Information about Zu Chongzhi

Zu Chongzhi (429-500), whose courtesy name was Wenyuan.

A famous mathematician, astronomer and mechanical manufacturer during the Southern and Northern Dynasties.

Overview

Zu Chongzhi’s ancestral home was Qiuxian County, Fanyang County (now Laishui, Hebei). In order to avoid the war, Zu Chongzhi’s grandfather Zuchang moved from Hebei to Jiangnan. Zuchang once served as the "Great Craftsman" of the Liu Song Dynasty, in charge of civil engineering; Zu Chongzhi's father was also an official in the court, and he was knowledgeable and respected.

Zu Chongzhi was born in Jiankang (now Nanjing, Jiangsu) in 429 AD. The ancestral family has been studying astronomy and calendars for generations. Zu Chongzhi had the opportunity to be exposed to astronomy and mathematics knowledge since he was a child. In his youth, Zu Chongzhi gained a reputation as an erudite scholar. After Emperor Xiaowu of the Song Dynasty heard about it, he sent him to the "Hualin Academic Province" to do research. In 461 AD, he worked in the governor's office of South Xuzhou (now Zhenjiang, Jiangsu Province). He successively served as a historian in South Xuzhou and joined the army in the government office. In 464 AD, he was transferred to Lou County (now northeast of Kunshan, Jiangsu Province) as county magistrate. During this period, he compiled the "Da Ming Calendar" and calculated pi. At the end of the Song Dynasty, Zu Chongzhi returned to Jiankang and served as a minister. From then until the fall of the Song Dynasty, he spent more energy on the study of mechanical manufacturing. From 494 to 498 AD, he served as the captain of Changshui in the Southern Qi court and received a fourth-grade salary. In view of the continuous war at that time, he wrote an article "Anbian Lun", suggesting that the court reclaim wasteland, develop agriculture, stabilize people's livelihood, and consolidate national defense. Zu Chongzhi died in 500 AD when he was 72 years old.

Zu Chongzhi’s son Zu Xun is also a famous mathematician in ancient China.

To commemorate this great ancient scientist, people named a crater on the back of the moon "Zu Chong's Crater" and the asteroid 1888 "Zu Chong's Asteroid".

Zu Chongzhi was born in Jiankang (now Nanjing, Jiangsu) in 429 AD. The ancestral family has been studying astronomy and calendars for generations. Zu Chongzhi had the opportunity to be exposed to astronomy and mathematics knowledge since he was a child. In his youth, Zu Chongzhi gained a reputation as an erudite scholar. After Emperor Xiaowu of the Song Dynasty heard about it, he sent him to the "Hualin Academic Province" to do research. In 461 AD, he worked in the governor's office of South Xuzhou (now Zhenjiang, Jiangsu). He successively served as a historian in South Xuzhou and joined the army in the government office. In 464 AD, he was transferred to Lou County (now northeast of Kunshan, Jiangsu Province) as county magistrate. During this period, he compiled the "Da Ming Calendar". In the "Da Ming Calendar", he cited the precession of equinox for the first time, which was a major reform in the history of our country's calendar. He also adopted a new leap week with 144 leap months in 391 years, which is more precise than the 19-year leap week with 7 leap months invented in ancient times. The tropical year and nodal month number calculated by Zu Chongzhi are very close to the observed values. In mathematics, Zu Chongzhi calculated that the true value of pi should be between 3.1415926 and 3.1415927, more than a thousand years earlier than Europe. In terms of machinery manufacturing, they have produced copper-cast compasses, water push mills that use water power to pound rice and grind flour, ships that can travel hundreds of miles a day and thousands of miles, and timekeeping instruments such as clepsydras and squeegees. At the end of the Song Dynasty, Zu Chongzhi returned to Jiankang and served as a minister. From then on until the fall of the Song Dynasty, he spent more energy on the study of mechanical manufacturing. From 494 to 498 AD, he served as the captain of Changshui in the Southern Qi court and received a fourth-grade salary. In view of the continuous war at that time, he wrote an article "Anbian Lun", suggesting that the court reclaim wasteland, develop agriculture, stabilize people's livelihood, and consolidate national defense. Zu Chongzhi died in 500 AD when he was 72 years old.

Zu Chongzhi’s main achievements are in the three fields of mathematics, astronomy and calendar, and mechanical technology. In addition, Zu Chongzhi was proficient in music and good at playing chess. He also wrote the novel "Shu Yi Ji". Zu Chongzhi wrote many works, but most of them have been lost. Zu Chongzhi was a rare erudite and talented person.

Life writings

"Sui Shu·Jing Ji Zhi" records fifty-one volumes of "The Collection of Changshui Xiaowei Zuchong", but it has been lost.

The following works are also scattered in various historical records:

"Anbian Lun", lost.

"Shu Yi Ji", ten volumes, lost.

"Yi Laozhuang Yishi", lost.

"Annotations on the Analects of Filial Piety", lost.

The six volumes of "Zhushu" are lost.

"Nine Chapters of Arithmetic Notes", nine volumes, lost.

One volume of "Notes on Chongcha", lost.

"The Great Ming Calendar"

"The Great Ming Calendar"

"Rebuttal"

"The Art of Opening the Round"

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Zu Chongzhi wrote many works in his life, and their contents are also multi-faceted. In terms of mathematics, the book "Zhu Shu" written by him is one of the famous "Ten Books on Calculation". It was listed as an arithmetic textbook by the Imperial College of the Tang Dynasty and required four years of study. Unfortunately, it has been lost. In terms of astronomical calendar, he compiled the "Da Ming Calendar" and wrote a "refutation" of the Daming Calendar. In terms of annotations of ancient classics, Zu Chongzhi wrote "Yi Yi", "Lao Zi Yi", "Zhuang Zi Yi", "The Analects of Confucius", "The Book of Filial Piety" and other works, but they have also been lost. In terms of literary works, he is the author of "Shu Yi Ji", and fragments of this work can be seen in books such as "Taiping Yulan".

Contributions to the astronomical calendar

Most of Zu Chongzhi's achievements in the astronomical calendar are included in the "Da Ming Calendar" he compiled and the refutations he wrote for the Daming Calendar.

Before Zu Chongzhi, the calendar used by people was the "Yuanjia Li" compiled by the astronomer He Chengtian. After years of observation and calculation, Zu Chongzhi discovered that there were big errors in the "Yuanjiali". So Zu Chongzhi set out to formulate a new calendar. In the sixth year of the Ming Dynasty (462 AD), Emperor Xiaowu of the Song Dynasty compiled the "Da Ming Calendar". The Ming Calendar was never adopted during Zu Chong's lifetime, and it was not officially promulgated until the ninth year of Emperor Wu of Liang's reign (510 AD). The main achievements of the "Da Ming Calendar" are as follows:

It distinguished tropical years from sidereal years, introduced precession into the calendar for the first time, and measured the precession to be one degree in November of 45 years (today's measurement is about 70.7 degrees per year) . The introduction of precession was a major progress in the history of Chinese calendar.

The year of return was determined to be 365.24281481 (today’s measurement is 365.24219878). This was the most accurate data until Yang Zhongfu established the celestial calendar in the fifth year of Qingyuan of Ningzong in the Southern Song Dynasty (1199 AD).

The new leap week with 144 leap days in 391 is more precise than the previous calendar with 7 leap weeks in 19 years.

The day of the month of the fixed node is 27.21223 (measured today as 27.21222). The precise measurement of the day number of the nodal month makes it possible to accurately predict the solar and lunar eclipses. Zu Chongzhi once used the Daming calendar to calculate the 4 events that occurred in 23 years from the 13th year of Yuanjia (AD 436) to the third year of Daming (AD 459). At the time of the sub-lunar eclipse, the results are completely consistent with reality.

The conclusion is drawn that Jupiter exceeds its celestial state once every 84 years, and the orbital period of Jupiter is determined to be 11.858 years (11.862 years as measured today).

A more accurate five-star conjunction period is given, in which the conjunction periods of Mercury and Jupiter are also close to modern values.

Proposed a method of measuring the length of the sun’s shadow at noon using a standard watch to determine the time of the winter solstice.

To commemorate this great ancient scientist, people named a crater on the far side of the moon the Zu Chongzhi crater, and named the asteroid 1888 the Zu Chongzhi asteroid.

Pi

Calculating the value of pi is a very important and difficult research topic in mathematics. Many mathematicians in ancient China devoted themselves to the calculation of pi, and the achievements made by Zu Chongzhi in the 5th century AD can be said to be a leap forward in the calculation of pi. After arduous study, Zu Chongzhi inherited and developed the excellent achievements of previous scientists. His research on pi is his outstanding contribution to our country and even the world. Zu Chongzhi's precise calculation of the value of pi was named "Zu Chongzhi's Pi" after him, or "Zu Rate" for short.

What is pi? A circle has its circumference and center. The distance from any point on the circumference to the center is called the radius. Double the radius is the diameter. The diameter is a line segment passing through the center of the circle, and the circumference is an arc. The number of times the arc is the straight line is called pi in mathematics. Simply put, pi is the ratio between the circumference of a circle and its diameter. It is a constant, represented by the Greek letter "π", and is obtained by the formula 355÷113. In terms of astronomy, calendar and production practice, all issues involving circles must be calculated using pi.

How to correctly derive the value of pi is an important issue in the history of world mathematics. Ancient Chinese mathematicians attached great importance to this issue and studied it very early. In "Zhou Bi Suan Jing" and "Nine Chapters of Arithmetic", it is proposed that the diameter of a circle is three times, and the pi ratio is three times, that is, the circumference of a circle is three times the diameter. Since then, through successive explorations by mathematicians of all generations, the calculated pi value has become increasingly accurate. At the end of the Western Han Dynasty, when Liu Xin was designing and making a round copper dendrobium (a kind of measuring instrument) for Wang Mang, he found that the ancient ratio of one diameter and three circumference was too rough. After further calculation, the value of pi was found to be 3.1547. Zhang Heng, a famous scientist in the Eastern Han Dynasty, calculated the pi value to be 3.162. During the Three Kingdoms period, mathematician Wang Fan calculated the value of pi to be 3.155. Liu Hui, a famous mathematician during the Wei and Jin Dynasties, created a new method of calculating pi-circle cutting when he was annotating "Nine Chapters on Arithmetic". He set the radius of the circle to be 1, divided the circle into six equal parts, and constructed an inscribed regular hexagon of the circle. He used the Pythagorean theorem to find the perimeter of this inscribed regular hexagon; then he constructed the inscribed dodecagon in turn, Twenty-four polygons..., when the circle is inscribed in one hundred and ninety-two polygons, the sum of its side lengths is 6.282048, and the more sides a circle inscribes in a regular polygon, the closer its side lengths are. The actual circumference of the circle, so the value of pi at this time is the side length divided by 2, and its approximate value is 3.14; and it shows that this value is smaller than the actual value of pi. In the art of cutting circles, Liu Hui has realized the concept of limit in modern mathematics. The circle cutting technique he created was a major breakthrough in the process of exploring the numerical value of pi. In order to commemorate Liu Hui's achievements, later generations called the pi value he obtained "Hui Rate" or "Hui Shu".

After Liu Hui, scholars who made great achievements in exploring pi include He Chengtian, Pi Yanzong and others in the Southern Dynasties. The value of pi obtained by He Chengtian is 3.1428; the value of pi obtained by Pi Yanzong is 22/7≈3.14. The above scientists have all made great contributions to the research and calculation of pi, but compared with Zu Chongzhi's pi, they are much inferior.

Zu Chongzhi believed that Liu Hui was the scholar who made the greatest achievements in studying pi in the hundreds of years from the Qin and Han Dynasties to the Wei and Jin Dynasties, but he did not reach an accurate level, so he further studied to find a more accurate value. The results of its research and calculations prove that pi should be between 3.1415926 and 3.1415927. He became the first person in the world to calculate the accurate value of pi to seven digits after the decimal point. It was not until a thousand years later that this record was broken by the Arab mathematician Al Qasi and the French mathematician Viette. The "density ratio" proposed by Zu Chongzhi was not called the "Antoninz ratio" by Germany until a thousand years later. Some people with ulterior motives said that Zu Chongzhi forged the pi ratio after Western mathematics was introduced to China in the late Ming Dynasty. This is an intentional fabrication. The ancient book that records Zu Chongzhi's research on pi is the "Sui Shu", a history book written in the Tang Dynasty. The modern "Sui Shu" has a version published in the Bingwu Year of the Yuan Dynasty (1306 AD), including and other modern versions. The same record about Zu Chongzhi's pi occurred more than 300 years before the end of the Ming Dynasty. Moreover, many mathematicians before the Ming Dynasty quoted Zu Chongzhi's pi in their works. These facts prove Zu Chongzhi's outstanding achievements in pi research.

So, how did Zu Chongzhi achieve such a major scientific achievement? To be sure, his achievements are based on previous research. Judging from the level of mathematics at that time, Zu Chongzhi probably inherited the circle cutting technique founded and first used by Liu Hui, and developed it, thus achieving major achievements that surpassed his predecessors. Earlier, when we mentioned the art of cutting circles, we already knew this conclusion: the more sides a circle has inscribed in a regular n-gon, the closer the sum of the lengths of each side is to the actual length of the circle. But because it is inscribed and it is impossible to increase the number of sides to infinite, the sum of the side lengths is always less than the circumference.

Zu Chongzhi followed Liu Hui's method of cutting a circle and set up a circle with a diameter of one foot, and cut and calculated within the circle. When he cut the one hundred and ninety-two polygons inscribed in the circle, he obtained the value of "hui rate".

But he was not satisfied and continued cutting, making 384 polygons, 768 polygons... until he cut to 24576 polygons, and found each inscribed regular polygon in turn. The side length of the polygon. Finally, find a circle with a diameter of one foot. Its circumference is between three feet, one foot, four inches, one minute, five centimeters, two seconds, seven seconds to three feet, one foot, four inches, one minute, five centimeters, nine millimeters, two seconds, six seconds. , the length units above are no longer common to us, but in other words: if the diameter of a circle is 1, then the circumference is less than 3.1415927, which is less than one ten millionth. Their introduction greatly facilitates calculation and practical application. .

To make such precise calculations is an extremely detailed and arduous mental work. We know that in Zu Chongzhi’s time, the abacus had not yet appeared. The calculation tool commonly used by people was called abacus. It was a small square or flat stick a few inches long. There were various kinds of bamboo, wood, iron, jade, etc. material. Various numbers can be represented by different ways of placing chips, which is called the counting method. The more digits there are to calculate, the larger the area required for placement. Calculating with an arithmetic chip is not like using a pen. The pen calculation can be left on the paper, but the arithmetic must be re-swung to perform a new calculation after each calculation. The calculation results can only be written down with a notebook, and more intuitive graphics and calculation formulas cannot be obtained. . Therefore, as long as there is an error, such as a miscalculation or an error in the calculation, you can only start from the beginning. To obtain the value of Zu Chongzhi's pi, it is necessary to perform more than ten steps of calculation on decimals with nine significant figures, such as addition, subtraction, multiplication, division and square root calculations, and each step must be repeated more than ten times to calculate the square root. There are 50 operations, and the final calculated number reaches sixteen or seven decimal places. Today, even using an abacus and pen and paper to complete these calculations is not an easy task. Let us think about it. During the Southern Dynasty more than 1,500 years ago, a middle-aged man kept counting and memorizing in his hands under a dim oil lamp, and he had to frequently rearrange tens of thousands of items. This is such an arduous task, and it needs to be repeated day after day. If a person does not have great perseverance, he will never be able to complete this work.

This glorious achievement also fully reflects the high level of development of ancient mathematics in our country. Zu Chongzhi is not only admired by the Chinese people, but also respected by scientific figures from all over the world. In 1960, after studying photos of the far side of the moon, Soviet scientists named the valleys on it after some of the world's most contributing scientists. One of the craters was named "Zuchong Crater."

Zu Chongzhi’s research on pi had positive practical significance and adapted to the needs of production practice at that time. He personally studied weights and measures and used the latest pi results to correct the calculation of ancient measuring volume.

In ancient times, there was a measuring device called a "cauldron". It was usually one foot deep and cylindrical in shape. What was the volume of this measuring device? To find this value, you need to use pi. Zu Chongzhi used his research to find the precise value. He also recalculated the "Lüjia Liang" created by Liu Xin of the Han Dynasty (another type of measuring instrument, which is similar to the "liter" equal measuring instrument we use now, but they are both cylindrical. .), because the calculation method and the pi value used by Liu Xin are not accurate enough, the volume value he obtained is different from the actual value. Zu Chongzhi found his mistake and corrected the value using "Zu Rate".

After that, people used Zu Chongzhi's "zu rate" value when making measuring instruments. Based on the work of his predecessors, Zu Chongzhi, after painstaking study and repeated calculations, calculated pi to 7 digits after the decimal point, and obtained an approximate value of pi in fractional form. It is currently impossible to investigate what method Zu Chongzhi used to obtain this result; if we assume that he followed Liu Hui's "Circle Cutting Technique" method, he would have to calculate 16,000 polygons inscribed in the circle. How much time and effort would this take? Huge labor!

According to "Sui Shu·Lü Li Zhi", Zu Chongzhi used one hu (one hundred millionth of one zhang) as the unit to find the circumference of a circle with a diameter of one zhang, and found the surplus number as 3.1415927, the number is 3.1415926, the true value of pi is between the two numbers.

"Book of Sui" does not specify the method used by Zu Chongzhi to calculate the number of Ying and Xie. It is generally believed that Zu Chongzhi used Liu Hui's circle-cutting technique, but there are also many other speculations. These two approximations were accurate to the 7th decimal place and were the most advanced achievements in the world at that time. It was not until more than a thousand years later that the 15th-century Arab mathematician Cassie and the 16th-century French mathematician F. Veda obtained more precise results. Zu Chongzhi determined two asymptotic fractions of π, the approximate rate 22/7 and the density 355/113. Among them, the density is 355/113 (≈3.1415929). The West was not discovered until the 16th century by the German V. Otto. It is composed of three pairs of odd numbers 113355 and then folded into two sections. It is beautiful, regular and easy to remember. In order to commemorate Zu Chongzhi's outstanding contribution, some foreign mathematics historians call the density of pi "Zu rate".

Zu Chongzhi’s achievements in the field of mathematics are only one aspect of ancient Chinese mathematics achievements. In fact, before the 14th century, China had been one of the most developed countries in mathematics in the world. For example, the Pythagorean theorem in geometry is discussed in the early Chinese mathematical treatise "Zhou Bi Suan Jing" (written about the 2nd century BC); another important mathematical treatise "Nine Chapters" written in the 1st century AD "Arithmetic" was the first to propose the concept of negative numbers and the rules of addition and subtraction of positive and negative numbers in the history of world mathematics. In the 13th century, China already had the solution to the tenth-degree equation, and it was not until the 16th century that Europe proposed the solution to the cubic equation.

The contributions of Zu Chongzhi and his son

Zu Chongzhi and his son Zu Xun also used ingenious methods to solve the calculation of the volume of the sphere. A principle they adopted at the time was: "Since the power potentials are the same, the products are indifferent." That means: two solids located between two parallel planes are intercepted by any plane parallel to the two planes. If the two If the areas of the cross-sections are constant, the volumes of the two solids will be equal. It is called "Cavalieri's principle" in the West, but it was discovered by the Italian mathematician Cavalieri more than a thousand years after Zu Chongzhi. In order to commemorate the great contribution of Zu and his son in discovering this principle, this principle is also called "Zu Xing's Principle" in mathematics.

The Zuxin principle is also the "equal product principle". It was first proposed by Zu Xun, the son of Zu Chongzhi, an outstanding mathematician in the Southern and Northern Dynasties of my country. The content of Zuxin's principle is: two geometric bodies sandwiched between two parallel planes are intercepted by a plane parallel to the two parallel planes. If the areas of the two sections are always equal, then the volumes of the two geometric bodies equal.

Zu Chongzhi’s son Zu Xun is also a famous mathematician in ancient China. When he was a child, he studied the studies passed down from his family. He studied deeply and meticulously, and he also had a clever mind. His skills have reached such a level that even craftsmen such as Lu Ban and Jue (legendary craftsmen of the Shun Dynasty) in ancient legends cannot surpass him. When he thought deeply, the sound of thunder was hard to hear. Once when he met the servant Xu Mian while walking, his head bumped into Xu Mian's body, and Xu Mian didn't realize it until he called him. He Chengtian's calendar revised by his father had not yet been implemented at that time. In the early years of Emperor Wu of Liang's Tianjian, Xun Zhi revised it again and it was not implemented until then. The position reaches Taizhouqing.

The Story of Zu Chongzhi

Zu Chongzhi’s grandfather was named Zuchang, and he was an official in charge of court buildings in the Song Dynasty. Zu Chongzhi grew up in such a family and read many books since he was a child. People praised him as a learned young man. He was particularly fond of studying mathematics and astronomy and calendars. He often observed the movements of the sun and planets and kept detailed records.

Emperor Xiaowu of the Song Dynasty heard about his reputation and sent him to work in the "Hualin Academic Province", an official agency specializing in academic research. He was not interested in being an official, but there he could concentrate more on studying mathematics and astronomy.

There have been officials who studied astronomy in all dynasties of our country, and calendars were formulated based on the results of astronomical research. By the time of the Song Dynasty, the calendar had made great progress, but Zu Chongzhi thought it was not accurate enough. Based on the results of his long-term observations, he created a new calendar called the "Daming Calendar" ("Daming" is the reign name of Emperor Xiaowu of the Song Dynasty).

The number of days measured in each tropical year (that is, the time between the two winter solstice points) measured by this calendar is only fifty seconds different from that measured by modern science; the number of days it takes for the moon to circle around is not different from that measured by modern science. One second. This shows how accurate it is.

In 462 AD, Zu Chongzhi asked Emperor Xiaowu of the Song Dynasty to promulgate a new calendar, and Emperor Xiaowu convened ministers for discussion. At that time, Dai Faxing, a favored minister of the emperor, came out to object, believing that Zu Chongzhi's unauthorized change of the ancient calendar was an act of treason. Zu Chongzhi used the data he studied to refute Dai Faxing on the spot. Dai Faxing relied on the emperor's favor and said arrogantly: "The calendar was established by the ancients and should not be changed by future generations." Zu Chongzhi was not afraid at all. He said solemnly: "If you have factual basis, just use it to argue. Don't scare people with empty words." Emperor Xiaowu of Song Dynasty wanted to help Dai Faxing, so he found some people who knew the calendar to argue with Zu Chongzhi, but they were all refuted by Zu Chongzhi. . However, Emperor Xiaowu of Song Dynasty still refused to promulgate the new calendar. It was not until ten years after Zu Chongzhi's death that the Daming Calendar created by him was implemented.

Although the society was very turbulent at that time, Zu Chongzhi still studied science tirelessly. His greater achievement was in mathematics. He once commented on the ancient mathematical work "Nine Chapters on Arithmetic" and compiled a book "Zhu Shu". His most outstanding contribution was the fairly accurate calculation of pi. After long-term and painstaking research, he calculated that pi is between 3.1415926 and 3.1415927, becoming the first scientist in the world to calculate the pi value to more than seven digits.

Zu Chongzhi was a generalist in scientific inventions. He built a kind of compass. No matter how the car turned, the bronze figure on the car always pointed south. He also built a "thousand-mile ship" and tried it on the Xinting River (southwest of today's Nanjing City). It could sail more than a hundred miles a day. He also used water power to turn stone mills and pound rice to grind millet, which was called "water mill".

In Zu Chongzhi's later years, Xiao Daocheng, who controlled the imperial guards of the Song Dynasty, destroyed the Song Dynasty.

"Southern History·Zu Chong's Biography" Volume 72, Biography 62

Zu Chong's courtesy name was Wenyuan, and he was a native of Fan Yangqiu. His great-grandfather was Taizhi, and he served as an official in the Jin Dynasty. Zuchang, the great craftsman of the Song Dynasty. My father Shuo Zhi was invited by the court.

In order to reflect on the past and have some thoughts, Song Xiaowu envoy went to Hualin to study in the province, and he was given a house, a car, and clothes. Xie Brown was engaged in Xuzhou in the south and joined the army in the government.

In Jiazhong of the First Yuan Dynasty, He Chengtian made a calendar, which is more secret than the ancient eleven. I thought it was still sparse, so I created a new method, as stated above. The filial piety and military order made it difficult for the courtiers who were good at history and could not give in. It will not be carried out after the death of Emperor Hui.

His previous position was the magistrate of Lou County, and those who visited him were servants. At the beginning, when Wu of the Song Dynasty was in Guanzhong, he got Yao Xing's compass. It had an outer shape but no mechanical stick. Every time it moved, it made people turn it inside. During the rise of the Ming Dynasty, Emperor Qi Gao assisted in the administration and asked Chong to pursue the ancient methods. Chongzhi modified the copper machine, making it endlessly round and smooth, which was unprecedented since Ma Jun. At that time, there were people from the north who were able to build a compass. Emperor Gao sent him and Chong to build a compass respectively, and sent them to Leyou Garden for the imperial examination. However, they were quite out of place, so they destroyed and burned them. During the Jin Dynasty, Du Yu had an ingenious idea to make a Qianqiu, but failed after three modifications. In the Yongming Dynasty, Prince Jingling was very good at ancient times, so he made a pewter vessel to offer it, which was the same as in Zhou Temple. Prince Wenhui was in the East Palace. When he saw the calendar, Emperor Qi Wu implemented it. Wen Hui died and went to bed again.

Transferred to Changshui Xiaowei and assumed his duties. Chongzhi built a border theory and wanted to open up farmland and expand farming. During the construction of military affairs, Emperor Ming wanted to send Chongzhi to patrol all directions to build great undertakings that would benefit the people. However, the military alliance was not successful.

Chongzhijie Zhonglu Bosai was unique at that time and could not be matched. Zhuge Liang had a wooden ox and a flowing horse, so he built a tool that would move by itself without relying on feng shui, without laboring on manpower. He also built a thousand-mile boat and tried it on the Xinting River. It traveled more than a hundred miles a day. A water mill was built in Leyou Garden, and Emperor Wu personally came to see it. He is also very good at calculating. He died in the second year of Yongyuan at the age of seventy-two. He wrote Yi Lao Zhuang Yi, commented on the Analects of Confucius and the Classic of Filial Piety, annotated nine chapters, and composed dozens of chapters.

External Biography

He (Zu Chongzhi) also wrote the book "Zhushu", which compiled the mathematical research results of Zu Chongzhi and his son. The content of this book is so profound that "no academic officials could understand its profoundness, so they discarded it and ignored it." "Zhu Shu" was included in the "Ten Books of Calculation" in the Tang Dynasty and became the textbook of arithmetic for the Imperial Academy in the Tang Dynasty. At that time, it took four years to learn "Zu Shu", which shows how difficult "Zu Shu" was.

"Zhushu" was once spread to North Korea, but by the Northern Song Dynasty, the book had been lost.