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What did Zhang Heng invent?

Zhang Heng (78- 139) was born in Xi, Nanyang (now stonebridge, Nanyang City, Henan Province). He was a great astronomer in the Eastern Han Dynasty and made an indelible contribution to the development of astronomy in China. In mathematics, geography, painting and literature, Zhang Heng also showed extraordinary talent and extensive knowledge.

Zhang Heng is one of the representatives of Huntian theory in the middle of Eastern Han Dynasty. He pointed out that the moon itself does not shine, and moonlight is actually a reflection of the sun's light; He also correctly explained the cause of the solar eclipse and realized the infinity of the universe and the relationship between the speed of planetary motion and the distance from the earth.

Zhang Heng observed and recorded 2,500 stars, created the world's first leaky ball that can accurately perform astronomical phenomena, the first instrument to test earthquakes-the waiting wind seismograph, and also made a South Locomotive, an automatic drum car, a wooden bird flying to Wan Li and so on.

Zhang Heng * * * is the author of 32 scientific, philosophical and literary works, among which astronomical works include Ling Xian and Ling Xian Tu.

In order to commemorate Zhang Heng's achievements, people named the crater on the back of the moon as "Zhang Heng Crater" and the asteroid 1802 as "Zhang Heng Asteroid".

Guo Moruo, a famous writer and historian in China in the 20th century, commented on Zhang Heng: "Such an all-round development figure is rare in world history, and it has been admirable for thousands of years."

Later people called Zhang Heng a wooden saint. Zhang Hengzi Hirako. Nanyang County (now Nanyang, Henan Province) is a native of Xi 'e County. Born in the third year of the Eastern Han Dynasty (AD 78); Yonghe died in the fourth year (AD 139). Astronomy, mechanical technology, seismology.

Zhang Heng is a versatile scientist. His achievements involve astronomy, seismology, mechanical technology, mathematics, literature and art and many other fields.

Zhang Heng has two most important jobs in astronomy-writing spiritual lines and making armillary sphere. In addition, the calendar was studied.

Lingxian is Zhang Heng's masterpiece on astronomy, which fully embodies Zhang Heng's achievements and development in astronomy. The original text was quoted by Liu Zhao in the Book of the Later Han Dynasty and passed down from generation to generation. The main points of astronomy introduced in this paper are as follows:

(1) The origin of the universe. Lingxian believes that the universe is an invisible and colorless yin essence, quiet and lonely. This is a long stage, called "I". This stage is the root of Tao. From Doggett's root, the trunk is produced and the gas is colored. But "chaos does not distinguish", you can't see any shape, and you can't measure its moving speed. This gas is called "Tai Su". This is another long stage, called "Pang Hong". With the trunk, objects begin to come into being. At this time, "the vitality is judged, just divided, turbid, sex is outside, and the ground is inside." The cooperation between heaven and earth produces everything. This stage is called "Tai Xuan", which is the reality of Tao. Lingxian called the three stages of the evolution of the universe "Daogen", "Daogan" and "Daoshi". When explaining the chaotic Tai Su Qi, I quoted a sentence from the Tao Te Ching: "Things are born in harmony, and they are born naturally." All these explain the concept of the origin of the universe in Lingxian, which originated from Laozi's Taoist philosophy. The theory of the origin of the universe in Lingxian and Huainanzi? The idea of astronomical training is very similar, but Huainanzi believes that after the qi is clear and turbid, "those who clear the yang are thin and extravagant, and those who are heavy and turbid are stagnant." Heaven and earth, Gaitian said so. Lingxian advocates that the sky made by pure gas is outside, and the land made by turbid gas is inside. This is the saying of Huntian. In a word, Zhang Heng inherited and developed China's ancient ideological tradition, thinking that the universe is not inherently perfect, but has a process of emergence and evolution. The ideological tradition represented by Zhang Heng is quite different from the ancient western tradition that the structure of the universe is eternal, but it is similar to the spirit of modern cosmology.

(2) About the infinity of the universe. During the Warring States period, the definition of "corpse" was as follows: "Up and down in all directions, talk about the universe, talk about ancient and modern times." Space is space and the universe is time. China's traditional thought is to connect space and time. This is also very different from the concept of treating them as two independent concepts in ancient western countries. However, China, like the West, has been debating whether they are finite or infinite. There is a saying in Zhuangzi that the universe is infinite in space and time. At the end of the Western Han Dynasty, Yang Xiong thought that "closing the sky for the universe and opening the sky for the universe" had a space limitation and a time starting point. Although Zhang Heng studied Yang Xiong's Taixuan Jing for a long time and was deeply influenced by Yang Xiong, he didn't want to follow Yang Xiong in the infinite universe. Lingxian believes that the size of the world seen by human eyes is limited, but beyond this range, people will "don't know it and don't know it." I don't know, I don't know, the universe is also called. The list of the rest is infinite, and the end of the universe is infinite. "The universe has no boundaries in space and no starting point in time. Yang Xiong's thought and the most famous Big Bang cosmology in astronomy are interlinked in the ultimate essence. But Zhang Heng's conclusion is consistent with contemporary dialectical materialism philosophy. It seems that the problem of finite universe will be debated for a long time.

(3) About the structure of heaven and earth. Lingxian describes the sky as the place where the stars are. It is an ellipsoid with minimal eccentricity: "The dimension of octupole is 232,300 li in diameter. The north and south are shortened by thousands of miles, and the east and west are widened by thousands of miles. If you wear it, you will be embarrassed. " There is a north pole in the sky, and the pivot star is in this position. The sun, the moon and five stars all revolve around it. There is also a south pole in the sky, which is invisible to people underground. The ground seen by human eyes is flat, in the center of the sky, "from the ground to the sky, half of the octupole;" Then the depth of the land is the same. " This shows that the land in Zhang Heng's mind is a hemisphere. On the ground, if the length of the sun shadow is measured at noon on the same day with an 8-foot-high watch, the difference between the length of the sun shadow measured at two locations thousands of miles apart from the north and the south is 1 inch.

Why do you think that heaven and earth are ellipsoid structures? We can't understand, perhaps, one possibility is that we are bound by tradition. As early as Lu Chunqiu? "A Tour of Shi Lan" mentioned that "within the four seas, things are 28,000 Li, and north and south are 26,000 Li", and things are 2,000 Li longer than north and south. Huainanzi? These two values are also quoted in Fall Training. It can be seen that the ancients probably thought that things in heaven and earth were longer than things in the north and south.

Horizon theory and "the difference between surface and shadow is 1 inch" were once considered as the contents of Gaitian theory. However, it is not appropriate to think that the structure of heaven and earth in Lingxian covers the sky. The main difference between Huntian model and Gaitian model is that Huntian sky is spherical, which can turn to the ground. The sky has not only the North Pole from the ground, but also the South Pole hidden underground. The sky that covers the sky is either covered on the flat ground like a cover (recently called the first theory of covering the sky) or forms two parallel planes with the ground (recently called the second theory of covering the sky). In short, the sky is always above the ground. There is only the North Pole in the sky, and there can be no South Pole. Therefore, from the understanding of the structure of the sky, the spirit fairy can only be classified as the theory of muddy sky, but not as the theory of covering the sky. Regarding the land issue, it must be pointed out that the dispute over mud cover in history mainly lies in the sky, not the land. Until the Tang Dynasty and his party completely denied the old saying that the shadow of the sun 1 inch away, the concept of horizon still existed in Huntian Theory. Even after some quarrels, until the introduction of western astronomy, China still failed to establish a clear mathematical model of the spherical earth. On the contrary, the theory of "heaven is round and earth is flat" in Lingxian still occupies an important position.

(4) About the angular diameters of the sun and the moon. Lingxian records that the diameter of the sun and the moon is "one-seventh of the whole day". The modern universal angle unit is 29'2 1 ". According to Qian Baoyu's textual research, it is considered that "the diameter of (Sun and Moon) is one seventh of that day's week and one quarter of the earth's width" in Lingxian should be corrected to "the diameter of (Sun and Moon) is one third of that day's week and the earth's width is 242". In this case, the angular diameter of the sun and the moon should be 29' 35.3 "]. Compared with the average angular diameters of the sun and the moon measured by modern astronomy of 365,438+0 ′ 59 ″ and 365,438+0 ′ 5 ″, the error is only about 2 ′. According to the observation conditions two thousand years ago, Zhang Heng's measurement is accurate.

Zhang Heng also introduced an observation in his previous Weekly Parallel Calculations: an 8-foot-high pole stands vertically on the ground, and the shadow length of the pole is measured whenever the sun crosses the meridian. When the shadow is 6 feet long, watch the sun with an 8-foot-long bamboo tube with an aperture of 1 inch. Zhou Kuai and suan Jing think that the sun's visual circle at this time is just a circle of bamboo tubes. Therefore, according to the proportional relationship of "the difference of thousands of miles is 1 inch", it is concluded that the distance between the sun and human eyes at this time is 10 Wan Li, and the line diameter of the sun is 1250 Li. Because the basic starting points such as "the difference of a thousand miles 1 inch" are all wrong, the result of the book "Weekly Parallel Calculation" is extremely absurd (the diameter of the sun's line is actually1.39.5438+00,000 kilometers). As far as the observation itself is concerned, the results of Zhou Bi and Shu Jing are quite rough. According to the bamboo tube length of 8 feet and the aperture 1 inch, the diameter of the sun angle is 42 ′ 58 ″. The error is much larger than that of Lingxian County.

(5) The reasons for the eclipse. Before Zhang Heng, people already knew the cause of the solar eclipse. Liu Xiang once said in the Western Han Dynasty, "An eclipse will be covered by the moon" (see Kaiyuan Zhan Jing, Volume 9). Wang Chong of the Eastern Han Dynasty wrote in Lun Heng? The Japanese article quoted others as saying more clearly: "Or, an eclipse will cover the moon." . The sun is above and the moon is below, which is blocked by the shape of the sun. "For the reason of the eclipse, Zhang Heng did not have a clear explanation before. Probably in view of this situation, Zhang Heng did not mention the cause of solar eclipse in Lingxian, but specifically discussed the cause of lunar eclipse: "Moon, light is born in the sun; Born in the sun. The day is full of light, the day is full of light. The stars are shining, because water becomes light. A day's rush, the light is often inconsistent, but also all over the ground, which is called virtual. In the stars, the moon will eat. "This passage, said the moon itself does not shine, the sun shines on the moon to produce a bright moon. The reason why the moon is in deficit is that it can't get sunlight. Therefore, when the moon is opposite to the sun, there will be a full moon. As the moon gets closer and closer to the sun, the moon's deficit is getting bigger and bigger, and finally it disappears completely. Such a theory of the moon phase has been roughly stated in the book Zhou Pian Shu Jing: "The sun shines on the moon, and the moonlight is born, so it becomes a bright moon. "Jing Fang in the Western Han Dynasty put it more clearly:" The former teacher thought that the sun was like a projectile and the moon was like a mirror; Or think that the moon is like a projectile, the sun is shining, and it is dark if it is not bright "(Volume 1 of Kaiyuan Zhan Jing). There is no essential difference between Zhang Heng's moon phase theory and theirs. What is outstanding is that Zhang Heng emphasizes the relationship between the moon phase and the relative position of the sun and the moon. But in this way, people naturally have to ask, since there is a "total solar eclipse", why is there sometimes a lunar eclipse on that day? In this regard, Zhang Heng replied: "Covered in the ground", that is, the earth blocked the sunlight, so that the sunlight could not reach the moon. Zhang Heng named the shadow produced by this land "virtual". When the moon enters the void, the eclipse occurs. The explanation of the eclipse in Lingxian is very scientific.

But if you think about it, people will ask questions again. According to the celestial structure of Lingxian, the earth is a semi-ellipsoid, and its lower part is in close contact with the celestial sphere. Then: (1) In order to make the sun and the moon sink into the ground level and move underground, the sun and the moon can only be two round surfaces without thickness, which is in contradiction with the moon phase theory mentioned above. (2) When the sun sinks below the horizon, the light will be completely blocked by the hemisphere and will not be projected on the moon at any time. In this way, the moon should always be invisible at night, so there is no eclipse at all. To explain these two contradictions, we can only think that the land in Lingxian has two different meanings. The first meaning is that the earth is a semi-ellipsoid relative to the sky. The second layer means a small solid hanging in the center of the celestial sphere relative to the sun and the moon. Or, we can unify these two meanings: a piece of land is hanging alone in the sky, and the other piece of land is full of water, so it can be closely combined with the lower part of the celestial sphere. In this understanding, the sun and the moon can still be a ball; But after the sun reaches the water surface, the sunlight can still penetrate the water surface and shine on the moon, and only that relatively small piece of land can produce void. Of course, when speculating in this way, it needs to be added that in Zhang Heng's view, water is a highly transparent substance, so the sunlight after going deep underground can still penetrate the thick water layer and shine on the moon, thus producing a bright moon.

(6) About the five-star movement. Lingxian put forward four extremely valuable opinions. First, the sun, the moon and the five stars are not on the spherical shell of the celestial sphere, but run between heaven and earth at different distances from the ground. Second, the seven celestial bodies move at different speeds. The speed near the ground is fast, and the speed away from the ground is slow. Thirdly, Lingxian explained why the planets have motion changes such as stopping, reversing, delaying and speeding with the power of heaven. It's late recently, but it's far away. If you do this, you will bend, if you bend, you will stay behind. If you stay back, you will violate it, it will be too late, and you will be forced by heaven. Fourth, five stars can be divided into two categories according to their distance from the ground and their running speed. A kind of lunar attachment, which belongs to Yin, includes Mercury and Venus. The other is attached to and belongs to the sun, including Mars, Jupiter and Saturn.

Four o'clock above Lingxian is very interesting. The first point can be said to be basically correct, although the actual situation is much more complicated than this generalization. The second point is exactly the same as that of the ancient Greeks. In China, Zhang Heng was not mentioned before, and nobody paid attention to it after, which greatly limited the development of ancient mathematical astronomy in China. Although the third point is vague and completely incorrect, it is obviously seeking to explain the mechanical reasons why planetary motion is backward and forward. This kind of effort itself is worth writing into the whole history of astronomy. More than 65,438+0,500 years later, Wang Xichan also mentioned similar ideas in the Interpretation of Five Elements, and further proposed that the sky has a force similar to a magnet to attract needles to the sun, the moon and the five stars. The mechanism of Wang Xizhi's thought is clearer. Although the ideas of Zhang Heng and Wang Xichan are incorrect, the motion of the planet and its satellites (the moon is the satellite of the earth and the earth is the planet) is indeed governed by the law of universal gravitation. Therefore, it is undoubtedly a correct direction to investigate the mechanical reasons in the movement of these celestial bodies. In the west, there is still no discussion about this mechanical reason for more than 1000 years after Zhang Heng. Many great Greek astronomers only described the movements of the sun, the moon and the five stars in detail, but never thought of explaining their mechanical reasons. The discussion of mechanical causes was put forward only after the scientific revolution began in16th century. The fourth point is also interesting. The classification of the planets of Lingxian is only the classification of the planets in the solar system and the planets outside. Of course, now we know that all planets, including the earth, revolve around the sun, while the moon revolves around the earth. Therefore, the statement of "attachment to the moon" is of course wrong. The reason for this mistake is that Zhang Heng, like other ancients, regarded the moon as the representative of Yin. However, from the movement of inner planets, gold and water, what people see is rarely completely different from that of outer planets. That is, exoplanets can only start a rendezvous cycle from the morning in the east. On the other hand, the inner planet can not only rise from the east in a rendezvous period, but also dim in the west like the moon. It is precisely because of this similarity that Lingxian put forward the idea that it is attached to the moon.

(7) about the star officer. The sky is full of stars. In order to identify and observe them, the ancients combined them into a group of stars. These constellations range from one star to dozens of stars. Such stars were called star officials by the ancients. Because astronomers have different methods of choice and combination, many different star official systems have been formed. Until the era of Zhang Heng, the system of star officials spread all over the world was based on historical records? The system represented by Tian Guan Shu includes the system of history, dry, yellow emperor and "sea occupation". Zhang Heng compared, sorted out and summarized these distinctive systems, and developed a new system with the largest number of stars. "Lingxian" records that "the total wisdom of Chinese and foreign officials is 24, which can be named as 320, which is 2,500 stars, but the proportion of sea people does not exist." Zhang Heng's arrangement of this star official system is more than 100 years earlier than the time when astronomer Chen Zhuo summarized the three-star officials of Gan, Shi and Hsien Wu, and it includes many more star officials and stars than Chen Zhuo (Chen Zhuo summarized 283 officials with 1464 stars), and its achievement is certainly greater than that of Chen Zhuo. Unfortunately, Zhang Hengxing's official system has been lost, which is a great loss in the history of stargazing in China.

One of the problems related to the official stars is that it is proposed in Lingxian that there is also a kind of "microsatellite" in the sky, that is, very weak stars, the number of which is 1 1520. Strictly speaking, this figure does not come from the actual measurement, but from the mysterious "number of everything" in the Book of Changes. The figures are of course incorrect. However, Zhang Heng believes that there are microsatellites, and the number is much more than that of bright stars, which is in line with objective reality.

(8) Meteors and meteorites. In the sky, except the sun, the moon and the stars. Stars including planets and stars are common members, and meteors and other celestial bodies are also seen from time to time. "Lingxian" holds that "and (according to: referring to the three light) decline, God rests, so there are meteorites. However, when the star falls, it will be a stone on the ground. " Here, Zhang Heng inherited the predecessor's saying that "the stars are also stones when they fall to the ground" (Historical Records? The viewpoint of "Tianguanshu" gives a more correct explanation to the source of meteorites. At the same time, Zhang Heng also discussed the causes of meteorites, which were related to the decline of the sun, moon and stars. Although this idea is not correct (there are some large and small meteoroids in the solar system, which become meteors when they meet the earth in operation, and burn due to friction after entering the atmosphere; Large meteoroids fall to the ground and become meteorites before they burn out in the atmosphere, but every celestial body has a stage of "decline" and death, which is a very scientific conclusion. Zhang Heng's thought is dialectical, which is also lacking in ancient western astronomy.

Associated with meteorites is the explanation of the stars in Lingxian: "There are mountains on the ground to announce their qi and gather the stars. Stars are also born in the earth and refined in the sky. " This view that stars were born on the earth is of course completely wrong. It was a reflection of the thought of correspondence between heaven and earth that was popular for hundreds of years at that time. "Spirit Fairy" said: "It seems to be in the sky, and it seems to be underground. There are nine places in the sky and nine domains in the earth. There are three days in the sky and three shapes in the earth. Some images are effective and tangible. Different emotions, thin empathy, and natural life. " These so-called correspondence between heaven and earth are purely subjective and have no scientific connection in connotation. For example, the so-called land of nine days (that is, nine days as the ancients said) and the land of nine domains (that is, Kyushu) were artificially divided by ancient people in China. Therefore, this correspondence is purely digital coupling. However, the reason why Zhang Heng has the idea that the essence of mountains rises to stars is because all the meteors he sees are stones, and mountains are the place with the most stones. How can stones go to heaven? Therefore, it is inevitable that this is the essence of mountains, which can ascend to heaven and become stars. These reflect the view that meteorites come from outer space. In the west, until the17th century, there were still astronomers who believed that meteorites did not come from extraterrestrials.

As an excellent ancient astronomical work, Lingxian still has many shortcomings. In addition to the points mentioned above, for example, the myth of the Goddess Chang'e flying to the moon is recorded as a fact, and it is even said that Chang 'e became a toad after she entered the month. As for the various thoughts of astrology revealed in the article, it was the ethos of the whole era at that time, and it was not necessary to demand Zhang Heng. In a word, although Lingxian has some shortcomings, its significance in the history of astronomy is not inferior. Liu Zhao in the Liang Dynasty praised Zhang Heng as "the wonder of astronomy, the best in a generation", and one of the main bases of his evaluation was Lingxian, an outstanding work.

Secondly, he pointed out that the moon itself does not shine, and moonlight is actually a reflection of the sun's light; He also correctly explained the cause of the solar eclipse and realized the infinity of the universe and the relationship between the speed of planetary motion and the distance from the earth.

Zhang Heng observed and recorded 2,500 stars, created the world's first leaky ball that can accurately perform astronomical phenomena, the first instrument to test earthquakes-the waiting wind seismograph, and also made a South Locomotive, an automatic drum car, a wooden bird flying to Wan Li and so on.

Zhang Heng * * * is the author of 32 scientific, philosophical and literary works, among which astronomical works include Ling Xian and Ling Xian Tu.

In order to commemorate Zhang Heng's achievements, people named the crater on the back of the moon as "Zhang Heng Crater" and the asteroid 1802 as "Zhang Heng Asteroid".

Guo Moruo, a famous writer and historian in China in the 20th century, commented on Zhang Heng: "Such an all-round development figure is rare in world history, and it has been admirable for thousands of years."

China has a long history of astronomy. By the Han dynasty, there had been schools of thought such as covering the sky, announcing the night and turbid the sky. Gaitian said that the sky is like a lid, the center of the lid is the North Pole, the lid turns left, and the sun, moon and stars turn right. Michelle Ye said that the sky is amorphous, and the sun, moon and stars "naturally float in the void" and are not attached to "celestial bodies". Huntian said that the sky is like an eggshell and the ground is like an egg yolk. Heaven and earth stand by and watch, carrying water and moving. Michelle Ye's theory was unfortunately lost, and the two theories, Another Day and Huntian, competed with each other, and the more scientific Huntian theory gradually gained the upper hand. At the same time, instruments for observing astronomical phenomena are constantly appearing. For example, Luo made an armillary sphere in the period of Emperor Wu of Han Dynasty, Geng Shouchang made an armillary sphere in the period of Emperor Wu of Han Dynasty, and Jia Kui, a teacher of Cui Yuan in the period of Emperor Wu of Han Dynasty, made ecliptic bronzes. ?

Zhang Heng inherited and developed the achievements of predecessors. After Ren Taishi ordered, he worked harder to "study Yin and Yang" and finally "perfected the meaning of Xuan Ji". In the fourth year of Yuan Dynasty (A.D. 1 17), Zhang Heng made a bronze armillary sphere with unprecedented achievements.

The main body of the armillary sphere is a circle, and there are several layers that can run. The circumference of the outermost layer is 10 foot, 4 feet and 6 inches. Each floor is engraved with internal and external rules, such as south, north, yellow, equator, 24 solar terms and 28 solar terms, as well as "middle" and "outer" stars, the sun, the moon and the five latitudes. There are two leaking pots attached to the instrument, and there are holes in the bottom of the pot. The water drops push the circle and the circle rotates slowly according to the scale. As a result, all kinds of celestial phenomena are displayed in front of people. This instrument is placed in the secret room of the hall of GV. At night, the indoor observers report the sky phenomena at a certain moment to the sky observers on the platform in time, and the result is that the instruments are completely consistent with those in the sky.

There is a jade shovel (dragon) on each side of the bronze musical instrument, which spits water into the pot, with night on the left and sun on the right. There are gold and bronze immortals and Xu disciples on the pot respectively. "They all hold arrows in their left hands and carve arrows in their right hands, so different days will be sooner or later." Even more amazing: there are Swiss wheels and two pots with built-in mechanical devices under the steps. Driven by dripping water, the pod keeps rotating and opening and closing according to the coming and going changes of the moon, indicating the new moon, the moon, strings and signals, just like an activity calendar. It can be seen that this armillary sphere and its accessories have many similarities with modern fake celestial spheres. In the year before the birth of this instrument, Zhang Heng? First, a model named "Little Soul" was made with bamboo sticks. After a series of tests and corrections, it was cast into a big musical instrument. Who is the armillary sphere? Rolling? The crystallization of blood and sweat. He went on to write two explanations, namely "Illustration of the Amazonian Instrument" and "Annotation of the Water Leakage Turning to the Amazonian Instrument", and then wrote a book "Lingxian County" and a book "Lingxian County Map". In these works? Rolling? This paper systematically expounds his own astronomical theory and embodies his simple materialistic view of nature. He believes that the universe is infinite and the movement of celestial bodies is regular; Moonlight is the reflection of the sun's light, and an eclipse is because the earth blocks the sun's light, and the moon goes around the earth and rises and falls. He realized some laws of the movement of the sun (which should be the revolution of the earth) and correctly explained the causes of the long nights in winter, short nights in summer, vernal equinox and autumnal equinox. He pointed out that there are 2,500 stars that can be seen in the Central Plains, which is slightly close to what is known today. After observing the movement of some celestial bodies, he came to the conclusion that the number of days in a week is 365 degrees and a quarter degrees, which is almost the same as the modern measured value that the earth orbits the sun for 365 days, 5 hours, 48 minutes and 46 seconds.

Because of studying astronomy, calendar and making instruments, Zhang Heng? The study of mathematics has also been strengthened accordingly. After making the armillary sphere, he wrote The Theory of Computing to "calculate it in the network world". He used the method of "progressive fraction" to calculate that the square root of pi is ten, which is 3. 16. This is a big step forward than the value of π=3 recorded in Zhou Xie. It was not until five or seven centuries later that Indian and Arab mathematicians put forward this value. ?

In the first year of Jianguang (A.D. 12 1), Zhang Heng was transferred to be a coach and always took charge of the imperial edict. He was not overwhelmed by complicated official duties, but stepped into the fields of physics, machinery manufacturing and so on, and made many amazing achievements. He became the leading mechanical manufacturing expert at that time, known as the "Wood Sage", and his exquisite artifacts were unparalleled. He used the principle of differential gear to build the south guide car and the drum car in his mind. He also carefully built a wooden bird, "fake feather purlin, belly machine, can fly for miles", which was simply a unique wooden "plane" in the world at that time! Unfortunately, like many of his masterpieces, most of the objects and detailed methods have been lost. ?

Zhang Heng also made a surveying instrument, the Earth Gauge, to study astronomical geography. He drew a topographic map, which has been passed down to the Tang Dynasty. He is good at painting landscapes and animals, and he is known as one of the four great painters in the Eastern Han Dynasty with Zhao Qi, Liu Bao and Cai Yong (the father of Wenxi). I also have a deep research on music and dance. For example, in "Ode to Watching Dance", he once described the dancer's dancing skills so skillfully: "Continuous flow, sudden continuation, fluttering like a phoenix, sleeves like snow." ?