Chinese celebrities – Zu Chongzhi

Zu Chongzhi (429-500 years), written by Wenyuan, was born in Qiuxian County, Fanyang County (now Laishui County, Hebei Province), and was an outstanding mathematician and astronomer during the Northern and Southern Dynasties.
Born in Fan Yang Zu clan. He has studied natural sciences all his life, and his main contributions are in mathematics, astronomical calendar, and mechanical manufacturing. Based on Liu Hui’s precise method of exploring Pi, he actuated the “pi” to the seventh decimal place for the first time, that is, between 3.1415926 and 3.1415927. The “Zu rate” he proposed has a significant contribution to the study of mathematics. It was not until the 16th century that Arab mathematician Al Qassim broke this record.
The “Da Ming Calendar” written by him was the most scientific and advanced calendar at that time, and it provided a correct method for astronomical research in later generations. His main works include “A Bian Lun”, “Zhu Shu”, “Shu Yi Ji”, “Lian Yi” and so on.
Zu Chongzhi stele

Main influence


A Pioneering Work in the History of Mathematics-“Zu Shi”
Zu Chongzhi calculated that the true value of Pi (π) is between 3.1415926 and 3.1415927, which is equivalent to the 7th decimal place, simplified to 3.1415926. So Zu Chongzhi was selected as the world’s first scientist who calculated the value of Pi to 7th decimal place by the World Record Association . . Zu also gives pi ([pi]) in the form of two fractions: 22/7 ( about rate ) and 355/113 ( density ratio ), wherein the adhesion rate is accurate to 7 decimal places. Zu Chongzhi’s accurate calculation of the value of Pi is a major contribution to China and the world. Later generations named the “Yue Rate” after him as “Zu Chong’s Pi”, or ” Zu Rate ” for short.
The application of pi is very wide, especially in astronomy and the calendar. All problems involving the circle must be calculated by using the pi. How to correctly calculate the value of Pi is an important topic in the history of world mathematics. Ancient Chinese mathematicians attached great importance to this problem, and the research was also very early. In ” Zhou Tu Suan Jing ” and ” Nine Chapters Arithmetic “, the ancient ratio of diameter one week to three weeks is proposed, and the fixed circumference ratio is three, that is, the circumference of the circumference is three times the length of the diameter. Since then, after successive explorations by mathematicians of the past generations, the calculated value of Pi has become more and more accurate.
The value of Pi calculated by Zhang Heng in the Eastern Han Dynasty was 3.162. During the Three Kingdoms period, Wang Fan calculated the value of Pi to be 3.155. Liu Hui, a famous mathematician in the Wei and Jin Dynasties, created a new method of calculating pi when he made a note for “Nine Chapters Arithmetic”—circle-cutting. The value of pi is divided by the length of the side by 2, and its approximate value is 3.14, and explain This value is smaller than the actual value of Pi. After Liu Hui, some scholars were successful in exploring Pi, such as He Chengtian and Pi Yanzong in the Southern Dynasties. The value of Pi obtained by He Chengtian is 3.1428, and Pi Yanzong obtained the value of Pi as 22/7≈3.14.
Zu Chongzhi believes that the scholar who has studied Pi with the greatest achievement in the hundreds of years from the Qin and Han Dynasties to the Wei and Jin Dynasties is Liu Hui, but he has not reached the level of accuracy, so he further researched and explored more precise values.
According to the record of “Sui Shu · Lv Li Zhi” on the pi (π): “At the end of the Song Dynasty, Southern Xuzhou engaged in Shizu Chongzhi, and changed the density method. The circle diameter is 100 million yuan, and the circumference is three feet and four inches. One minute, five cents, nine milliseconds, seven moments, one minute, three feet, one foot, four inches, one minute, five cents, nine milliseconds, six moments, and a positive number is between the two limits of Yingju. The secret rate, the diameter of the circle is one hundred and thirteen. , The circumference is three hundred and fifty-five. Approximately, the diameter of the circle is seven, and it is twelve on Tuesday.” Zu Chongzhi converted one meter to 100 million, huh, using this as the diameter to find the pi. The result of his calculation is a total of two numbers: one is the surplus (that is, the approximate value of surplus), which is 3.1415927; the other is the surplus (that is, the approximate value of insufficient), which is 3.1415926.
The two numbers of surplus can be listed as inequalities, such as 3.1415926(*)<π(true pi)<3.1415927 (surplus), which indicates that the pi should be between the two numbers of surplus. According to the habit of using fractions for calculations at the time, Zu Chongzhi also used two fractional values ​​of pi. One is 355/113 (approximately equal to 3.1415927). This number is more precise, so Zu Chongzhi called it the “secret rate.” The other is 22/7 (approximately equal to 3.14). This number is relatively rough, so Zu Chongzhi called it the “approximate rate .”
Zu Chongzhi’s research on pi has positive practical significance, and his research adapted to the needs of production practice at that time. He personally studied weights and measures and used the latest Pi results to modify the calculation of the volume of ancient measuring instruments. In ancient times, there was a kind of measuring instrument called a “kettle”, which was generally one foot deep and cylindrical in shape. Zu Chongzhi used his research on the circumference of the circle to find a precise value. He also recalculated the “Law Jia Liang” created by Liu Xin in the Han Dynasty and used the “Zu rate” to correct the value. Later, people used Zu Chongzhi’s “Zu rate” value when manufacturing measuring instruments.
Zu Chongzhi pi


Zu Chongzhi designed and manufactured water mills, guide cars driven by copper mechanical parts, long-distance boats, timers, etc. The name of the guide car in ancient China has been around for a long time, but its mechanism has not been spread. In the Three Kingdoms period, Ma Jun once built a guide car and lost again in the Jin Dynasty. In the late Eastern Jin Dynasty, Liu Yu attacked Chang’an and obtained many artifacts from the post-Qin rulers, including guide cars, but “the number of machines is not precise, although it is called a guide, many do not review the steps, and the steps are still needed.” Southern Song Shengming years (477–479 years) Daocheng Colonial, “the chase Chong Chong renovation repair ancient copper machine, round to no party like a poor and Secretary, since Ma Jun is also No..” The Zu The internal parts of the guide car are all copper. Its structure is exquisite and flexible. No matter how it turns, the wooden man’s hand often points to the south.
Zu Chongzhi improved the watermill. In the early years of the Western Jin Dynasty, Du Yuqiang invented “Continuous Machine and Continuous Grinding” and “Water-turned Continuous Grinding”. One continuous machine can drive several stone pestles to grind the rice together; one water-revolving continuous mill can drive eight mills to grind at the same time. Zu Chongzhi made further improvements on this basis. Combining the water dumper and the water mill, the production efficiency was even more improved. This processing tool is still in use in some rural areas in southern China.
Zu Chongzhi also designed and built a ship of thousands of miles, historical records “built a ship of thousands of miles, tried it in Xintingjiang, and traveled more than a hundred miles a day.” It may be caused by the principle of using wheels to drive water forward, and it can travel more than 100 miles a day.
Zu Chongzhi once made the ” Jiqi “. This kind of utensil was used to hold water, “the middle is right, and the full is full”. The ancients often placed it around to warn themselves, “During the Jin Dynasty, Du had ingenuity, and it was impossible to make three changes.” In the next year, Nan Qiyong Jingling Wenxuan Wang Xiao Ziliang “is a good old man, and Chongzhi made a sculling device and presented it.”


Zu Chongzhi’s achievements are not limited to natural sciences, he is also proficient in music theory. He has a lot of research on rhythm. Zu Chongzhi wrote “Yi Yi”, “Lao Zi Yi”, “Zhuang Zi Yi”, “The Analects of Confucius” and other books on philosophy, all of which have been lost. In terms of literary works, he is the author of ” Su Yi Ji “, and fragments of this work can be seen in ” Taiping Yu Lan ” and other books.


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