzhi calculated the true value of pi (π) between 3. 14 15926 and 3. 14 15927, which is equivalent to being accurate to the seventh decimal place and simplified to 3.141. Therefore, Zu Chongzhi was ranked first in the world record association world. Zu Chongzhi also gave two fractional forms of pi: 22/7 (approximate rate) and 355/ 1 13 (density rate), in which the density rate is accurate to the seventh decimal place. Zu Chongzhi's accurate calculation of pi is a great contribution to China and even the world. Later generations named him "Zu Chongzhi Pi".
Pi is widely used, especially in astronomy and calendar. All problems involving circles should be calculated by pi. How to correctly calculate the value of pi is an important topic in the history of mathematics in the world. Ancient mathematicians in China attached great importance to this problem and began to study it very early. The ratio of the ancient diameter to one week and three weeks was put forward in Parallel Calculation of Weeks and Nine Chapters Arithmetic, and the pi was set at three, that is, the circumference of a circle was three times the diameter. Since then, after successive explorations by mathematicians of past dynasties, the calculated pi value has become more and more accurate.
The pi calculated by Zhang Heng in the Eastern Han Dynasty was 3. 162. The pi calculated by Wang Fan during the Three Kingdoms period was 3. 155. Liu Hui, a famous mathematician in Wei and Jin Dynasties, created a new method to calculate pi when he annotated Nine Chapters Arithmetic. The value of pi divided by the side length is approximately 3. 14. It shows that this value is less than the actual value of π. After Liu Hui, scholars who have made great achievements in exploring pi have successively included He Chengtian, Pi Yanzong and others in the Southern Dynasties. He Chengtian's pi is 3. 1428, and Pi Yanzong's pi is 22/7≈3. 14.
Zu Chongzhi thinks that Liu Hui is a scholar who has made the greatest achievements in the study of pi during the hundreds of years from Qin and Han Dynasties to Wei and Jin Dynasties, but it has not reached an accurate level, so he makes further in-depth research in order to find a more accurate value.
According to the record of π (π) in the Annals of Sui Calligraphy: "At the end of the Song Dynasty, South Xuzhou engaged in the history of Zu Chongzhi and opened a more secret method. The diameter of the circle is 100 million, the circumference of the circle is three feet four inches, one minute five minutes nine seconds seven seconds, and the number is three feet one foot four inches five minutes nine minutes two seconds six seconds. The positive number is between the surplus and the limit. Density, circle diameter 1 13, circumference 355. Regarding the rate, the diameter of the circle is seven, and it is on the 22nd of the week. " Zu Chongzhi changed a 10-foot into a 100-million-foot, and took this as the path to find pi. He calculated the result of * * * and got two numbers: one is the abundant remainder (approximate value of surplus), which is 3.1415927; One is the number (that is, the approximate value of the loss), which is 3. 14 15926.
These two numbers can be listed as inequalities, such as: 3. 14 15926 (*).
Zu Chongzhi's research on pi has positive practical significance, and his research meets the needs of production practice at that time. He personally studied weights and measures and revised the ancient calculation of measuring volume with the latest pi results. In ancient times, there was a measuring instrument called "kettle", which was generally one foot deep and cylindrical. Zu Chongzhi got an accurate value by his research on pi. He also recalculated the "law quantity" created by Liu Xin in Han Dynasty, and revised the value with "ancestral rate". In the future, people will use Zu Chongzhi's "ancestral rate" value when making measuring instruments.
Mathematical masterpiece "Composition"
Zu Chongzhi composed five volumes of music, which were included in the famous Ten Books of Computing Classics. Sui Shu commented that "scholars can't study its profundity, so they don't pay attention to it", and thought that the theory of Zhuanshu was very abstruse and the calculation was quite precise, so it was difficult for scholars with high knowledge to understand its contents. At that time, it was the most difficult book in mathematical theory.
In his creation, Zu Chongzhi raised the issues of "distraction" and "distraction position". The word "difference power" is found in the note of Liu Hui's Nine Chapters Arithmetic, which refers to the difference in area. "Open variance power" is the difference between the area and the length and width of a known rectangle, and its length and width are calculated by the method of square root. Its concrete solution is to solve the positive root problem with quadratic algebraic equations. And "deviation" means knowing the difference between the volume and the length, width and height of a cuboid, and finding its side length by drawing a square; At the same time, it also includes the problem of knowing the volume of cylinders and spheres and finding their diameters. The calculation method adopted is to solve the positive root problem with cubic equation. The solution of cubic equation has never been done before, and Zu Chongzhi's solution is a pioneering work.
"Seal script" also spread to North Korea and Japan, and was mentioned in the ancient education system and bibliography of North Korea and Japan.
In the Biography of Chu Yan in the History of Song Dynasty, it is said that the calculations in Nine Chapters, Ancient Collection, Composition and Island are particularly wonderful. Tiansheng (1023- 103 1) made a new calendar first.
Debate on People's Behavior Calendar
In 462 (the sixth year of the Southern Song Dynasty and the Ming Dynasty), Zu Chongzhi presented the carefully compiled Da Li Ming to Emperor Xiaowu of Song Dynasty for promulgation and implementation. Emperor Xiaowu of Song ordered officials familiar with the calendar to discuss the advantages and disadvantages of this calendar. During the discussion, Zu Chongzhi was opposed by Dai Faxing, and Zu Chongzhi refuted it in the article Yi Lee. In Li Yi, he wrote two famous sayings: "I am willing to listen and give evidence, I am willing to check the facts" and "I am afraid of stealing words." In order to distinguish right from wrong, he is willing to produce obvious evidence to discuss with the other party, and he is not afraid of those unfounded accusations. Dai Faxing believes that the way to continue the tradition in the calendar is "the ancient man-made chapter", "the world is not easy"; He called Zu Chongzhi "false chanting" and thought that the astronomical calendar was "too numerous for people to measure" and "you should not make mistakes lightly". Zu Chongzhi defy spirit. He retorted that we should not "believe in the past and doubt the present". If "the ancient method is sparse, it should be commonly used", what is the truth! The movement of the sun, the moon and the five stars is "non-supernatural, tangible and measurable". As long as accurate observation and research are carried out, Mencius said that "it is possible to sit at the age of chitose".
Strive for perfection
In Zu Chongzhi's time, abacus did not appear, and the commonly used calculation tool was called calculation. It is a square or flat stick several inches long, made of bamboo, wood, iron, jade and other materials. Different calculation and financing methods are used to represent various numbers, which is called financing algorithm. If there are more digits, the larger the area needs to be placed. It is not like using a pen to calculate with a calculation formula, it can be left on paper, and every time the calculation is completed, it must be swung again to make a new calculation; You can only write down the calculation results with notes, and you can't get more intuitive graphics and formulas. So as long as there are errors, such as calculation errors or calculation errors, we can only start from scratch. In order to get the accurate value of pi, Zu Chongzhi needs to calculate the decimal of nine significant figures, including more than ten steps of addition, subtraction, multiplication, division and square root operation, and each step has to be repeated for more than ten times and 50 times of square root operation, and finally the calculated number reaches 16 or 17 digits after the decimal point.
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