The pi calculated by Zu Chongzhi and Zhang Heng in the Eastern Han Dynasty is 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.
On the basis of Liu Hui's scientific method of finding pi by secant, Zu Chongzhi adopted the secret method, and after repeated calculations, he got pi of 3.1415927 &; gt； π& amp； gt； 3. 14 15926。 This was the most accurate numerical value in the world at that time, and he became the first person in the world to make Pi accurate to the seventh place after the decimal point. It was not until 1000 years later that this record was broken by Europeans. The calculation of pi is Zu Chongzhi's outstanding contribution in mathematics. Some mathematicians abroad call π "ancestral rate".
In the calendar of Daming Calendar, Zu Chongzhi introduced the concept of precession for the first time, which made the calendar more accurate. This is the second major calendar reform in China.
Also known as "Jia Zi Yuan Li". Advanced calendars in the Southern and Northern Dynasties. Zu Chongzhi's creation. The length of the first lunar month used in Daming Calendar is 29.5309 days, which is less than one second different from that measured by modern astronomical means. In Da Li Ming, Zu Chongzhi proposed inserting 144 leap month into 39 1. According to the length of the new leap week and the new moon, we can find that the annual length of the tropic of cancer in Daming calendar is 365.438+04438+0 days, which is only about six ten thousandths of the annual length of the tropic of cancer measured in modern times, that is to say, there are only more than 50 seconds in a year, which is very accurate information. The winter solstice is the starting point of making a calendar, so it is very important to determine its position in the sky for making a calendar. However, before Zu Chongzhi, calendar mathematicians always thought that the position of the winter solstice was fixed, which made the calendar formula wrong from the beginning. Therefore, after Zu Chongzhi introduced the concept of precession into the calendar, the accuracy of calendar calculation was greatly improved.
meaning
This is the second major reform in the history of China. First, the leap method is improved, and the leap of the old calendar proposed by astronomer He Chengtian is changed from every 19 7 to every 39 1 year 144, which is more in line with the reality of astronomical phenomena. For the first time in China, the so-called "moon-crossing" day is set at 27.2 12223, which is very close to the modern measured data (27.438+0220). Second, precession is considered within the duration of the system, with a difference of one hundred years. The so-called "intersection moon" means that the route of the moon running on the celestial body has two intersections (also called yellow and white intersection), and the time when the moon passes through the same intersection twice is called intersection. After the completion of the calendar, it was presented to Liu Jun, Emperor Xiaowu of Song Dynasty, but it was suppressed and opposed by Dai Faxing and others. Zu wrote Li Yi to refute it. Ten years after the ancestors died, that is, nine years of imprisonment (AD 5 10) was executed for 80 years. "Biography of Books and Documents in Southern Qi Dynasty": "The calendars made by He Chengtian in Jiazhong, Song and Yuan Dynasties are more dense than those made by the ancient eleven schools, and they think that they are still sparse, so they are new (Daming Calendar)." "Sui Calendar": "By the first month of nine years, the new moon was issued in Zu Chongzhi's Jiazi Yuan calendar ... Chen's calendar was also made in Zu Chongzhi's calendar, and nothing changed."