Pi is the ratio of circumference length to diameter length. This is an infinite acyclic decimal, that is to say, it is an endless decimal, and the change of each digit is irregular. Usually, when calculating, we set pi to 3. 14 16, which is actually slightly larger than pi. Zu Chongzhi determined pi between 3. 14 15926 and 3. 14 15927 years ago, which is much more accurate than 3. 14 16. A thousand years after him, an Arab mathematician broke this accuracy record.
Pi is hard to calculate. We know that only by drawing a regular polygon inscribed in a circle and calculating the total side length of this regular polygon can we get the approximate value of the circle. The more sides of a regular polygon, the closer the total side length is to the perimeter. Zu Chongzhi must start with a circle inscribed with a regular hexagon, first calculate the side length of the inscribed regular hexagon 12, then calculate the side length of the inscribed regular hexagon, and then calculate the side length of the inscribed regular hexagon 48 ... The number of sides will double again and again, until the side length of 12288 regular hexagons is calculated.
It seems simple to double the number of sides inscribed with regular polygons, but it is not. Every time you double the number of edges, you have to perform at least seven operations, including addition and subtraction, two powers and two roots.
The result calculated by Zu Chongzhi has six decimal places, so it is estimated that he should keep at least twelve decimal places in the operation. Addition and subtraction are simple, the power of twelve decimal places. Especially calculating the square root is extremely troublesome.
Without skilled technology and strong perseverance, Zu Chongzhi could not have completed these hundreds of complicated operations.
Before Zu Chongzhi, it was suggested that pi was close to 22/7. Zu Chongzhi called 22/7 "sparsity" and proposed another approximate value of pi, 335/ 1 13, as "density" because it is more accurate and closer to pi. One thousand years later, Otto, a German, and Antuoni, a Dutchman, successively put forward the approximate value of pi of 335/ 1 13. Europeans didn't know that Zu Chongzhi put forward the "secret rate" at that time, so they called it "Antoine rate" in the history of mathematics they wrote. Japanese mathematicians call 335/ 1 13 "ancestral rate", which is quite fair.
Zu Chongzhi's grandfather and father are very good at astronomical calendars. Zu Chongzhi loved astronomical calendars since childhood, and often observed the movements of the sun, moon and stars in the sky and made detailed records. He found that there were still some mistakes in the Yuan family calendar adopted at that time. The direction of the sun and moon, the existence of planets and the time of winter solstice and summer solstice are not accurate. He compiled a new calendar called Daming Calendar. Zu Chongzhi was only 33 years old.
One of the achievements of "Da Liming" is to take care of "precession" for the first time. It turns out that every time the earth goes around the sun, the winter solstice will move back a little, that is, to the west, which is called precession. Astronomers in Jin Dynasty first discovered precession. After careful observation and research, Zu Chongzhi calculated that the precession is once every 45 years 1 1 month (in ancient China, Sunday was divided into 365 and a quarter degrees).
Now we know that precession is caused by the wobble of the earth's axis, and it retreats every 7 1 year and 8 months. Zu Chongzhi's grasp of astronomical historical materials is not rich enough and accurate enough, and mistakes are inevitable. He calculated the precession in the calendar, which is a revolution in the calendar. Li Yuanjia has seven leap months every seventeen years. The Da Ming Calendar compiled by Zu Chongzhi was changed to-1year, which is much more accurate than the Yuan Jia calendar.
In 462 ad. Zu Chongzhi asked Liu Jun, Emperor Xiaowu of Song Dynasty, to issue "Da Li Ming", and Liu Jun had a favorite named Dai Faxing, who came out to oppose it. Zu Chongzhi, with his profound knowledge and practical experience, refuted the difficulties made by Daifaxing. Dai Faxing finally said arrogantly: "The calendar was handed down from ancient times and cannot be changed. If you change it, you will blaspheme against heaven and betray your ancestors. " Zu Chongzhi fearless, best decission said, "if you have something solid basis, just say it. Empty talk can't scare me. " Dai Faxing refuted with arguments. The ministers agreed with Dai Faxing for fear of offending him. There is only one person on Zu Chongzhi's side. Chao Shangzhi checked four eclipses in recent years, which proved that Zu Chongzhi's method was accurate, while Dai Faxing's method was quite different. He insisted on Zu Chongzhi's Da Li Ming. The debate lasted for nearly two years, and Emperor Xiaowu of Song decided to promulgate the Ming calendar next year. Unexpectedly, when he died that year, things were put on hold.
Later dynasties changed and Zu Chongzhi died. His son, Zuxuan, asked for imperial edicts many times. It was not until 5 10 that Xiao Cai Yan of Liang Wudi officially promulgated and adopted the Daming Calendar. At this point, Zu Chongzhi has been dead for 10 years.
Zu Chongzhi has also made great achievements in machinery manufacturing. The compass made by Ma Jun of Wei State was lost in the war of Jin State. In the Northern and Southern Dynasties, Shi Hu and Yao Xing, the rulers of the Northern Dynasties, ordered courtiers to make the South Guide Car, but the things made could only be used as decorations in the honor guard.
In 478 AD, Zu Chongzhi rebuilt a bronze compass car. No matter how the car turns, the copper man in the car always points south.
Zu Chongzhi saw that it was difficult for farmers to grind rice and grain, so he tried water hammer mill in Leyou Garden. In spring, he used hydraulic rotary stone mill to grind rice and grain. This kind of water hammer mill is still widely used in rural areas of China.
There are many rivers in the south, and boats are important means of transportation. Zu Chongzhi built a ship with a distance of thousands of miles, which was tried on the river and could sail 100.
Zu Chongzhi's scientific achievements will shine forever in the history of China's scientific and technological development. His spirit of assiduous study, earnest study, courage to create and persistence in truth is worth learning.