How did Zu Chongzhi get pi?

Pi is widely used in production practice. In ancient times when science was not very developed, the calculation of pi was quite complicated and difficult. Therefore, the theory and calculation of pi reflect the mathematical level of a country to some extent. In the 5th century, Zu Chongzhi, an outstanding mathematician in China's Southern and Northern Dynasties, used the wood cutting method founded by Liu Hui to calculate pi more accurately and made brilliant achievements.

According to Sui Shu's record of this law, Zu Chongzhi determined that the approximate value of pi is 3. 14 15926, and the approximate value of pi is 3. 14 15927, and the true value is between these two approximate values. According to the modern calculation method, if calculated by the secant method, the side length of the polygon inscribed by 12288 must be found, and the area is 24576 to get 3. 14 15927. The pi calculated in this way can be accurate to 7 decimal places. In ancient China, calculation was based on calculation. Therefore, it is a very arduous and complicated calculation work to do hundreds of operations of addition, subtraction, multiplication, division and square root for 9-digit numbers, and properly select the effective digits to ensure the accurate error range. Obviously, only by mastering skilled theories and skills and having a down-to-earth and indomitable research spirit can we achieve such outstanding achievements. Zu Chongzhi's short approximation and multiple approximation of pi are accurate to 7 decimal places, which makes him the first person in the history of the world to accurate pi to 7 decimal places. Using these two approximations to calculate can not only meet certain accuracy requirements, but also be very simple. It was very advanced in the world at that time, which marked the highly developed mathematical level in ancient China and made a great contribution in the history of world mathematics. It was not until 1000 years later that the Arab mathematician Al Cassie worked out a more accurate value in 1427' s Key to Arithmetic, and the French mathematician violette worked out a more accurate value from 1540 to 1603.

According to the habit of using fractions in calculation at that time, Zu Chongzhi also adopted two fractional values of pi. One is 355/ 1 13, which is relatively accurate, so Zu Chongzhi calls it "secret rate". The other is 22/7, which is rough, so Zu Chongzhi called it "approximate rate". Among them, the secret rate is the best value within 1000. In Europe, it was not until 1573 that German mathematician Otto and Dutchman Antuoni reached the same conclusion. Therefore, Japanese mathematician Mishima suggested that the value of pi of 355/ 1 13 be called "ancestral rate" to commemorate China, a great mathematician.

Zu Chongzhi's research achievements are world-renowned: the wall of the Discovery Palace Science Museum introduces the pi obtained by Zu Chongzhi, the corridor of the Moscow University Auditorium is inlaid with a marble statue of Zu Chongzhi, and there is a crater named after Zu Chongzhi on the moon. ...