In mathematics, he wrote a book "Composition", which was included in the famous "Ten Books of Calculating Classics" as a textbook of imperial academy in the Tang Dynasty, but it was later lost. There is a brief record of pi in the Book of Rites of Sui Dynasty. The true value of pi calculated by Zu Chongzhi is between 3. 14 159265356 and 3. 14 159275357, which is equivalent to being accurate to decimal 1 1. This record was not broken by Arabian mathematician Cassie until15th century. Zu Chongzhi also gave two fractional forms of π: 22/7 (approximate rate) and 355/ 1 13 (secret rate), in which the secret rate was accurate to the seventh place after the decimal point, and it was not rediscovered by the Dutch mathematician Otto until the west16th century. Zu Chongzhi, together with his son Zuxuan, successfully solved the problem of calculating the volume of the ball by using "Mu He Fang Gai" and got the correct formula of the volume of the ball. In the astronomical calendar, Zu Chongzhi created the Daming Calendar, which introduced precession into the calendar at the earliest. New leap weeks of 39 1 year and 144 leap months are adopted. For the first time, the data such as the number of months and days at the intersection (27.25438+0223) and the number of days in the tropical year (365.2428) were accurately measured, and the method of measuring the length of the sun shadow at noon from winter to the days before and after was invented, and the time of winter solstice was determined. In mechanics, he has designed and manufactured a water hammer mill, a compass driven by copper parts, a thousand-mile ship, a timer and so on. In addition, he is also quite accomplished in melody, literature and textual research. Proficient in melody, good at playing chess, and also wrote a novel "The Story of Different Notes". He is one of the few well-read figures in history.
To commemorate this great ancient scientist, people named a crater on the back of the moon "Zu Chongzhi Crater" and the asteroid 1888 "Zu Chongzhi Asteroid".
Zu Chongzhi worked hard to calculate the value of pi to seven decimal places for the first time in the history of mathematics in the world, that is, between 3. 14 15926 and 3. 14 15927. He put forward the agreement rate of 22/7 and the secret rate of 355/ 1 13, which were the earliest in the world, more than a thousand years earlier than in Europe, so some people advocated calling them "the ancestor of pi". He compiled his mathematics research results into a book called Seal Characters, which was once regarded as a mathematics textbook by Chinese studies in the Tang Dynasty. His Da Ming Li introduced precession into the calendar for the first time. It is suggested that 39 1 year set 144 leap month. The length of a tropical year is 365.338+04438+0 days, and the error is only about 50 seconds. He is not only an outstanding mathematician and astronomer, but also an outstanding mechanic expert. Rebuild all kinds of exquisite machinery, such as South Guide Car and Thousand-mile Ship, which have long been lost. Besides, he also studies music. His works, such as Explaining the Analects of Confucius, Explaining the Classic of Filial Piety, Yi, Lao, Zhuang and the novel Yi Shu Ji, have long been lost.
From the demise of the Eastern Jin Dynasty in 42O A.D. to the unification of the whole country by the Sui Dynasty in 589 170 years, a situation of opposition between the North and the South was formed in the history of our country, which was called the Northern and Southern Dynasties in history. Since Emperor Wudi of the Eastern Jin Dynasty seized the throne in 420 A.D. and established the regime of the Song Dynasty, the Southern Dynasties experienced four dynasties: Song, Qi, Liang and Chen. Against the Southern Dynasties was the Northern Dynasties, which experienced the Northern Wei, the Eastern Wei, the Western Wei, the Northern Qi and the Northern Zhou Dynasties. Zu Chongzhi was born in Song Dynasty and died in Nanqi.
At that time, 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. So during this period, some very successful scientists appeared in the Southern Dynasties, and Zu Chongzhi was one of the most outstanding figures.
Zu Chongzhi's native place is Qiuxian County, Fanyang County (now Laishui County, Hebei Province). At the end of the Western Jin Dynasty, the ancestral home was destroyed by war and moved to the south of the Yangtze River. Zu Chongzhi's grandfather, Zuchang, once worked as a great craftsman in the Song Dynasty government, in charge of building projects. He has mastered some scientific and technological knowledge. At the same time, ancestors have been studying astronomical calendars for generations. So Zu Chongzhi was exposed to technology since he was a child.
Zu Chongzhi has a wide range of interests in natural science, literature and philosophy, especially in astronomy, mathematics and mechanical manufacturing. As early as his youth, he had a reputation as a scholar and was sent by the government to Hualin University, an academic research institution at that time, to do research. Later, he served as a local official. In 46 1 year, he worked in the secretariat of southern Xuzhou (now Zhenjiang, Jiangsu). In 464, the Song government transferred him to Lou County (now the northeast of Kunshan County, Jiangsu Province) as a county magistrate.
During this period, although Zu Chongzhi's life was very unstable, he still persisted in academic research and made great achievements. His attitude towards academic research is very strict. He attached great importance to the research results of the ancients, but he was never superstitious. In his own words, it is: never "blindly push (worship) the ancients", but "collect the ancient and modern (absorb the essence from a large number of ancient and modern works)". On the one hand, he deeply studied the works of ancient scientists such as Liu Xin, Zhang Heng, Ze, Liu Hui and others, and fully absorbed all useful things. On the other hand, he dared to doubt the conclusions of his predecessors in scientific research, and revised and supplemented them through practical observation and research, thus achieving many valuable scientific achievements. Among the astronomical calendars, his Da Ming Calendar was the most accurate one at that time. In mathematics, he calculated pi accurately to six decimal places and achieved the best results in the world at that time.
At the end of the Song Dynasty, Zu Chongzhi returned to Jiankang (now Nanjing) and served as a servant. From then on, up to the early years of Qi Dynasty, he spent a great deal of energy on the study of mechanical manufacturing, the transformation of the compass, the invention of the thousand-mile ship, the water hammer mill and so on, and made outstanding contributions.
In Zu Chongzhi's later years, the ruling group of Qi was in civil strife, political corruption and darkness, and people's lives were very painful. Wei of the Northern Dynasties took the opportunity to send troops to attack the south.
From 494 AD to 500 AD, the south of the Yangtze River fell into war again. Zu Chongzhi is very concerned about this political situation with internal troubles and foreign invasion. From about 494 to 498 AD, he served as a captain of Changshui. At that time, he wrote "On Security", suggesting that the government reclaim wasteland, develop agriculture, enhance national strength, stabilize people's livelihood and consolidate national defense. When Emperor Qi Ming saw this article, he planned to send Zu Chongzhi to travel around the world and set up some undertakings beneficial to the national economy and people's livelihood. However, due to years of war, his proposal never came true. Soon, this outstanding great scientist lived to be 72 years old and died in 500 AD.
Reform the calendar and introduce precession
Due to the needs of animal husbandry and agricultural production, the working people in ancient China discovered the basic laws of the movement of the sun and the moon through long-term observation. They set the period from the first full moon or lack of moon to the second full moon or lack of moon as one month, each month is a little more than twenty-nine days, and twelve months is called a year. This method of calculating the year is called the lunar calendar. They also observed that it takes 365 days 1/4 days from the first winter solstice to the second winter solstice (in fact, the earth goes around the sun once), so it is also called a year. Calendars calculated in this way are usually called solar calendars. However, the number of days in the lunar year and the solar year is not exactly equal. According to the lunar calendar, there are 354 days in a year; According to the solar calendar, a year should be 365 days, 5 hours, 48 minutes and 46 seconds. The lunar calendar is more than eleven days shorter than the solar calendar. In order to make the dates of the two calendars consistent, we must find ways to adjust the dates of the lunar year. For this problem, our ancestors found a solution long ago, that is, adopting the method of "leap moon". Arrange a leap year in several years, and add a leap month to each leap year. Leap year every year, there are thirteen months in a year. Because of this leap year method, the lunar year and the solar year are more consistent.
Ancient calendar experts in China have always used 19 years as the unit of leap year calculation, which is called "one chapter", and each chapter has seven leap years. In other words, after nineteen years, seven years is thirteen months. This leap method has been used for more than 1000 years, but it is not thorough and accurate enough. In 4 12 A.D., Zhao Zuo of Beiliang wrote Yuan Li, which broke the limitation of the annual chapter and stipulated that 22 1 leap month should be inserted in the middle of 600 years. Unfortunately, Zhao Xu's reform did not attract people's attention at that time. For example, when He Chengtian, a famous calendar mathematician, made Li Yuanjia in 443 AD, he still used the ancient method of seven jumps in nineteen years.
Based on Zhao CuO's advanced theory and his own observation, Zu Chongzhi thinks that there are too many jumps in 19 years, one day less every 200 years, while the leap number of 22 1 in Zhao CuO's 600 years is too thin and inaccurate. So he proposed a new leap method of 39 1 year 144 leap. This leap method was the most advanced at that time.
In addition to reforming the leap method, Zu Chongzhi's other great achievement in calendar research is the first application of "precession"
According to the principle of physics, when a rigid body rotates, the direction and speed of rotation should be the same if it is completely free from external forces; If it is affected by external force, its rotation speed will change periodically. The earth is a rigid body with uneven surface and irregular shape, which is often influenced by the gravity of other planets in its operation, so the rotation speed always changes periodically and cannot be absolutely consistent. Therefore, it is impossible to completely return to last winter when the sun went around once a year (actually, the earth went around the sun once a week), and there will always be subtle differences. According to the accurate calculation of astronomers, the difference of one year is about 50.2 seconds, and it goes backwards every 7 1 year and 8 months. This phenomenon is called precession.
With the gradual development of astronomy, scientists in ancient China gradually discovered the precession phenomenon. Deng Ping in the Western Han Dynasty, Liu Xin and Jia Kui in the Eastern Han Dynasty all observed the phenomenon of winter moving to the future, but they did not explicitly point out the existence of precession. It was not until the early years of the Eastern Jin Dynasty that astronomers began to affirm the existence of precession and advocated the introduction of precession into the calendar for the first time. He put forward the first data of precession, and calculated that the winter solstice will recede every 50 years. Later, in the early years of the Southern Song Dynasty, He Chengtian thought that the precession was once in a hundred years, but he did not apply it in his Yuan Jiali Calendar.
Zu Chongzhi inherited the scientific research achievements of predecessors, not only confirmed the existence of precession, but also calculated precession once every forty-five years and eleven months, and applied precession in his Da Liming. Because the astronomical historical materials he relied on were not accurate enough, the data he proposed could not be very accurate. Nevertheless, Zu Chongzhi's application of precession to the calendar is a pioneering work in astronomical history, which opens a new page for the improvement of China's calendar. After the Sui Dynasty, precession was valued by many historians, such as Daye calendar and Huangji calendar in the Sui Dynasty.
Zu Chongzhi's third contribution to calendar research is that he can find out the number of days in the calendar, which is usually called "crossing the moon".
The so-called intersection month is the time when the moon passes through the intersection of the ecliptic and the white road twice in a row. The ecliptic refers to the orbit of the sun as seen by the earth people, and the ecliptic refers to the orbit of the moon as seen by the earth people. You can calculate the number of days in intersecting months. The number of intersecting months measured by Zu Chongzhi is 27.2 1223, which is much more accurate than that measured by astronomers in the past and very similar to that measured by modern astronomers. With the astronomical level at that time, it was remarkable that Zu Chongzhi could get such accurate figures.
Since both eclipses occur near the intersection of the ecliptic and the ecliptic, it is more accurate to calculate the time of the eclipse after calculating the number of days of the intersection. In his Ming Li, Zu Chongzhi calculated the time of the solar eclipse with the intersection month, which is more accurate than in the past and very close to the actual time of the solar eclipse.
Based on the above research results, Zu Chongzhi finally succeeded in making the most scientific and progressive calendar at that time-Daming Calendar. This is the genius of Zu Chongzhi's scientific research and his most outstanding contribution to the astronomical calendar.
In addition, Zu Chongzhi also observed and calculated the orbits of the five planets-wood, water, fire, gold and earth-in the sky and the time required for one cycle. Scientists in ancient China calculated that Jupiter (known as the year-old star in ancient times) runs once every twelve years. When Liu Xin wrote "San Li" in the Western Han Dynasty, he found that Jupiter had been running for less than twelve years. Zu Chongzhi went further and calculated that Jupiter's orbital time was 1 1.858 years. Modern scientists estimate that the period of Jupiter is about 1 1. In 862. The result calculated by Zu Chongzhi is only 0.04 years away from this figure. In addition, Zu Chongzhi calculated that the time of Mercury's orbit is 1 15.88 days, which is completely consistent with the two decimal places determined by modern astronomers. He calculated that the time for Venus to orbit was 583.93 days, which was only 0.0 1 day away from the figure determined by modern scientists.
In 462 AD (the sixth year of Song Daming), Zu Chongzhi presented the carefully compiled Da Liming to the court for promulgation and implementation. Emperor Xiaowu of Song ordered officials familiar with the calendar to discuss the advantages and disadvantages of this calendar. During the discussion, Zu Chongzhi was opposed by conservative forces represented by Dai Faxing. Dai Faxing is a trusted minister of Emperor Xiaowu of Song Dynasty, and he has great power. Because he took the lead in opposing the new calendar, all the officials in the imperial court, big and small, echoed it, and everyone was not in favor of changing the calendar.
In order to stick to his correct opinion, Zu Chongzhi had a heated argument with Defarge.
This debate about the advantages and disadvantages of the new calendar actually reflected the sharp struggle between science and anti-science, progress and conservatism at that time. Dai Faxing wrote to the emperor first, and performed miracles of ancient sages and sages from ancient books to suppress Zu Chongzhi. He said that during the winter solstice, the sun was always in a certain position, which was decided by ancient sages and could never be changed. He said that Zu Chongzhi thought that the winter solstice moved every year, slandering the sky and violating the Bible. This is a heinous act. He also said that the prevailing seven-leap calendar of 19 was formulated by ancient sages and must not be changed. He even called Zu Chongzhi a humble and ordinary person who was not qualified to talk about reforming the calendar.
Zu Chongzhi showed no fear of attacks by powerful forces. He wrote a famous rebuttal article. According to the ancient literature and the records of observing the sun at that time, he proved that the winter solstice changed. He pointed out: the facts are clear. How can we believe in the past and doubt the present? He also listed in detail the changes of shadow length around noon from the winter solstice for many years, and accurately calculated the date and time of the winter solstice, which showed that the seventh leap in the nineteenth year was very inaccurate. He asked, "The old calendar is not accurate. Should it be used forever and never reformed? " Anyone who wants to say that Li Ming is not good should produce conclusive evidence. If there is evidence, I am willing to accept it. "
At that time, Dai Faxing could not point out the shortcomings of the new calendar, so he argued about the speed of the day, the length of the shadow, the speed of the month and so on. Zu Chongzhi refuted them one by one.
Under the refutation of Zu Chongzhi's righteous words, Dai Faxing had nothing to answer, but said rudely, "No matter how good the new calendar is, it can't be used." Zu Chongzhi was not intimidated by Dai Faxing's outrageous attitude, but said firmly, "Never trust the ancients blindly. Since the shortcomings of the old calendar have been discovered and the new calendar has many advantages, it should be replaced with a new one. "
In this big debate, many ministers were convinced by Zu Chongzhi's incisive and thorough theory, but they were afraid of the power of Dai Faxing and dared not speak for Zu Chongzhi. Finally, a minister named Chao Shangzhi came out to support Zu Chongzhi. He said, "Daming Calendar" is the result of Zu Chongzhi's years of research. According to the records in Daming Calendar, the four eclipses in the 13th year of Yuanjia (436), 14th year (437), 28th year (45 1) and 3rd year of Daming (459) are all accurate, and the results calculated by the old calendar have great errors. Since Daming Calendar,
As a result, Defarge was speechless. Zu Chongzhi won the final victory. In the ninth year of Daming (465), Emperor Xiaowu of the Song Dynasty decided to switch to a new calendar. Who knows that Emperor Xiaowu died in the eighth year of Daming, and then the ruling clique had an accident, so the matter of changing the calendar was put on hold. It was not until Liang Chaotian was imprisoned for nine years (5 1O) that the new calendar was officially adopted, but by then Zu Chongzhi had died for ten years.
Writing and typesetting with the law of circumference
Zu Chongzhi was not only proficient in astronomical calendars, but also made great contributions to mathematics, especially his outstanding achievements in the study of pi, which surpassed the previous generation and made him shine in the history of mathematics in the world.
We all know that pi is the ratio of the circumference of a circle to the diameter of the same circle, and this ratio is a constant, which is now commonly expressed by the Greek letter "π". Pi is an infinite decimal that can never be divided, and it cannot be completely and accurately expressed by fractions, finite decimals or cyclic decimals. Due to the progress of modern mathematics, pi of more than two thousand decimal places has been calculated.
Pi is widely used. Especially in astronomy and calendars, all problems involving circles should be calculated by pi. 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 = 3. 1622. Of course, these values have made great progress compared with π=3, but they are far from accurate. At the end of the Three Kingdoms, mathematician Liu Hui created the method of secant to find pi, and the research on pi has made great progress.
The method of secant to find pi is roughly as follows: first make a circle, and then make a regular hexagon inscribed in the circle. Suppose the diameter of this circle is 2, then the radius is equal to 1. The inscribed side of a regular hexagon must be equal to the radius, so it is also equal to1; Its circumference is equal to 6. If the circumference 6 inscribed with a regular hexagon is taken as the circumference of a circle and divided by the diameter 2, the ratio of circumference to diameter π=6/2=3, which is the ancient value π=3. However, this value is incorrect. We can clearly see that the perimeter of an inscribed regular hexagon is much smaller than that of a circle.
If we double the number of inscribed sides of a regular hexagon to become an inscribed regular dodecagon, and then find its circumference by an appropriate method, then we can see that this circumference is closer to the circumference of a circle than that of an inscribed regular hexagon, and the area of this inscribed regular dodecagon is closer to the area of a circle. From this, we can draw a conclusion that the more sides in a circle are connected with a regular polygon, the smaller the difference between the total length (circumference) of its sides and the circumference of the circle. Theoretically, if the number of inscribed sides of a regular polygon increases to infinity, the perimeter of the regular polygon will closely coincide with the circumference, and the inscribed area of the infinite regular polygon calculated from this will be equal to the area of the circle. But in fact, it is impossible for us to increase the number of inscribed sides of a regular polygon to infinity, so that the circumference of this infinite regular polygon coincides with the circumference. We can only increase the number of sides inscribed with a regular polygon, so that its perimeter and circumference almost coincide. Therefore, by increasing the number of inscribed regular polygon sides of a circle, the number of pi is always slightly less than the true value of π. According to this principle, Liu Hui begins with a circle inscribed with a regular hexagon, and the number of sides gradually doubles until the inscribed regular hexagon is calculated, and the pi is 3. 14 1024. Turn this number into a fraction, which is 157/50. The pi obtained by Liu Hui was later called "Hui rate". His calculation method actually has the concept of limit in modern mathematics. This is a brilliant achievement in the study of ancient pi in China.
Zu Chongzhi has made great achievements in deducing pi. According to "Sui Shu Law and Discipline", Zu Chongzhi changed ten feet into one hundred million feet, so as to find pi. The result of his calculation is two numbers: one is abundance number (approximate value of surplus), which is 3.1415927; One is the number (that is, the approximate value of the loss), which is 3. 14 15926. The true value of pi is just between these two numbers. "Sui Shu" has only such a simple record, without specifying how he calculated it. However, judging from the mathematical level at that time, there was no better method except Liu Hui's cyclotomy. Zu Chongzhi probably adopted this method. Because of Liu Hui's method, when the number of inscribed sides of a regular polygon of a circle increases to 24,576, Zu Chongzhi's result can be obtained accurately.
The remainder can be listed as inequality, such as: 3. 14 15926 (*) < π (true pi) < 3. 14 15927 (remainder), indicating that pi should be between the remainder. According to the habit of using fractions in calculation at that time, Zu Chongzhi also adopted two fractional values of pi. One is 355/ 1 13 (about equal to 3. 14 15927), which is relatively accurate, so Zu Chongzhi calls it "the secret rate". The other is (about 3. 14), which is rough, so Zu Chongzhi calls it "approximate rate". In Europe, it was not until 1573 that the German mathematician Walter worked out the value of 355/ 1 13. Therefore, Japanese mathematician Mishima suggested that the value of pi of 355/ 1 13 be called "ancestral rate" to commemorate China, a great mathematician.
Because Zu Chongzhi's mathematical monograph "Zhuanshu" has been lost, and Sui Shu has not specifically recorded his method of seeking pi, experts who study China's mathematical heritage still have different opinions on his method of seeking pi.
Some people think that the numbers in Zu Chongzhi's Pi. It is obtained by inscribed regular polygons of a circle. And "abundance" is obtained by the method of circumscribed regular polygon of a circle. If Zu Chongzhi continues to use Liu Hui's method, he will double the number of sides inscribed with a regular hexagon and become a regular polygon inscribed with 24,576. The sum of the sides can only approximate and be smaller than the circumference of a circle, and the area of a regular polygon can only approximate and be smaller than the area of a circle. From then on, pi is 3. 14 1592 1. Judging from Zu Chongzhi's mathematical level, it is also possible to break through Liu Hui's method and try to find pi step by step from the circumscribed hexagon. If Zu Chongzhi multiplies the number of sides of the circumscribed regular hexagon by a positive 24576, he should get the pi of 3. 14 15970208. This figure is obtained by a limited method. Because the sum of the sides of the circumscribed regular polygon is always greater than the perimeter, and the area of the regular polygon is always greater than the area of the circle, this number is always greater than the real pi. A remainder can be obtained by rounding seven decimal places.
There is no exact historical data to prove whether Zu Chongzhi used the internal cutting method and the external cutting method to find pi and abundance at the same time. However, the two values obtained by this method are basically consistent with the original results obtained by Zu Chongzhi. Therefore, some historians of mathematics think that it is very reasonable for Zu Chongzhi to get pi by using the method of circumscribed regular polygon as a circle.
However, according to the research of other mathematical historians, the remainder and the remainder can also be obtained by calculating the side lengths of the regular 12288 polygon and the regular 24576 polygon inscribed in the circle. However, this calculation is difficult to understand, so I won't say it here.
Although there are discrepancies, it is certain that Zu Chongzhi once came up with the "density ratio", and clearly used the upper and lower limits to explain the range of pi. 1500 years ago, he had such achievements and knowledge, which really deserves our admiration.
When calculating pi, Zu Chongzhi put a lot of effort into it. If you count from a regular hexagon to 24,576 sides, you have to repeat the same operation program for twelve times, and each operation program includes more than a dozen steps such as addition, subtraction, multiplication, division and root. It is also extremely difficult for us to do such calculations with a paper-and-pencil abacus now. At that time, Zu Chongzhi had to use chips (small bamboo sticks) to do such complicated calculations. If you don't have a very calm mind and perseverance, you will never succeed. Zu Chongzhi's perseverance and assiduous study are highly commendable.
After Zu Chongzhi's death, his son Zuxuan continued his father's research and further discovered the method of calculating the volume of a sphere.
There is a formula for calculating the volume of a sphere in China's ancient mathematical work Nine Chapters Arithmetic, but it is not accurate. Although Liu Hui once pointed out its mistakes, he didn't find a way to calculate them. After studying hard, Zuxuan finally found the correct calculation method. The formula he worked out to calculate the volume of a sphere is: the volume of a sphere =π/c D(D stands for the diameter of a sphere). This formula has been used by people ever since.
Zu Chongzhi also wrote five volumes of composition, which is a wonderful mathematical work and highly praised by people. In the mathematics discipline of government-run schools in the Tang Dynasty, students were required to study "composition" for four years; When the government holds a math exam, it often comes up with composition questions. Later, this book spread to Korea and Japan. Unfortunately, in the middle of the Northern Song Dynasty, this precious book was lost. It remains to be seen until now.
Mechanical dexterity, sound and philosophical bypass
A compass is a car used to indicate the direction. The car is equipped with machinery, and the car is equipped with Woodenhead. Before the car starts, put Woodenhead's finger to the south. No matter how the car turns, Woodenhead's hand always points to the south. The structure of this kind of car has been lost, but according to the literature, it is composed of gears driving each other. According to legend, in ancient times, when the Yellow Emperor fought against Chiyou, he used a compass to tell the direction, but this is only a legend. According to historical documents, Ma Jun, an inventor in the Three Kingdoms period, once made this kind of compass, but it was later lost. In 4 17 AD, Emperor Wu of the Eastern Jin Dynasty (later the founding emperor of the Song Dynasty) marched straight into Chang 'an, and he was given an old compass by Yao Xing, the ruler of the late Qin Dynasty. The machinery in the car has been lost, so when the car is walking, it can only be turned by people to point to the south. Later, Xiao Daocheng, the Emperor of Qi Gao, asked Zu Chongzhi to copy it. The inner parts of the south guide car made in Zu Chongzhi are all made of copper. After it was made, Xiao Daocheng sent two ministers, Wang Sengqian and Liu Xiu, to test it. Practice has proved that the system is exquisite in structure and flexible in operation. No matter how you turn, Woodenhead's hand always points to the south.
When Zu Chongzhi was making a compass, a man named Suo Yuqian came to the Southern Dynasty, claiming that he could also make a compass. So Xiao Daocheng asked him to build one and compete with the South Compass made by Zu Chongzhi in the amusement park in the palace. As a result, Zu Chongzhi's compass works freely, but Suoyu's is very inflexible. Suo Yuqian had to give up and destroy his compass. Although you can't see the original compass made in Zu Chongzhi, you can imagine that its structure must be exquisite.
Zu Chongzhi also made very useful labor tools. He saw that the working people threshed and milled rice very hard, so he created a food processing tool called water hammer mill. Ancient working people invented water reefs and water mills for milling rice with water very early. In the early years of the Western Jin Dynasty, Du Yu improved it and invented "continuous mill" and "water-to-water continuous mill". A connecting machine can drive several stone pestles to land together; A water mill can drive eight mills to grind at the same time. On this basis, Zu Chongzhi has further improved it, combining water hammer with water mill to further improve the production efficiency. This processing tool is still used in some rural areas in southern China.
Zu Chongzhi also designed and built a thousand-mile ship. It may be caused by the principle of using wheels to push water forward, and it can travel 100 miles a day.
Zu Chongzhi also made a "ritual vessel" and gave it to Xiao Liang Zi, the second son of Emperor Wu of Qi. Fences were used by the ancients to warn against complacency. When there is no water in the container, it is horizontal. After it is filled with water, it will stand up if the amount of water is moderate; If the water is full, it will fall to one side and spill it. Tu Yu, a scholar in Jin Dynasty, tried this instrument three times, but failed. Zu Chongzhi copied successfully. Thus, Zu Chongzhi has a profound research on all kinds of machinery.
Zu Chongzhi's achievements are not limited to natural science. He is also proficient in music theory. He knows a lot about temperament.
In addition, Zu Chongzhi's philosophical works such as Zhouyi, Lao, Zhuang and Interpretation of the Analects of Confucius have been lost.
Zu Chongzhi's son Zu Xuan is also an outstanding mathematician. He inherited his father's research and founded the correct algorithm of sphere volume. In astronomy, he can follow in his father's footsteps. He once wrote thirty volumes of astronomical records and one volume of astronomical records, but unfortunately these books have been lost. Da Li Ming, compiled by his father, was formally adopted after he suggested to the Liang government three times. He also made a punctual broken kettle wine, which was very accurate and made a "missed classic".
Sui Shu Jing Ji Zhi contains 51 volumes of Zu Chongzhi Collection, a captain of Changshui, which has been lost.
Scattered in various historical records are the following works:
Safety theory.
Ten volumes of Yi Shu.
Laozi and Zhuangzi of Yi nationality, Yi nationality.
Notes on filial piety in the Analects of Confucius.
"compose" six volumes, oh.
Notes on arithmetic meaning in nine chapters and nine volumes.
The first volume of "Notes on Heavy Difference", yeah.
Daliming
Go to Daming calendar
refute
Open circle