Zu Chongzhi

Zu Chongzhi

Zu Chongzhi (429-500) was born in Qiu county, Fanyang county (now Laishui County, Hebei Province). He was an outstanding mathematician and astronomer in the northern and Southern Dynasties.

He was born in Fan Yang. He devoted his whole life to natural science, and his main contributions were mathematics, astronomy and calendar, and mechanical manufacturing. On the basis of Liu Hui's precise method of exploring PI, he first calculated pi to the seventh decimal place, which is between 3.1415926 and 3.1415927. His "Zuli" has made great contribution to the study of mathematics. It was not until the 16th century that Al qassi, an Arab mathematician, broke the record.

The Daming calendar written by him was the most scientific and progressive calendar at that time, which provided a correct method for astronomical research of later generations. His main works include anbianlun, Zhuozhu, shuyiji, Liyi, etc.

Life of the characters

Family background

From the end of the Western Jin Dynasty to the period of the Sixteen Kingdoms, large-scale war broke out in the north. Zu Chongzhi's ancestors migrated from Fanyang county (now Laishui County, Hebei Province) to Jiankang, the capital of the Eastern Jin Dynasty (now Nanjing City, Jiangsu Province). Zu Chongzhi was born in Jiankang. His grandfather, Zu Chang, was a civil engineering official of the imperial court. His father, Zu Shuozhi, was knowledgeable and often invited to do "fengchaoyue" Attend a royal ceremony or banquet.

Zu Chongzhi received a good family education since childhood. His grandfather told him that "the stars change with each passing day". His father led him to read scriptures and classics. His family's edification and influence, together with his own diligence, made him have a strong interest in natural science, literature, philosophy, especially astronomy. In his youth, he had a reputation of erudition.

Early experience

Zu Chongzhi once said in his works that since he was very young, he had been "specialized in mathematical skills, searching ancient and modern times". He collected almost all kinds of documents, records and materials from ancient times until his time. At the same time, he advocates never "falsely infer the ancients", never tie himself to the stale and wrong conclusions of the ancients, and personally carry out precise measurement and careful calculation. As he himself said, he often "measures the ruler personally, bows to examine the instrument, makes every effort, and is poor in planning.".

Because of his reputation of erudition and resourcefulness, Zu Chong was sent by Emperor Xiaowu of the Southern Song Dynasty to hualinxue Province, the academic research institution of the imperial court at that time, to do research work, and later to zongmingguan. At that time, zongmingguan was the highest scientific research institution in China, equivalent to the Chinese Academy of Sciences. There are five subjects in Zongming Temple: literature, history, Confucianism, Taoism, yin and Yang. The system of teaching by subject is implemented. Famous scholars from all over the world are invited to teach. Zu Chongzhi is one of them. Here, Zu Chongzhi came into contact with a large number of national books, including astronomy, calendar, and arithmetic books, which had the prerequisite for reference and expansion.

Concentrate on Science

In the fifth year of the Ming Dynasty (461), Zu Chongzhi served as an official in the governor's office of Southern Xuzhou (now Zhenjiang, Jiangsu Province). He successively served as an official in southern Xuzhou and a government official in the army. During this period, although his life was very unstable, he still persisted in academic research and made great achievements.

In the sixth year of the Ming Dynasty (462), Zu Chongzhi sent the carefully compiled Daming calendar to Emperor Xiaowu of the Song Dynasty for publication and implementation. Emperor Xiaowu of the Song Dynasty ordered officials who knew the calendar to discuss the advantages and disadvantages of the calendar. Finally, Emperor Xiaowu of the Song Dynasty decided to change to the new calendar in the ninth year of the Ming Dynasty (465).

In 464, Zu Chongzhi was transferred to Lou county (now the northeast of Kunshan County, Jiangsu Province) as magistrate. After that, he went to Jiankang (now Nanjing, Jiangsu Province) to serve as an official official official. From then on, until the early years of Qi Dynasty in the Southern Dynasty, he spent a lot of energy on machinery manufacturing. He rebuilt the guide car driven by copper parts, invented the "thousand mile boat" and "wooden ox and flowing horse" that could walk a hundred miles a day, water wheel mill (a tool for processing grain by water), and also designed and manufactured leaky pots (ancient timers) and ingenious utensils.

Life in old age

Zu Chongzhi's later years were in the late period of the Southern Qi Dynasty. The internal contradictions of the ruling class were sharp, the politics were dark, and the society was turbulent. In this case, the research direction of Zu Chongzhi has changed a lot. He focused on literature and Social Sciences, but also more concerned about politics.

Between the first year of Longchang (494) and the fifth year of Jianwu (498), he held the position of commander of Changshui school. At that time, he wrote an article on Anbian, which suggested that the government should reclaim wasteland, develop agriculture, enhance national strength, stabilize people's livelihood, and consolidate national defense. When Emperor Qi Ming saw it, he wanted to make him "patrol all over the country, make great achievements, and benefit the common people". Later, the rule of the Southern Qi Dynasty could not be maintained. The state power is on the verge of collapse, coupled with years of war between the northern and Southern Dynasties, Zu Chongzhi's good political ideas can not be implemented within the country, let alone realized.

In the second year of Yongyuan (500 years), this outstanding scientist died at the age of 72. His painstaking work of astronomy and calendar, Daming calendar, was published in the name of Jiazi Yuanli in the ninth year of Tianjian (510).

Main impact

mathematics

The pioneering work in the history of Mathematics -- "Zulu"

Zu Chongzhi calculated that the true value of PI is between 3.1415926 and 3.1415927, which is equivalent to the seventh decimal place and is simplified to 3.1415926. Therefore, Zu Chongzhi was selected as the world's first scientist who calculated pi to the seventh decimal place by the world record association. Zu Chongzhi also gives two fractional forms of PI: 22 / 7 (approximate ratio) and 355 / 113 (density ratio), in which the density ratio is accurate to the seventh decimal place. Zu Chongzhi's accurate calculation of PI value is a great contribution to China and even the world. Later generations named "Yue Li" after him as "Zu Chongzhi's Pi", which is called "Zu Li" for short.

The application of PI is very extensive, especially in astronomy and calendar. All problems involving the circle must be calculated by PI. How to calculate the value of PI correctly is an important subject in the history of mathematics in the world. Ancient Chinese mathematicians attached great importance to this problem and studied it very early. In Zhoubi Suanjing and Jiuzhang suanzu, the ancient rate of jingyizhou was put forward, which determined the circumference as three, that is, the circumference is three times the diameter. Since then, after successive explorations by mathematicians, the calculated value of PI has become increasingly accurate.

The PI calculated by Zhang Heng in the Eastern Han Dynasty is 3.162. During the Three Kingdoms period, the pI value calculated by Wang Fan was 3.155. Liu Hui, a famous mathematician in the Wei and Jin Dynasties, created a new method to calculate the PI when he annotated nine chapters of arithmetic. He divided the side length by 2, and the approximate value was 3.14. He also explained that this value was smaller than the actual value of PI. After Liu Hui, he Chengtian, PI Yanzong and other scholars who had made great achievements in searching PI ratio in the Southern Dynasty. He Chengtian calculated 3.1428, PI Yanzong calculated 22 / 7 ≈ 3.14.

Zu Chongzhi believed that Liu Hui was the most successful scholar in the study of PI in the hundreds of years from the Qin and Han Dynasties to the Wei and Jin Dynasties, but he did not reach the degree of accuracy, so he further studied to find more accurate values.

According to the records of PI in the book of Sui Dynasty, southern Xuzhou was engaged in shizuchongzhi and kaimi method in the end of Song Dynasty. The diameter of the circle was 100 million, the circumference surplus was 30.1 foot 4 inch 1.5% 9.2 second 7 Hu, the circumference surplus was 30.1 foot 4 inch 1.5% 9.2 second 6 Hu, and the positive number was between the two limits. Density ratio, diameter 113, circumference 355. About rate, diameter 7, Tuesday 12 Zu Chongzhi changed one Zhang into one hundred million Hu and used it as diameter to calculate pi. He calculated two numbers: one is surplus (i.e. the approximate value of surplus), which is 3.1415927; the other is 朒 (i.e. the approximate value of deficiency), which is 3.1415926.

Two numbers can be listed as inequalities, such as: 3.1415926 (*) < π (real PI) < 3.1415927 (Ying), which indicates that Pi should be between two numbers. According to the habit of using fractions in calculation at that time, Zu Chongzhi also used the Pi of two fractions. One is 355 / 113 (approximately equal to 3.1415927), which is more precise, so Zu Chong called it "Mi ratio". The other is 22 / 7 (about equal to 3.14), which is a rough number, so Zu Chong called it "approximate rate".

Zu Chongzhi's research on PI has positive practical significance. His research meets the needs of production practice at that time. He personally studied weights and measures, and revised the calculation of ancient measuring instrument volume with the latest results of PI. In ancient times, there was a kind of measuring instrument called "cauldron", which was generally one foot deep and cylindrical in shape. Zu Chongzhi used his research on PI to find out the accurate value. He also recalculated the "Lu Jia Liang" created by Liu Xin in the Han Dynasty, and corrected the value with "Zu Li". Later, people used Zu Chongzhi's "Zuli" value when they made measuring instruments.

A masterpiece of Mathematics

Zu Chongzhi wrote five volumes of Zhuozhu, which was included in the famous ten books of Suanjing. "Sui Shu" commented that "scholars can't study its profound, so they ignore it." they think that the theory of Zhuozhu is very profound, the calculation is quite precise, and it's difficult for scholars with high knowledge to understand its content. At that time, it was the most difficult book of mathematical theory.

In Zhu Shu, Zu Chongzhi put forward the questions of "power of difference" and "establishment of difference". The word "difference power" has been used in Liu Hui's annotation of Jiu Zhang Suan Shu, which refers to the difference of area. "To leave

Chinese PinYin : Zu Chong Zhi