The story of Shen Kuo.

Shen Kuo (A.D. 103 1 ~ 1095) was born in Qiantang County, Hangzhou (now Hangzhou, Zhejiang), Han nationality. Scientists and politicians in the Northern Song Dynasty. 1 year-old, moved south to Wuyishan and Jianyang generation in Fujian, and then lived in Youxi area in Fujian. Injong Jiayou was a scholar in the eighth year (AD 1063). Zong Shen participated in Wang Anshi's political reform. In the fifth year of Xining (A.D. 1072), he was promoted to supervisor of Tianbu, and the following year he went to Zhejiang to inspect water conservancy and officers. In the eighth year of Xining (AD 1075), he sent envoys to Liao to refute Liao's land claims. The following year, he served as a bachelor of Hanlin, and made the third secretary right, rectifying Shaanxi salt policy. Later, Yanzhou (now Yan 'an, Shaanxi) was famous for strengthening its defense against Xixia. In the fifth year of Yuanfeng (1082), Song Jun was defeated by Xixia in the battle of Yongle City and was demoted. In his later years, he wrote Meng Qian Bi Tan in Meng Xi Park, Zhenjiang.

Shen Kuo's scientific achievements are manifold. He devoted himself to astronomy and advocated a new calendar similar to today's solar calendar. In physics, he recorded the principle of compass and various production methods; The existence of magnetic declination was discovered more than 400 years before Europe. The principle of concave mirror imaging is expounded. The law of * * * vibration is also studied. In mathematics, he founded "gap product" (second-order arithmetic progression summation method) and "meeting circle" (knowing the diameter of the circle and the height of the bow, finding the chord and arc length of the bow). In geology, he studied the formation of alluvial plain and water erosion, and put forward the name of oil for the first time. In medicine, there are many records of effective prescriptions and many medical works. In addition, he also recorded the scientific development and production technology at that time, such as movable type printing and metal smelting method invented by Bi Sheng.

Shen Kuo was interested in astronomy and geography since he was a child. He is curious and eager to learn. When he was a teenager, he lived in Quanzhou, Fujian for many years with his father, who was a state official in Quanzhou. Some of his experiences at that time were included in Meng Qian's Bi Tan. In astronomy, Shen Kuo has also made great achievements. He once made the armillary sphere, which was the main instrument for observing astronomy in ancient China. A scene table showing the shadow of the sun, etc. In order to measure the exact position of Polaris, he used an armillary sphere to observe the position of Polaris every day for three months, and drew the directions of Polaris on the map on the first night, midnight and last night respectively. After careful study, he finally came to the conclusion that Polaris is three degrees away from the North Pole. This scientific basis is recorded in detail in Meng Qian Bi Tan. Shen Kuo's contribution to mathematics is also recorded in Meng Qian's Bi Tan. He developed arithmetic progression from "Nine Chapters Arithmetic" and created a new summation method of advanced numbers-gap sequence. In geometry, he invented the rounding method, that is, the method of finding the bottom and arc of the bow from the diameter and height of the known circle. Because of this, Japanese mathematician Kazuo Sanshi once gave Shen Kuo a very high evaluation. (Excerpted from Applied Writing No.2, 1987, written by Shen Kuo)

[Edit this paragraph] Shen Kuo's concept of environmental protection

Shen Kuo has a strong sense of environmental protection, and has long pointed out not to cut down trees casually. On one occasion, Shen Kuo read in a book that "there is water in Gaonu County, which is flammable". Later, he went to the field to inspect the contents of the book. During the investigation, Shen Kuo discovered a brown liquid, which was called "stone paint" and "stone grease" by local people, and was used for cooking, lighting and heating. Shen Kuo gave this liquid a new name, oil. This name has been used to this day. At that time, he wanted to use oil instead of pine as fuel. He said that trees, especially ancient forests, must not be cut down at will unless necessary, let alone destroyed! At present, his view is absolutely correct, but it was not taken seriously at that time.

[Edit this paragraph] Biography of Shen Kuo

In the Northern Song Dynasty in China, there was a very knowledgeable and outstanding scientist. He is Shen Kuo, one of the most outstanding scientists in the history of China. He is proficient in astronomy, mathematics, physics, chemistry, biology, geography, agriculture and medicine; He is also an outstanding engineer and diplomat. At the same time, he is knowledgeable, good at writing and proficient in other people's calendars, music, medicine, divination and so on. Meng Qian Bi Tan, written in his later years, recorded in detail the outstanding contributions of working people in science and technology and their own research results, reflecting the brilliant achievements of natural science in ancient China, especially in the Northern Song Dynasty. Meng Qian's pen talk is not only an academic treasure house in ancient China, but also occupies an important position in the history of world culture. Known as "the coordinates in the history of science in China".

Shen Kuo was born in Qiantang, Zhejiang (now Hangzhou, Zhejiang) to a bureaucratic family. His father Shen Zhou worked as a local official in Quanzhou, Kaifeng and Jiangning. Mother Xu Shi is a well-educated woman. Shen Kuo was born in the ninth year of Tiansheng in Song Renzong (A.D. 103 1). He studied hard since he was a child. Under the guidance of his mother, he finished reading at home at the age of fourteen. Later, he followed his father to Quanzhou, Fujian, Runzhou, Jiangsu (now Zhenjiang), Jianzhou, Sichuan (now Jianyang) and Kaifeng, the capital of China. He had the opportunity to get in touch with the society, understand the life and production of the people at that time, increase his knowledge and show his superhuman intelligence. At the age of twenty-four, he started his career. He was the chief book of Shuyang County (now Jiangsu Province) in Haizhou, and then the county magistrate of Donghai (now Jiangsu Province), Ningguo (now Anhui Province) and Wanqiu (now Huaiyang County, Henan Province). At the age of 33, he was appointed as the governor of Yangzhou to join the army and was in charge of criminal trial. Three years later, he was recommended to Zhao Wen Concert Hall in Shi Jing to edit and proofread books. Here he began to study astronomical calendars. Song Shenzong Xining five years (A.D. 1072), who was also the supervisor of astronomical phenomena, was responsible for observing astronomical phenomena and calculating almanac. Then, Shen Kuo served as the review of the history museum, and in the sixth year of Xining (A.D. 1073), he became the general manager of Jixian College. Due to the convenience of his position, he has the opportunity to read more royal books and enrich his knowledge. 1075 was sent to Liao for border negotiations, and the following year he served as a bachelor of Hanlin and was appointed as the third secretary.

In the second year of Xining in Song Shenzong (A.D. 1069), Wang Anshi was appointed as prime minister and began a large-scale political reform movement. Shen Kuo actively participated in the political reform movement and was trusted and valued by Wang Anshi. He has served as the highest official in charge of state finance, three secretaries and many other important positions. In the ninth year of Xining (AD 1076), Wang Anshi's political reform failed. As usual, Shen Kuo learned about Xuanzhou (now Xuancheng, Anhui Province) because of his involvement and the exposure of his poems. Three years later, in order to resist Xixia, he changed to Yanzhou (now Yan 'an, Shaanxi) and served as the envoy of Yan 'an Road. In the fifth year of Yuanfeng (A.D. 1082), he was promoted to a bachelor's degree in Longtuge for his meritorious service in resisting the invasion of the Tangut aristocratic group headed by Queen Liang of Xixia. But not long after, due to Xu Xi, general manager of Yan Yandao, Qu Zhen, deputy general manager of Yan Yandao and others, they were greedy and reckless, did not listen to the advice of Chamberlain Li Shunju who accompanied them, and built the city to their death, resulting in a fiasco in Yongle City, with 20,000 soldiers lost and no civilian worker. Both Heng and Li Shunju died heroically. This war was one of the great defeats in the history of the Northern Song Dynasty, which destroyed the good unification situation after Xia Pingcheng's great victory. Although it is not the first time for Shen Kuo to commit this crime, he has the leadership responsibility after all. In addition, due to his poor rescue in the battle, he was demoted to Zhou Jun (now Xunxian County, Hubei Province) as Ying Yong's deputy, and was placed in Suizhou. Since then, his political life has come to an end, so he devoted himself to writing. In the second year of Zhe Zongyuan (A.D. 1087), Shen Kuo spent 12 years compiling the Map of Counties and Counties in the World, which was submitted in Bianjing by special permission. The following year, he settled in Meng Xi Park in Runzhou (now the eastern suburb of Zhenjiang, Jiangsu) to spend his old age.

In his later years, Shen Kuo carefully summed up his life experience and scientific activities in Meng Xi Park, and wrote famous scientific masterpieces such as Meng Qian's Pen Talk and Forgetting His ambition. Song Zhe died in the second year of Zong Shaosheng (AD 1095). He wrote dozens of books in his life, but so far, except Meng Qian's Bitan, there are only works such as Changxing Ji and Yi Fang. Shen Kuo is still an outstanding astronomer. In the fifth year of Xining (A.D. 1072), when he was in charge of Bianhe construction in Shen Kuo, Shen Kuo was also in charge of leading the Tianjian Supervision Department. During his tenure, he successively dismissed six uneducated old calendar officials, regardless of their origins, and recommended Wei Pu, a Huainan native who was proficient in astronomical calendar calculation and was born in a civilian, to enter the Tianjian Supervision Department to preside over the important work of revising the new calendar. Shen Kuo and Wei Puzhi took a serious attitude and were very dissatisfied with the calendar revision method that the old calendar officials relied on calculus. They advocate starting with observing the astronomical phenomena and taking the measured results as the basis for revising the calendar. Therefore, Shen Kuo first studied and reformed the old astronomical observation instruments, such as armillary sphere, floating leak and shadow table.

The armillary sphere is an instrument for measuring the orientation of celestial bodies. After the development and evolution of the past dynasties, by the Song Dynasty, the structure of the armillary sphere had become very complicated, three times, intertwined and inconvenient to use. Therefore, Shen Kuo reformed the armillary sphere for many times. On the one hand, he canceled the small white ring, simplified the instruments and division of labor, and then linked the relationship between them with mathematical tools ("the moon ring is omitted, and the difference between the moon and the moon is only a step based on the calendar"); On the other hand, it is suggested to change the position of some rings so that they do not block the line of sight. These reform measures in Shen Kuo have opened up a new road for the development of musical instruments. Later, in the 13th year of Zhiyuan (A.D. 1276), Guo Shoujing of Yuan Dynasty created a new astronomical instrument-Jane Instrument, which was produced on this basis.

The clepsydra is an ancient instrument for measuring time. It is composed of several water containers in the form of steps, and the lower side of each container has holes, which drip from the next container in turn. There is no hole in the bottom container, but there is an "arrow" engraved with the time scale. As the dripping water level rises, the "arrow" slowly floats, and the time can be read from the exposed scale. Shen Kuo also reformed leaky cauldron. He changed the copper leaky pipe of the curved barrel into a straight-necked jade mouth and moved it to the lower part of the pot body. This makes the running water smoother, and the spout is much stronger and more durable.

In addition, Shen Kuo has formulated the standard for measuring the sun's shadow and improved the method for measuring the shadow.

Shen Kuo introduced his research achievements in three papers: On the Hunyi, On the Floating Leak and On the Landscape, elaborated the principle of instrument transformation in detail, and expounded his own astronomical views, which played an important role in the history of astronomy in China.

A series of innovative activities of Shen Kuo and Wei Pu were attacked and framed by conservative forces. Under the resolute struggle of Shen Kuo and Wei Pu, the revised Fengyuan Calendar presided over by Wei Pu was finally completed and promulgated in the eighth year of JaeHee Ning (A.D. 1075). However, due to the obstruction and destruction of conservative forces, the relatively advanced abundant calendar was abolished after only 18 years. However, Shen Kuo didn't lose heart because of this. In his later years, he further put forward the idea of replacing the original calendar with the "Twelve-qi Calendar". The original calendars in China were all based on the combination of yin and yang, but the "twelve-qi calendar" was a pure solar calendar. The year is divided into four seasons, and each season is divided into three months: Meng, Zhong and Ji, and the month is determined according to the solar terms. Beginning of spring's day is 1 month 1 day, and the day of fright is February 1 day, and so on. Thirty-one days for the big moon and thirty days for the small moon. The big moon and the small moon appear alternately. Even if there is a situation that "two little moons are combined into one", it is only once a year. There are "two small pictures", with 365 days in a year; No, 366 days a year. In this way, the days of the year are very neat, there is no need to set up a leap month, and the four seasons are fixed dates. As for the moon's profit and loss, it has nothing to do with the season when the cold comes and goes, as long as you indicate "new moon" and "hope" in the almanac. The calendar designed by Shen Kuo is scientific, which is not only in line with the reality of celestial bodies, but also conducive to the arrangement of agricultural activities. He foresaw that his ideas would be attacked and scolded by diehard conservatives, and he tried his best to obstruct them, but he firmly believed that "different times will be useful to speakers." Sure enough, nearly 800 years later, the basic principles of the calendar promulgated by the great peasant revolutionary regime, the Taiping Heavenly Kingdom, were completely consistent with Shen Kuo's Twelve Qi Calendars. The Gregorian calendar adopted by countries all over the world, that is, the solar calendar, is actually not as reasonable as the "twelve-year calendar" in Shen Kuo.

[Edit this paragraph] Physicists, chemists and mathematicians

Shen Kuo's achievements in physics research are also extremely rich and precious. The opinions and achievements recorded in Meng Qian's Bi Tan involve mechanics, optics, magnetism, acoustics and other fields. In particular, he has made outstanding achievements in magnetic research. Shen Kuo explicitly talked about the deflection angle of the magnetic needle for the first time in Meng Qian Bi Tan. In terms of optics, Shen Kuo made a popular and vivid exposition on pinhole imaging, concave mirror imaging, and the zoom-in and zoom-out functions of concave-convex mirror through personal observation experiments. He also made some scientific explanations for the light transmission reason of the so-called "transparent mirror" (a bronze mirror that can see the front pattern on the back) handed down from ancient China, which promoted the later research on "transparent mirror". In addition, Shen Kuo also did experiments on the piano to study the phenomenon of acoustic vibration. Shen Kuo first discovered that the north and south poles of geography do not coincide with the north and south poles of geomagnetic field, so there is a small deviation angle between the horizontal magnetic needle and the true north and south poles of geography. It is called magnetic declination.

In chemistry, Shen Kuo has also made some achievements. When I was in Yanzhou, I studied Lu Yan's oil reserves and uses. Taking advantage of the fact that oil is not easy to burn completely to produce carbon black, he pioneered the process of making cigarette ink with petroleum carbon black instead of pine carbon black. He has noticed that oil resources are abundant, "born in infinity" and predicted that "this thing will be popular in the world", which has been verified today. In addition, the name "petroleum" was first used in "Shenkuo", which is much more appropriate than the previous names such as stone paint, stone grease water, fierce fire oil, kerosene, naphtha and stone candle. In Meng Qian Bitan's "Taiyin Xuan Jing" (gypsum crystal), Shen Kuo distinguished several kinds of crystals from morphology, deliquescence, cleavage and heating dehydration, and pointed out that although they have the same name, they are not the same thing. He also talked about examples of metal transformation, such as the physical phenomenon of changing iron into copper with copper sulfate solution. These means of identifying substances described by him show that people's research on substances at that time has broken through the observation of simple surface phenomena and began to explore the internal structure of substances.

Shen Kuo also has excellent research in mathematics. Starting from the actual calculation needs, he founded "gap product technology" and "convergence technology". Shen Kuo put forward a correct method. By studying the volumes of the jars and chess pieces with gaps, the total pile number of jars and chess pieces can be obtained. This is the "gap product method", that is, the second-order arithmetic progression summation method. Shen Kuo's research has developed the arithmetic progression problem since Nine Chapters of Arithmetic, and opened up the research direction of higher-order arithmetic progression in the history of ancient mathematics in China. In addition, Shen Kuo also studied the relationship among arc, chord and vector in a circular bow from the calculation of field, and put forward the first simple and practical approximate formula for calculating arc length from the length of chord and vector in the history of mathematics in China, which is called "the skill of meeting circles". The establishment of this method not only promotes the development of plane geometry, but also plays an important role in astronomical calculation and makes an important contribution to the development of ball science in China.

[Edit this paragraph] Geographer and medical scientist

Shen Kuo also made many outstanding conclusions in geosciences, which reflected that China's geosciences reached the advanced level at that time. He correctly discussed the reasons for the formation of the North China Plain: according to the banded distribution of snail shells and oval gravel between the cliffs of Taihang Mountain in Hebei Province, it was inferred that this area was a seashore in ancient times, and the North China Plain was formed by sediment carried by rivers such as the Yellow River, Zhangshui River, Hutuo River and Sanggan River. During his inspection in eastern Zhejiang, he observed the geomorphological features of Yandang Mountain peak, analyzed its causes, and clearly pointed out that it was the result of water erosion. He also made a similar explanation based on the geomorphological features of the loess area in northwest China. He also observed and studied similar bamboo shoots and various fossils such as peach pit, reed root, pine tree, fish and crab excavated from underground, clearly pointed out that they were the remains of ancient animals and plants, and inferred the ancient natural environment from the fossils. All these show Shen Kuo's valuable materialism. In Europe, it was not until the Renaissance that the Italian Leonardo da Vinci began to discuss the nature of fossils, more than 400 years later than Shen Kuo. When Shen Kuo visited the border of Hebei Province, he made a three-dimensional geographical model of the mountains, roads and terrain he visited on the board. This practice was quickly extended to the border States. In the ninth year of Xining (A.D. 1076), Shen Kuo was ordered to compile the map of counties in the world. He consulted a large number of files and books, and after nearly 20 years of unremitting efforts, he finally completed the masterpiece "Shouling Map" in the history of cartography in China. This is a large atlas, with 20 maps, including a large map, one foot high and two feet wide; Small picture; Eighteen maps for each road (according to the administrative divisions at that time, the whole country was divided into eighteen roads). The scale and detail of the map are rare before. In painting, Shen Kuo put forward nine methods, such as grading, quasi-viewing, mutual integration, side inspection, competition, square inclination and straight pedaling, which are generally consistent with Pei Xiu's famous six-body painting method in the Western Jin Dynasty. He also subdivided all directions into twenty-four directions, which further improved the accuracy of the map and made important contributions to ancient cartography in China.

Shen Kuo is also proficient in medicine and biology. He was interested in medicine since he was a child and devoted himself to medical research. He collected many prescriptions and cured many critically ill patients. At the same time, his knowledge of medicinal botany is also extensive, and he can actually find out, distinguish authenticity and correct mistakes in ancient books. He once put forward a new theory of "five difficulties"; Shen Kuo's medical works include Prescription, etc. The existing Su Shen Liang Fang was made by later generations attaching Su Shi's Miscellaneous Treatise on Medicine to the Prescription. I counted several. Meng Qian Bi Tan is the coordinate of Chinese science history and the summary of Shen Kuo's social science activities all his life. Its content is extremely rich, including more than 600 articles on astronomy, calendar, mathematics, physics, chemistry, biology, geography, geology, medicine, literature, history, archaeology, music and art, among which 200 articles belong to science and technology, recording many of his inventions, discoveries and opinions. Shen Kuo is a scientific generalist. Shen Kuo, who is both civil and military, not only made brilliant achievements in science, but also made important contributions to defending the territory of the Northern Song Dynasty. During the Northern Song Dynasty, class contradictions and ethnic contradictions were very sharp. The aristocratic rulers of Liao and Xixia often invaded the Central Plains and plundered the population and livestock, which brought great damage to the social economy. Shen Kuo is firmly on the side of the hawk. Zaixi (AD 1074) served as the governor of Hebei West Road and the chief inspector of military equipment during the seven years of Ning. He studied the art of war, seriously studied military issues such as city defense, array law, personnel vehicles, weapons, strategy and tactics, and compiled military works such as the Treaty of Repairing the City of France and the Array Law of Frontier States, and successfully applied some advanced science and technology to military science. At the same time, Shen Kuo has also made in-depth research on the manufacture of crossbow armor, knives, guns and other weapons, which has made certain contributions to improving the quality of weapons and equipment.

Medical source database: Shen Kuo (103 1 ~ 1095), a scientist and physician in Song Dynasty. In the word, Qiantang (now Hangzhou, Zhejiang) was born. In the last year of Jiayou (1063). From officials to Hanlin bachelor, they have a wide range of knowledge. His masterpiece Meng Qian Bi Tan involves various disciplines, including astronomy, calendar, art of war, music, divination, physics and so on. This book mentions important inventions in ancient China, such as compass device, movable type printing, petroleum smelting, etc. In medicine, we have tasted Liang Fang (called Liang Fang) in Shencun, and Meng Xi's nasal sputum and nasal sputum, all of which are involved, such as Qiu Shi's preparation, the morphology, compatibility, pharmacology, preparation, collection and growth environment of 44 drugs. His Prescription was merged with Su Shi's Miscellaneous Notes on Medicine to form Su Shen Liang Fang, which has been published in many versions.

Brief introduction of Meng Qian Bitan

Written by Shen Kuo in the Northern Song Dynasty. This is a literary genre of notes about history, literature, art, science, etc. It is named after it was written in Meng Xi Park in Runzhou (now Zhenjiang, Jiangsu). Shen Kuo and Bi Tan □ Lin (Zhejiang Quzhou No.1 Middle School) Shen Kuo was born in Qiantang County, Hangzhou in the Northern Song Dynasty. The History of Song Dynasty compiled by Yuan Dynasty praised Shen Kuo for his "erudition and good writing, and omnipotence in astronomy, local chronicles, music, medicine and divination". His Meng Xi Notes was called "a milestone in the history of science and technology in China" by Joseph Needham, a British expert in the history of science and technology.

Meng Qian Bi Tan is a note novel by Shen Kuo in Song Dynasty. Written in 1086 ~ 1093, it contains what Shen Kuo saw, heard and thought all his life.

The existing Meng Qian Bi Tan has 26 volumes, which are divided into 17 categories ***609 articles: stories, dialectics, music, images, personnel, public affairs, intellectual power, literature and art, calligraphy and painting, skills, instrumental techniques, magic, wonders, fallacies, jokes, magazines and medicine. It covers astronomy, mathematics, geography, geology, physics, biology, medicine and pharmacy, military, literature, history, archaeology and music. Meng Qian Bi Tan is an important document and encyclopedic work in the history of science and technology in China.

In mathematics, he pioneered "gap product" and "pi". Astronomy points out that Polaris is not at the celestial pole; It is concluded that the winter solstice is long and the summer solstice is short. Astronomical instruments have also been improved. Boldly innovate in the calendar and put forward "twelve calendars in one place". In geography, water erosion is used to explain the causes of strange landforms. Recording magnetic declination, concave mirror imaging experiment and acoustic vibration experiment in physics. The book also describes some important scientific and technological achievements at that time, such as compass, movable type printing, copper smelting, steelmaking, petroleum and so on. Among them, the word "oil" was first put forward in the book and is still in use today.

In his later years, Shen Kuo wrote 26 volumes of Meng Qian's Bi Tan, and 3 volumes of Supplementary Bi Tan and Continued Bi Tan. * * * 609 articles, covering astronomy, mathematics, physics, chemistry, geoscience, biology, metallurgy, machinery, architecture, paper technology and other aspects. This is an important work in the history of China's science. Many scientific achievements recorded in Meng Qian Bi Tan reached the highest level in the world at that time. Needham, a famous British expert on the history of science, called Meng Qian's pen talk "the coordinate of the history of Chinese science".

The contents related to physics in Meng Qian Bi Tan mainly include acoustics, optics and magnetism, especially magnetism.

Shen Kuo left the earliest compass record in the history in Mengqianbitan. He recorded in the twenty-fourth volume "Magazine One": "Fangjia can be guided by a magnet grinding needle, but it is often eastward, not completely southward." This is the earliest magnetic declination record in the world. It was not until A.D. 1492 that Columbus discovered the geomagnetic declination when he first sailed to America, which was 400 years later than Shen Kuo's discovery. Shen Kuo also recorded in the third volume of Meng Qian's Notes on Essentials: "If you use a magnet to grind the needle, it will always be sharp in the middle, pointing to the north who is afraid of the stone." Shen Kuo not only recorded the making method of the compass, but also summarized four ways to place the compass through experimental research: put the magnetic needle horizontally on the wick, put it on the bowl edge or nail, and hang it with silk thread. Finally, Shen Kuo pointed out that hanging the magnetic needle with silk thread is the best method.

In optics, the knowledge recorded in Meng Qian Bi Tan is also extremely rich. On the basis of predecessors, Shen Kuo had a deeper understanding of the linear propagation of light. Explain the characteristics of light propagation along a straight line. He made a small hole in the paper window, so that the shadows of birds and towers outside the window could be imaged on the paper screen indoors for experiments. According to the experimental results, he vividly pointed out the linear relationship among objects, holes and images. In addition, Shen Kuo also used the principle of straight-line propagation of light to vividly explain the changing law of the moon phase and the cause of the solar eclipse. In Meng Qian Bi Tan, Shen Kuo also made a popular and vivid exposition on the imaging of concave mirror and the zoom-in and zoom-out function of concave-convex mirror. He also made some scientific explanations for the light transmission reason of the so-called "light transmission mirror" handed down from ancient China, which promoted the later study of "light transmission mirror".

In acoustics, Shen Kuo carefully designed an acoustic vibration experiment in Mengqianbitan. He cut a paper man and fixed it on a string. When a string with a simple integer ratio is played, it vibrates and makes the paper man jump, while when playing other strings, the paper man does not move. Shen Kuo called this phenomenon "the answer". It is Shen Kuo's initiative to show the * * * vibration in this way. In the west, it was not until the15th century that Italians began to do vibration experiments. Up to now, in the physics class of middle schools in some countries and regions, teachers have also used this method to demonstrate the vibration phenomenon for students.

Song Dynasty is one of the most brilliant periods of ancient mathematics in China. There are 10 articles on mathematics in Shen Kuo's famous work "On Meng Xi, a great scientist in the Northern Song Dynasty". The content is wide and deep, and it can be called the treasure of ancient mathematics in China.

Shen Kuo's most important mathematical exposition is gap product and circle. Gap product opened up the research field of higher-order arithmetic progression summation in the history of mathematics in China, and the research on higher-order arithmetic progression began in Shen Kuo.

The so-called "gap product" refers to the accumulation body with gaps, such as jars and chess pieces piled up in hotels. This accumulation is like an upside-down bucket, much like a truncated rectangular cone (straw boy). However, the edge of notch product is uneven and there is a notch in the middle, so Chu Tong's volume formula cannot be copied. After thinking, Shen Kuo found the correct calculation method. He took the piled jars as an example to illustrate this problem: the top floor was set with two jars vertically and horizontally, and the bottom floor was set with two jars vertically and horizontally 12, and the vertical and horizontal difference between two adjacent floors was 1 jar. Obviously, this pile of cans has *** 1 1 layer; The volume of each jar may be set to 1, and the total volume is 3784/6, and the total number of jars should be the same. Obviously, the number of cans should not be non-integer. What's the problem? Shen Kuo proposed adding a term "(lower width-upper width) × height /6" to the size of straw boy, which is 1 10/6, and the actual number of pots should be (3784+ 1 10)/6 = 649. This added item is only a volume correction item. Here, on the basis of the volume formula, Shen Kuo changed the cumulative number of discontinuous individuals (summation of series) into a continuous integer to solve, which shows his idea of using a continuous model to solve discrete problems.

Roundness is a practical approximate formula of the sagittal relationship of a circle. The main idea is to use straight lines instead of curves locally. Shen Kuo further applied the approximate formula of arc field area in Nine Chapters Arithmetic to find the arc length, which is the rounding formula. Although Shen Kuo's formula is approximate, it can be proved that the relative error is less than 2% when the central angle is less than 45, so this formula has strong practicability. This is an important proof of Liu Hui's thought of secant replacing arc with chord (the edge of regular polygon), which has important theoretical significance. Later, Guo Shoujing and Wang Xun applied rounding technique in calendar calculation.

In "Meng Qian Bi Tan", Shen Kuo also calculated the possible chess number of Go as 336 1 by combinatorial mathematics, and put forward a method to express this large number with the concept of order of magnitude. In his book, Shen Kuo also recorded some operational ideas, such as guiding the surging Bianshui to the ruins of the ancient city to rescue the collapse of the river bank, digging the road to repair the palace into a river, taking soil and transporting soil, and finally filling the river with construction waste. Shen Kuo's understanding of the essence of logarithm is also profound, pointing out: "Everything has a definite shape, and the shape has a true number." Obviously, he denied the mystery of numbers and affirmed the relationship between numbers and things. He also pointed out: "However, arithmetic does not suffer because of learning more. Use it when you see simplicity, and change it when you see complexity. It is also for general skills. "

[Edit this paragraph] Grasp Shen Kuo in the text.

Traditional China, whose virtue, speech and merit are the "three immortals", can hardly produce great scientists. However, an encyclopedic scientist appeared in the Song Dynasty. He is a geographer, physicist, mathematician, chemist, medical scientist, astronomer, water conservancy expert, weapons expert and strategist, and wrote the famous scientific book On Meng Xi. He is known to modern people as Shen Kuo.