Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. On the basis of predecessors' achievements, he obtained a more accurate value of pi through repeated calculations, which was called "ancestral rate" by foreign mathematical historians.
Zu Chongzhi's grandfather Zuchang is a man of great scientific and technological knowledge. He used to be a master craftsman in the court of the Southern Dynasties and the Song Dynasty, and was responsible for presiding over construction projects. Grandpa often tells him stories about scientists, among which the story of Zhang Heng, a great scientist in the Eastern Han Dynasty, inventing the seismograph deeply touched Zu Chongzhi's young mind.
Zu Chongzhi often goes to the construction site with grandpa. In the evening, he enjoys the cool in the country and plays with the children. There are many stars in the sky, but rural children can name the stars, such as Altair, Vega and the Big Dipper. At this time, Zu Chongzhi felt that he really knew too little.
Zu Chongzhi doesn't like reading ancient books. At the age of five, his father taught him to learn The Analects of Confucius, and he could only recite more than 10 sentences in two months. Father is very angry. But he likes math and astronomy.
One night, he was lying in bed thinking that the teacher said during the day that "the circumference is three times the diameter" seemed wrong. The next morning, he took a rope that his mother used to make shoes and ran to the roadside at the head of the village to wait for a passing car.
After a while, a carriage came. Zu Chongzhi stopped the carriage and said to the old man driving, "Let me measure your wheels with a rope, ok?"
The old man nodded.
Zu Chongzhi measured the wheel with a rope, folded the rope into three sections with the same size, and then measured the diameter of the wheel. After measuring it, he always felt that the diameter of the wheel was not "one third of the circumference".
Zu Chongzhi stood on the side of the road and measured the diameters and perimeters of several carriage wheels continuously, and reached the same conclusion.
Why on earth is this? The problem has been haunting him. He is determined to solve the mystery. With the growth of age, Zu Chongzhi's knowledge is getting richer and richer. He began to study Liu Hui's "Circumcision".
Zu Chongzhi highly praised Liu Hui's scientific method, but Liu Hui's pi only got a regular 96-sided result, so it was no longer calculated. Zu Chongzhi is determined to calculate the polygon with positive 192 side and the quadrilateral with positive 380 side step by step along the road initiated by Liu Hui, so as to obtain more accurate results.
At that time, the number operation was not calculated with paper, pens and numbers, but with small sticks arranged vertically and horizontally, and then calculated by an abacus-like method.
Zu Chongzhi drew a big circle with a diameter of ten feet on the floor of the room, made a regular hexagon in it, then spread out many sticks made by himself and began to calculate.
At this time, Zu Chongzhi's son Zuxuan 13 years old also helped his father to work together. It took them more than 10 days to calculate the regular hexagon, and the result was less than that of Liu Hui.
0.000002 sheets. Zu Xuan said to his father, "We calculated it very carefully. This must be true. Maybe Liu Hui is wrong. " Zu Chongzhi shook his head and said, "To overthrow him, there must be a scientific basis." So, father
The two sons spent more than ten days recalculating, which proved that Liu Hui was right. In order to avoid further errors, Zu Chongzhi will repeat the calculation at least twice in each step until the results are exactly the same.
Zu Chongzhi is a polygon with positive 12288 side to a polygon with positive 24576 side, and the difference between them is only 0.00438+0. Zu Chongzhi knew that the calculation could be continued in theory, but it could not be done in practice, so he had to stop, thus drawing the conclusion that pi must be greater than 3. 14 15926 and less than 3. 14 15927. This achievement made him the first scientist in the world to calculate the value of pi to more than 7 digits at that time. It was not until 1000 years later that the German mathematician Otto came to the same conclusion.
Zu Chongzhi's success was related to the social background at that time. He lived in the Southern Song Dynasty during the Southern and Northern Dynasties. Due to the social stability in the Southern Dynasties, agriculture and handicrafts made remarkable progress, and the economy and culture developed rapidly, which also promoted scientific progress. At that time, some accomplished scientists appeared in the Southern Dynasties, among which Zu Chongzhi was one of the most outstanding figures.
Zu Chongzhi's main contribution to mathematics is to calculate more accurate values of pi. Pi is widely used, especially in astronomy and calendar. All problems involving circles should be calculated by pi. Therefore, how to correctly calculate the value of pi is an important topic in the history of mathematics in the world.
The earliest value of pi obtained by working people in ancient China in production practice is "3", which is of course inaccurate, but it has been used until the Western Han Dynasty. Later, with the development of astronomy, mathematics and other sciences, more and more people studied pi.
At the end of the Western Han Dynasty, Liu Xin first abandoned the inaccurate pi value of "3", and the pi he once adopted was 3.547. Zhang Heng of the Eastern Han Dynasty also calculated pi as 3. 1622.
Of course, these values have made great progress compared with "3", but they are far from accurate. It was not until the end of the Three Kingdoms that mathematician Liu Hui created the method of secant to find pi, and the research on pi made great progress.
However, judging from the mathematical level at that time, there was no better method except Liu Hui's cyclotomy. When Zu Chongzhi increased the number of sides of a circle inscribed with a regular polygon to 24,576 polygons, his result was just 3. 14 15926.