Zu Chongzhi's deeds are introduced in middle school textbooks, but his thought treasure house needs to be further explored. I will briefly introduce his scientific achievements and thoughts from several aspects, hoping to play a role in attracting jade.
(A) Zu Chongzhi's life
(B) Zu Chongzhi's mathematical achievements
(3) Zu Chongzhi's astronomical achievements.
(4) Zu Chongzhi's achievements in mechanical invention.
(5) Zu Chongzhi's scientific spirit.
(a), Zu Chongzhi's life
In ancient China, scientists were not valued. Zu Chongzhi is a rare scientist whose scientific contribution is recorded in official history. His biography can be found in the literary biographies of and. Although it is only a few pages, it is already considerable.
Zu Chongzhi was born in Fanyangqiu (now Laishui, Hebei Province). Great-grandfather's ancestral home is Taiwan Province, the word Chen, and he worked as a Shang Cheng, a Shi Zhong and a doctor of Guanglu in the Jin Dynasty. Grandpa Zuchang was a great craftsman in Liu and Song Dynasties. My father Zu Shuozhi was invited by Liu Song. At that time, the Northern and Southern Dynasties confronted each other, and the capital of Liu and Song Dynasties was Jiankang (Nanjing), where Zu Chongzhi probably grew up.
Zu Chongzhi first entered the official career in South Xuzhou (now Zhenjiang City, Jiangsu Province) as a junior official engaged in history and government joining the army. During the reign of Liu Song Emperor Xiaowu Liu Jun (454-464 AD), he worked in Hualin University and got a house, a car and some clothes. In the sixth year of Daming (462), he presented his "Da Li Ming" to the court, which triggered a great debate. After that, he left Beijing to serve as a county magistrate in Louxian County (now the northeast of Kunshan County, Jiangsu Province), and then returned to Beijing to be promoted to a servant. The following year (AD 477-479), Liu Songsheng made a compass. During the reign of Yong in the Northern Qi Dynasty (483-493), a sacrificial vessel was made. I also worked as a captain of Changshui in Beiqi, a fourth-level official, and reached the peak of my career. During this period, he wrote "On Security", and during the Jianwu period (494-498), he planned to let Chong travel around and do something big. However, due to successive military operations, it was not realized. In the second year of Yongyuan in the Northern Qi Dynasty (500 years), he passed away with regret at the age of 72.
Zu Chongzhi Zi Zuxuan, also known as Zuxuan, was a supreme official. Zuxuan is famous for his concentration. He inherited and carried forward the academic tradition of his family and made contributions to mathematics, astronomy and mechanical inventions. Father's calendar was promulgated with his efforts.
Zu Chongzhi was born in an official family and received a good education since childhood. Especially in his youth, he studied mathematics and astronomical calendar seriously, and formed a critical spirit of emphasizing motivation and not superstitious about the ancients. He reads widely and has a wide range of knowledge. In addition to mathematics, astronomy and mechanics, he is also good at temperament, history, Confucianism, Taoism, literature and even opera, and he is a rare all-rounder
Zu Chongzhi was diligent in writing, annotated the mathematical classics "Nine Chapters Arithmetic" and "Heavy Difference" in mathematics, and wrote his own "Zhuanshu" (or Zhuanshu); In astronomy, he is the author of Daming Calendar. He studied San Xuan and Confucian classics, and wrote notes for the Book of Changes, Lao Zi, Zhuangzi, The Analects of Confucius and Xiao Jing. He cares about the country and society, and he wrote The Theory of Security. In addition, he also wrote ten volumes of Yi Shuo Ji. Records of Gyeonggi said that "Liang has fifty-one volumes of Zu Chongzhi Collection, a captain of Changshui", and it is estimated that his works were collected after his death and passed down from generation to generation. It can be seen that he is indeed a knowledgeable scholar.
(2) Zu Chongzhi's achievements in mathematics.
When Zu Chongzhi was young, he was very interested in mathematics and made great efforts. He is familiar with the work of previous mathematicians and can criticize, revise and develop on the basis of inheritance. He made an in-depth study of Nine Chapters Arithmetic and the work of its researchers Zhang Heng, Zheng Xuan, Kan Ze, Wang Fan and Liu Hui. At the same time, he studied the astronomical calendar intensively, which also promoted his mathematics work. He studied and took notes for Nine Chapters of Arithmetic, and then wrote dozens of mathematical papers, which were included in Zhuanshu (or Zhuanshu). This book was used as a teaching material of imperial academy Mathematics Museum in Sui and Tang Dynasties, and also as an examination book for the subject of "Shu Ming" in the national imperial examination. Seal script was lost as early as 1 1 century. However, in the academic system of the Arithmetic Museum in the Tang Dynasty, the study time of Seal Script was as long as four years, which was the longest study period among all arithmetic classics, so it contained the most profound mathematical knowledge at that time. Zu Chongzhi's works also spread to Japan and Korea in the Tang Dynasty, showing its far-reaching influence.
As all Zu Chongzhi's mathematical works have been lost, we can't know his mathematical creation in detail. But now the remaining pieces of information are enough to illustrate his genius ability. Here is a brief introduction from three aspects.
1π
Pi is a data widely concerned by different civilizations, and its accuracy can reflect the developed degree of mathematical calculation methods in a civilization to some extent.
China's ancient mathematical classic Nine Chapters Arithmetic takes Wednesday as the rate, which is equivalent to π=3. Later, people constantly improved this data. For example, Liu Xin, Zhang Heng, Liu Hui, dorri and Pi Yanzong. The most concerned is the value of pi calculated by Zu Chongzhi.
He calculated a circle with a diameter of ten feet, and he got the excess approximation of the circumference of the circle "three feet one foot four inches one minute five millimeters nine seconds seven seconds" and the deficiency approximation "three feet one foot four inches one minute five millimeters nine seconds six seconds", divided by 1 foot, then according to the modern expression, the pi calculated by Zu Chongzhi satisfies: 3.14/kloc-. π& lt； 3. 14 15927。 This figure is accurate to seven decimal places, which is far ahead in the world. More than 900 years later,15th century mathematician and astronomer Al-Kashi (about 1380- 1429, born in today's Iran) wrote "Theory of Circles" to calculate.
In ancient times, it was customary to calculate by fractions. Zu Chongzhi got two fractional approximations of pi, the density is 355/ 1 13, and the approximate ratio is 22/7. The former is about 3. 14 15929, accurate to 6 decimal places. According to Mr. Liang Zongju's calculation, the denominator of pi is less than 16604, which is the approximate fractional value closest to the true value.
Before Zu Chongzhi, Liu Hui founded secant in the 3rd century, which proved that the area of a circle is equal to the product of radius and semi-circumference, and also established a scientific method for calculating pi. Zu Chongzhi's comments on "Nine Chapters" also mentioned his shortcomings. It is likely that he improved Liu Hui's method and got his pi.
Zu Chongzhi collated Li's quantity and Wang Mang's copper hoop with his Pi, and pointed out that Liu Xin, who designed Wang Mang's copper hoop, made a mistake in calculation because of his "bad mathematics".
Study on the volume formula of sphere 2
Ball, called pear garden and pill in ancient times. Nine chapters on arithmetic mentioned a method to find the diameter of a known sphere:
"The art of opening a circle says: multiply the number of rulers by sixteen, nine is one, and then divide it by the square, that is, the diameter of the pill."
Let v and d be the volume and diameter of the ball respectively, and the above method is equivalent to the formula.
d= .
Conversely, if the volume is to be calculated from the diameter of the ball, the above method is equivalent to the following formula.
V=. The ancients took π=3, so this is essentially V= d3.
If V= r3 is calculated according to the known radius, then pi = 3, which is essentially equivalent to V=.
There was something wrong with this method in ancient times. Zhang Heng once studied the relationship between cube and inscribed ball, circumscribed ball, ball and inscribed and circumscribed cube, but failed to solve this problem. The first person who took a big step was Liu Hui, who creatively designed a three-dimensional structure. First, cut it with the vertical inscribed cylinder in the cube, and then cut it with the horizontal inscribed cylinder to get an umbrella-shaped three-dimensional composite solid composed of upper and lower parts, which he called the square cover (umbrella). The inscribed sphere of the cube is also the inscribed sphere of the square cover. Liu Hui cut cubes with planes parallel to their upper and lower bottom surfaces, and found that every time a square was cut from the cover of the square, a circle tangent to the square was cut from the ball. Obviously, their area ratio is 4: π. Liu Hui's default solid consists of a series of areas, so he asserts that the ratio of the volume of the square cover to the volume of the inscribed sphere is also 4: π. The square cover of Mouhe is smaller than the circumscribed cylinder, and Liu Hui infers that the result calculated by the ancient spherical volume formula is larger.
Because the volume ratio of Mohe square cover to sphere is fixed at 4: π, the calculation formula of sphere volume is transformed into the calculation formula of Mohe square cover. Liu Hui does not directly calculate the volume of the square cover, but first considers the part between the cube and the square cover. He found this part difficult to ask, frankly admitted that he could not solve it, and left the problem to future generations.
The wise men of later generations are Zu Chongzhi and Zuxuan. Li's annotation in "Nine Chapters Arithmetic" quoted Zuxuan's opening circle method, which finally solved this problem. Zu Chongzhi said in "Da Ming Li" that "if old mistakes are made, Zhang Heng will change", and he also noted nine chapters. The name of Zuxuan's works is also called seal script. Therefore, it is reasonable to think that Li and Zuxuan's solution to the spherical volume formula is the result of the joint efforts of father and son.
They inherited Liu Hui's thought, and synthesized a two-inch square cube from eight one-inch square cubes, then made an inscribed sphere and a square cover, and then calculated the partial volume between the cube and the square cover. The specific solution is as follows: or use simulated chess to explain. Consider the part between two-inch square solids (8 cubes) and any one-inch square cube (1 cube). If this part is decomposed, multiply it by 8 to get the whole volume.
(The above picture is taken from Guo Shuchun's "Liu Hui, the Master of Mathematics in the Ancient World")
In Figure (2), the part of a harmonious square covered by a chess game (inner chess game) and the part between it and the cube can be divided into three pieces (outer chess game): (3), (4) and (5). Cut them with parallel bottom planes so that their height is = a. These three pieces cut out two rectangles and a square, which just forms a square. Its area is the difference between the cross section of square NKJI and the internal chess, which is equal to NK2-NM 2, m is the point on the cylindrical surface, and the radius OM is equal to OG, which is also equal to the side length NK of square NKJI, so the square area is equal to OM2-NM2. The cross section is parallel to the bottom ABCD and perpendicular to the height above (OA), so ONM is a right triangle. According to Pythagorean theorem, the area of a square is OM2-NM2=ON2=a2, which is exactly the cross section of a quadrangular pyramid (6) with the upper bottom (ABCD) of the cube as the bottom and one side (CF) of the cube as the height. Zu Xuan said: "The fate is the same, but the products cannot be different." . That is to say, if two solids are cut by a series of parallel planes, and the area of each cut has the same relationship, then their volumes also have the same relationship. On this issue, this relationship is equal, which is the origin of the axiom of ancestor propaganda learned in middle school. Accordingly, Zu Xuan transformed the outer three chess into a cone (6). Its volume is 1 of the cubic volume. So he calculated that the volume of the internal chess pieces was two-thirds that of the rest of the cube. Therefore, it can be calculated that the volume of the whole square cover is 2/3 of that of the whole (2 inches) cube. Now that the volume of the square cover has been calculated, the volume of the ball can be calculated by using its proportional relationship with the volume of the ball of 4: π.
It is estimated that there are still such fantastic ideas in seal script, but unfortunately we will never see them again.
3 Open Band Slave (Longitudinal) Method with Negative Numbers
In ancient China, square root was an important mathematical category. In addition to our current square roots, square roots and multiple roots, it also includes methods equivalent to solving univariate multiple equations (Xn+A 1xn- 1+ ... +An- 1x = n). If at least one of these AIs is not zero, it is said that the band is open from the (vertical) direction.
"Sui Shu Li Zhi" records that Zu Chongzhi "reset the right of the fork in the road, so that the fork in the road stands, with positive (round) [negative] participation".
Mr. Qian Baoyu thinks that "open difference power" means "knowing the area of a rectangle and the difference between its length and width, and finding its width or length by Kaiping method", while "open difference standing" means "knowing the volume of a cuboid and the difference between its length, width and height, and finding its side by opening method". The open difference power and open difference station show that Zu Chongzhi can open a band from the sum of squares to the cube. As far as we know, Zu Chongzhi was the first place to open the belt. Not only that, he also introduced positive and negative numbers in the band opening method. This is really a remarkable achievement.
Zu Chongzhi's seal script has been lost, but it can be inferred that it is ahead of the times. Sui Shu Li Zhi said that Zu Chongzhi "wrote a book called Zhuanshu, and scholars could not study its profundity, so they ignored it." It can be seen that although "Zhuanshu" was included in the textbook of computer science library and the book for imperial examination, it was too abstruse, and the professors at that time could not understand its abstruse characteristics, and may not have been taught in a down-to-earth manner. This is probably one of the reasons for the loss.
(3) Zu Chongzhi's astronomical achievements.
Zu Chongzhi's contribution to astronomy mainly lies in the calendar. He worked out a calendar, Daming Calendar, in which there was a great creation that surpassed the predecessors.
In the sixth year of Daming (AD 462), Zu Chongzhi, at the age of 33, presented a calendar to the court. In the above table, he said: "I visited the front grave and looked back at the past. The five emperors paid attention to it and the three kings paid attention to it. "Spring and Autumn Annals" is fresh and thin, and (Sima) talks about it and (Sima) moves it. (class) table, (class) sorting out his records, Wei's annotation calendar, daily life of Jin Dynasty. " The book has been written for more than two thousand years, which is a sign of the departure of the sun and the moon and a test of the density of stars. Specializing in work and thinking, there is also salt. I will personally measure the ruler, bow and check the instruments, and I will try my best to make a plan. As the exam goes on, I will prepare in detail. "
On the basis of studying various calendars and astronomical observation records of past dynasties and regions, and on the basis of careful observation, Zu Chongzhi used his profound mathematical skills to write this Daming Calendar with a rigorous and realistic attitude.
Previously, Liu Song used He Chengtian's Yuan Jiali (published in AD 443 and AD 445). Zu Chongzhi made a textual research and found that "Yuan Jiali" and "the sun and the moon are three degrees apart, two to the shadow, a few days lost, and the five stars fell, and the difference was forty days, so he stayed backward or moved for two nights. If the score is not accurate, it is that the festival is not correct and the accommodation is against the sky, that is, the service is not allowed. " It is impossible to accurately predict the serious consequences of ancient astronomical phenomena, so it is inevitable to change the calendar.
To this end, he made innovations and reforms in the new calendar. He summed up his innovation as "there are two things to change and three things to try."
The first point of change is to change the rules and the cycle of setting leap months. The old rule is to set 7 leap months in 19. Zu Chongzhi thinks that according to this leap period, there are too many leap months, and after 250 years (according to Chen Meidong's opinion, the original "200 years" will be changed to "250 years"), there will be a difference of one day. Zu Chongzhi put forward the rule that 39 1 year sets 144 leap month. This is the best leap week value in history.
The second point he changed was to introduce precession into the calendar.
Precession is a phenomenon that the earth's rotation axis changes slightly in space. In the history of China, astronomers in the Jin Dynasty discovered this phenomenon independently of Greek astronomers (about 330 AD): winter moved westward 1 degree every 50 years. In this way, the tropical year from winter solstice to winter solstice is distinguished from the sidereal year when a specific star returns to the star position, which opens the way for improving the accuracy of calendar calculation.
However, precession did not quickly enter the calendar calculation. Zu Chongzhi proposed an annual difference of 45 years 1 1 month. Although this value is not accurate for various reasons, he keenly noticed the importance of introducing precession into the calendar: the old calendar always thought that the position of the winter solstice was fixed, regardless of the existence of precession, which made the positions of the five stars of the sun and the moon more and more inconsistent with the actual positions. According to his practice, the precession is introduced into the calendar calculation, so that the winter solstice is slightly adjusted every year, which is very consistent with the records in Han Shu Zhu. In this way, the new calendar can be used for a long time in the future without repeated modification. What he thought of was a once-and-for-all approach. Of course, because his data is not very accurate, and the calendar is always checked with the actual observation, it is unrealistic to do it once and for all. But he introduced precession into calendar calculation, which is really a great progress.
Zu Chongzhi's three "Feelings of Finding the Road" are about the setting of the era: a day starts at midnight, and the winter solstice of the era begins at 1 degree; The calendar day is called Jiazi, and the year name also begins with Jiazi. He believes that the era began at 1 1 midnight of the moon in Jiazi era, which can make the sun and the moon merge into one and the five stars merge into one. This method should replace the multi-epoch method of Liu Xin, Yang Wei, Zhao, Jiang Ji and He Chengtian with the unitary method. This method has great subjective factors, a unified starting point for calendar calculation, and is convenient for calculation procedures. Although this processing method will sacrifice the accuracy of some observation data, and it will take a very large number of years, resulting in complicated calculation, the pursuit of this idealized astronomical phenomenon has promoted the study of a congruence problem in ancient mathematics in China, which is closely related to the later technology of calculating the total.
In addition to the above-mentioned "feeling of two changes and three trials", Zu Chongzhi's Da Ming Li has made the following important contributions.
First of all, a new method for calculating the winter solstice time was invented, paving the way for greatly improving the calculation accuracy. Second, his calculation of the length of the tropical year, although slightly adjusted the measurement results, is very successful from the method to the result. Its tropical years are 365 and 39495438+0.9589 days (= 365.438+048 days), which are among the best in China and far ahead in the world at that time. Zu Chongzhi also made it clear that the monthly length of the intersection is 27.2 1223 days, which is only 1.3 seconds away from the theoretical value, and its five-star rendezvous period is also greatly improved compared with the previous generation.
Although Daming Calendar is a very excellent and innovative calendar, its fate is ill-fated. After two dynasties, it was renamed Jiazi Yuanli in the ninth year of Tian Liang Prison (AD 5 10), which lasted for 48 years.
Zu Chongzhi's calendar work embodies his scientific spirit. We will deal with this problem later.
(4) Zu Chongzhi's achievements in mechanical invention.
Zu Chongzhi's grandfather, Zuchang, was a great craftsman during the period of Liu (in charge of civil engineering) in the Song Dynasty. Zu Chongzhi is ingenious and has many inventions in mechanical manufacturing, which are related to family traditions.
Zu Chongzhi's inventions in this field have not been preserved in kind, and the literature of specific details has not been circulated so far, so we can't know what specific contributions he made in technology. But according to the literature, he did invent and manufacture some exquisite utensils.
1 kit kat: south compass and fence.
The compass is a kind of kit kat. When it is moving, the car turns and the upper pointer can keep the direction unchanged. In 4 17, when Emperor Wu of Liu Song pacified Guanzhong (he had not ascended the throne at that time), he got Yao Xing's south guide car, which only had appearance but no control mechanism. Every time you use it, let someone turn around in the car to guide you. Later, Zu Chongzhi made a bronze machine, which can automatically adjust the direction when the car moves. It has become an ingenious device that has not been seen since Ma Jun, a famous craftsman of Wei State in the Three Kingdoms. Zu Chongzhi's bronze machine for Yao Xing's car is really the finishing touch. At that time, there was a man named Suo in the north, and he also claimed to be able to build a compass. The emperor ordered each of them to make one and compete in the Le Garden. As a result, the compass made by Suo was destroyed and burned because of its poor quality.
The water container is an inclined and repeatable water container in ancient times. If there is less water, it will tilt, if there is not much water, it will be positive, and if it is full, it will turn over. The ancient monarch put it on the right side of the seat as a warning. In the Jin Dynasty, Du Yu had a clever idea to build a sacrificial vessel, but it failed for three years. During the Yongming period of the Southern Qi Dynasty (AD 483-493), Prince Jingling lived before his death, and Zu Chongzhi successfully made a sacrificial vessel for him.
Transportation: wooden ox and flowing horse, thousands of miles boat.
In history, Zhuge Liang designed a wooden ox and a flowing horse. We don't know what it really looks like. Technical historians may think that it is a wooden cow. They are unicycles with four legs. But the former is like a cow and the latter is like a horse. Zu Chongzhi made a fool of himself, just a tool. Wind and water are not used, which is labor-saving and convenient.
Zu Chongzhi also built a ship, which traveled more than 100 Li a day ("a thousand Li" is not 1000 Li, but an exaggeration, meaning fast). Technical historians speculate that Zu Chongzhi's thousand-mile ship may be driven by paddles. Later, Zu Chongzhi's son Zuxuan was Tai Zhou Qing, who was in charge of shipbuilding and transportation, or was related to his father's invention.
3 farm tools: water hammer mill
Water hammer and water mill are two agricultural tools, both of which are driven by water. The former is mashed and ground into rice grains, and the latter is ground into rice grains. Zu Chongzhi made a water hammer mill in Leyuan Garden, which may be a combined hydraulic tool combining water hammer and water mill. Emperor Wu of Qi once personally observed it.
(5) Zu Chongzhi's scientific spirit.
We know that the most taboo in doing science is to listen to other people's suggestions, not to respect the facts, and to argue irrationally. Scientists are most afraid of power intervention. Zu Chongzhi's scientific spirit is embodied in such aspects as not being afraid of power, pursuing truth, being rigorous and realistic, and convincing people by reasoning.
Zu Chongzhi lasted until the Ming Dynasty. At first, because few people knew it, no one objected and no one agreed. At this time, my favorite Dai Faxing jumped out to attack, so a group of people who agreed jumped out to echo him.
At that time, Zu Chongzhi was only 33 years old, and his rank was very low. At this time, Dai Faxing was the commander of the Prince's Brigade and a five-product officer. The level is not very high, but it is still much higher than that of Zu Chongzhi. What is important is that Dai Faxing was a close minister of Emperor Xiaowu before he ascended the throne. After Xiaowu succeeded to the throne, he was named the Duke of Wuchang County, with a title, and was also a person around the Prince. At that time, Emperor Xiaowu loved him very much, and officials were rewarded and punished for their promotion. Xiaowu followed his advice. Therefore, wearing more bribes has become an outside market.
Faced with the power of powerful ministers and the one-sided situation of courtiers, Zu Chongzhi not only refused to admit his mistakes, but also did not take a laissez-faire attitude. Instead, he had nothing to hide and argued.
Dai disagreed with the theory of precession, thinking that the position of winter is not easy to live forever, and gave Zu Chongzhi the hat of "apocrypha"; He thinks that Zu Chongzhi's new leap week is "cutting the bad chapter of leap", and forcefully says that the rules and regulations are "afraid that you can't make mistakes if you don't hurry."
In the face of the attack, Zu Chongzhi did not take a negative attitude of admitting mistakes, nor did he fight back in an emotional way. Instead, he quoted classics to prove that Dai's view that the ancient six calendars were sacred and unchangeable was wrong, and proved the existence of precession on the basis of observation data. With a rigorous and realistic attitude, he proved that his opinion is not a superficial and incisive theory of "apocrypha", but a theory of "following the classics". In addition, the accusation of Dai's arrogance strongly shows his attitude of "talking nonsense and stealing without fear". Zu Chongzhi retorted, "I studied for a long time and did poorly in the exam. I am in harmony before the exam ",with observation and testing as the core, is the embodiment of the scientific spirit.
Probably because of Zu Chongzhi's dauntless bearing, rigorous and realistic spirit and well-founded refutation, he won the support of a junior official, Shang Chao. Although Chao's family was only a seven-rank official, as a calligrapher in China, he received and delivered documents for the emperor, and belonged to the emperor's trusted minister, holding an important position. Because Chao Shi defended Zu Chongzhi and "loved the wonders of the past", the emperor planned to adopt the Daming calendar. But Zu Chongzhi was unlucky, and the emperor died immediately, which delayed the promulgation of Da Ming Li. Later, when I came to Nanqi, there was another opportunity for the Prince to support me, which was also missed because of the death of the Prince. Therefore, it was not until 10 year after Zu Chongzhi's death that it was promulgated in the name of Jiazi Yuanli with the revision and efforts of his son.
Zu Chongzhi is not afraid of dignitaries as their agents, and dares to stick to the scientific spirit of truth, not because of his boldness and stubbornness, but because of his own advantages. Zu Chongzhi received a good education and extensive knowledge since childhood. He is not only good at mathematics, reasoning and calculus, but also practical and ingenious, personally making astronomical observations. This enables him to accurately grasp the relevant issues, so he can be confident and have answers when debating with politicians. This is unmatched by Dai Faxing, who has read a lot of books but has a narrow knowledge. It can be seen that scientific spirit and scientific knowledge complement and promote each other in this way. This is also an inspiration from Zu Chongzhi.
Zu Chongzhi is not perfect. He studied Zu Chongzhi for us and made no secret of his shortcomings. For example, Zu Chongzhi overemphasized the metaphysical method and excessively rejected the pluralistic method, which not only unified the style, but also increased the complexity of calculation, which had both advantages and disadvantages. In addition, Dai Faxing is not an ignorant person as most people understand. He was born in poverty, but he studied hard and read widely since childhood, but his knowledge was narrow and he was not good at mathematics and astronomy. Because of his humble background, he was deeply loved by the emperor and flattered by the ruling and opposition parties, so he got carried away and thought he could do anything. We should treat historical figures objectively and fairly, including Zu Chongzhi and Dai Faxing whom he denied, and seek truth from facts. This is also the attitude we should adopt when studying Zu Chongzhi's scientific spirit.
Main references
1[ Tang] li yanshou: History of the South, Zhonghua Book Company, 1987.
2[ Liang] Xiao Zixian: The Book of Southern Qi, Zhonghua Book Company, 1974.
3[ Liang] Book: Song Shu, Zhonghua Book Company, 199 1 year.
4 Qian Baoyu: History of Chinese Mathematics, Science Press, 1964.
5. Yan Dunjie: Collation and Interpretation of Zu Chongzhi's Scientific Works, Liaoning Education Press, 2000.
6 Du Shiran: Biography of Zu Chongzhi, Exploring the Victory of China's Traditional Science and Technology Culture-In Memory of Yan Dunjie, Science Press, 1992.
7 Chen Meidong: Astronomical Volume of the History of Science and Technology in China, Science Press, 2003.
8 Guo Shuchun's book: Liu Hui, Master of Mathematics in the Ancient World, Shandong Science and Technology Publishing House, 1992.
9 Guo Shuchun, editor-in-chief: History of Science and Technology in China, Mathematics Volume, Science Press, 20 10.
10 Yan Li: China Mathematics Outline (Revised Edition), Science Press, 1958.
1 1 edited by Lu Jingyan and Hua jueming: History of Science and Technology in China, Mechanical Volume, Science Press, 2000.
12 "al-kashi", encyclopedia Britannica 2009 student edition and home edition CD edition.
13 Liang Zongju: Historical Allusions of Mathematics, Liaoning Education Press, 1992.
14 The Star of Zu Chongzhi.