Zu Chongzhi (429-500) was born in Wen Yuan. Jiankang (now Nanjing) was an outstanding mathematician and astronomer in the Southern and Northern Dynasties.
Zu Chongzhi studied natural science all his life, mainly contributing to mathematics, astronomical calendar and mechanical manufacturing. On the basis of exploring the accurate method of pi pioneered by Liu Hui, he first calculated the "pi" to the seventh place after the decimal point, that is, between 3. 14 15926 and 3. 14 15927. His "ancestral rate" has made great contributions to mathematical research. It was not until the 6th century A.D./KLOC-that the Arab mathematician Al Cassie broke this record.
The Daming Calendar written by him was the most scientific and progressive calendar at that time, which provided a correct method for future astronomical research. His main works are In the Frontier, Composition, Explaining Words, Li Yi and so on.
Mathematical achievement
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 thought that Liu Hui was the most accomplished scholar in the study of pi during the hundreds of years from Qin and Han Dynasties to Wei and Jin Dynasties, but it did not reach an accurate level, so he made 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. [
Content of primary school mathematics handwritten newspaper: Zu Chongzhi approved.