Chapter 28 Section 8 Pi and Zu Chongzhi

Before the Han Dynasty, China generally used three as the value of pi, that is, "three diameters one".This is a big error when calculating the circumference and area of ​​​​a circle.Although many mathematicians and astronomers in the Han Dynasty adopted different values ​​of pi, none of them established a rigorous scientific calculation method.The first mathematician who proposed scientific calculation methods was Liu Hui. When he commented on "Nine Chapters of Arithmetic" in the fourth year of Wei Jingyuan (AD 263), he created the "circle cutting technique", which pushed the calculation of pi to a new height.This method uses the concept of limit to solve practical problems and breeds the idea of ​​using finiteness to approach infinity, which is an important achievement in the history of world mathematics.

The so-called "circle cutting technique" means that when the number of sides of a regular polygon inscribed in a circle increases continuously, its circumference gets closer and closer to the circumference of the circle. ", when the number of sides of a regular polygon inscribed in a circle is infinite, its perimeter is the perimeter of the circle.This method only needs to use the area of ​​the regular polygon inscribed in the circle to calculate pi, and does not need to calculate the area of ​​the regular polygon circumscribed in the circle, which greatly simplifies the calculation process.Liu Hui applied this method, counting from the regular hexagon inscribed in a circle, and gradually doubling the number of sides until he calculated the area of ​​the regular 192-gon inscribed in a circle, and obtained the approximate value of π as 3.14.Another approximate value π=(3927)/(1250) (equivalent to 3.1416) may also be calculated by Liu Hui, which was the best data in the world at that time.

Zu Chongzhi during the Southern and Northern Dynasties, on the basis of Liu Hui's work, advanced the calculation of pi to the highest peak in the ancient world.He used the "circle cutting technique" to find out the pi that is accurate to the seventh significant figure, 3.1415926http://www.99lib.net The calculation of pi is only one contribution of Zu Chongzhi. His scientific and technological achievements are many-sided, and he can be regarded as an outstanding mathematician, astronomer and mechanical manufacturer at that time. Zu Chongzhi, courtesy name Wenyuan, was originally from Fanyangqiu (qiuqiu) County, Hebei Province (now Laishui County, Hebei Province), and his family moved south to Jiankang (now Nanjing) during the Southern and Northern Dynasties.He was born in 429 AD and died in 500 AD.His family, starting from his great-grandfather, mostly studied astronomy, calendar, and mathematics. Under the influence of the family atmosphere, Zu Chongzhi was very interested in these sciences since he was a child. He studied hard, observed astronomical phenomena, and made calculations. .

In addition to pi, Zu Chongzhi's other important contribution in mathematics is to create the correct formula for finding the volume of a sphere: sphere volume=4/3π×(radius)3.This was also achieved through the joint research of Zu Chongzhi and his son Zu Jun [geng Geng Qu] on the basis of Liu Hui's work.In the process of research, Zu's father and son applied the axiom that "two solids with equal cross-sectional areas at equal heights must have equal volumes".This axiom was not cited in Europe until the 17th century by the Italian mathematician Cavalieri.Zu Chongzhi also wrote the book "Zishu", which was listed as one of the 10 Sutras in the Tang Dynasty.It is a pity that because its content is too profound, it was discarded by academic officials and lost.

In terms of astronomy, Zu Chongzhi boldly pointed out the shortcomings of the previous calendars, and proposed calendar reforms. In the sixth year of Liu Song Daming (AD 462), he completed the formulation of the new calendar "Daming Calendar".The Ming Dynasty introduced the precession difference into the calendar for the first time, and changed the seven leaps in 19 years to 144 leaps in 391 years, thus making the calendar more precise. At the same time, Zu Chongzhi also made brilliant achievements in machinery.He has made a compass car that "turns endlessly, and the direction is like one" ("The Book of Southern Qi: The Biography of Zu Chong"), a ship that "travels more than a hundred miles a day" ("The Book of Southern Qi: The Biography of Zu Chong"), and used Water-driven stone mills for pounding rice and grain mills, etc.

In order to commemorate Zu Chongzhi's outstanding contribution in science and technology, the international astronomy community named a crater on the back of the moon "Zu Chongzhi Crater".