What is the Dayan calendar made by monks and their party?

Monks and their entourage, whose real names were (683-727), were from Changle, Weizhou (now Nanle, Henan Province), and were the great-grandchildren of Tan, a famous minister of Zhenguan, and Zhang, a monarch of the country. Zhang Sui was smart since he was a child. When he was young, he read many classics and history, especially the study of elephant numbers, yin and yang and five elements. Yin Chong, a Taoist priest at that time, read widely and collected ancient books. Zhang Sui borrowed Yang Xiong Ty Xuan Jing's book and returned it to him after reading it at home. Yin Chong said that this book is extensive and profound. I've been looking for it for a long time, but I haven't figured it out yet. You can study it further, and you don't have to return it quickly. Zhang Sui said that he had grasped the gist of it, so he took out his book "Da Yan Xuan Tu and Yi Jue" and showed it to Yin Chong. Yin Chong was shocked. "It is said that people will give birth to scorpions from now on." Zhang Sui is famous far and wide. Wu Zetian's nephew Wu Sansi was invited to make friends with him. Zhang Sui fled to avoid it, and immediately became a monk, hiding in Songshan, where he studied Zen master Puji and his party. He traveled thousands of miles to visit teachers to study, and went to Tiantai Mountain in Tanzhou and Dangyang Mountain in Jingzhou to study Buddhist classics and astronomical mathematics. In the fifth year of Kaiyuan (7 17), Emperor Xuanzong of the Tang Dynasty greeted him, went to Chang 'an, settled in Guang Tai Hall, and asked him for advice on how to run the country. A line of direct advice, Xuanzong adopted. In the eighth year of Kaiyuan (720), King Kong, a monk from Tianzhu, went to Chang 'an to teach tantric Buddhism. Inspired by King Kong Zhi, the party became the leader of Tantric Sect in Tang Dynasty.

In the ninth year of Kaiyuan (72 1), due to many errors in the solar eclipse calculated by Linde calendar used at that time, Zhao Xuanzong and his party studied the previous calendar and formulated a new calendar.

It is very important to determine the positions of the sun, the moon and the five stars in their own orbits and master their operation conditions to improve the accuracy of the calendar. In the past, astronomical instruments were basically equatorial devices The equator is the intersection of the equatorial plane and the celestial sphere, perpendicular to the rotation axis of the earth. The positions of celestial bodies measured by such instruments are all expressed in equatorial coordinates, and the positions of celestial bodies in their own orbits can only be determined by coordinate transformation, which requires the application of spherics. However, scholars at that time had not mastered this method, and they all used approximate empirical formulas to calculate, with great errors. Knowing this shortcoming, he hopes to have an instrument that can directly measure the coordinate position of the sun and the moon in orbit, thus reducing a conversion program and avoiding the resulting errors. A team appraised the wooden model of the Zodiac Touring Instrument designed by Liang Lingzan and other workers, and supported Liang Lingzan to make the device out of copper and iron. The zodiac is the route of the sun's apparent motion in the celestial sphere, that is, when you look at the sun from the earth, you can feel the sun's trajectory in space for one year. Observing the celestial phenomena with the ecliptic can directly measure the coordinate positions of the sun, the moon and the stars in the orbit, thus eliminating the conversion procedure and avoiding errors. In the 12th year of Kaiyuan (724), the patrol instrument of the zodiac was officially manufactured successfully. Unfortunately, the history books lack detailed records and drawings, and the specific structure and shape can no longer be understood. It is roughly made up of several metal rings intertwined around a "middle fulcrum", much like a big ball. The "fulcrum" is parallel to the earth's rotation axis and points to the North and South poles. The instrument is supported by four carved dragon-shaped columns with a height of four feet and seven inches, which are located on a horizontal trough. Between the metal rings, an "Yuheng Telescope" was installed to observe celestial bodies, similar to later astronomical telescopes. The intersection of the ecliptic ring, the white ring (which is the route of the moon's apparent motion in the celestial sphere) and the equatorial ring in the metal ring is not fixed and can be opened and closed, so the observer can read the required numbers from the ecliptic ring. One group measured equatorial coordinates and relative positions of ecliptic of more than 50 stars in/kloc-0 with ecliptic navigator, and compared the results with those in Han Dynasty. The discovery is very different, so the phenomenon of star position movement is discovered for the first time in the world. This is a pioneering work in the history of world astronomy, which is about 1000 years earlier than that discovered by Englishman Harley in 1, 7 12.

In the 13th year of Kaiyuan (725), a group of people cooperated with Liang Lingzan to design and manufacture a hydraulic elephant (similar to a modern celestial globe), which is a spherical object. The direction in which the iron axis passes through the central axis of the sphere is the rotation direction of the earth. There are two intersections between the ball and the axis, namely the south pole and the north pole of the ball. The sphere is engraved with 28 constellations and other stars. There are two circles around the ball, one is the horizon and the other is the meridian circle, which intersect. In addition, there are ecliptic and equator on the sphere, which form an angle of 24 degrees with each other. Twenty-four solar terms are carved on the equator and the ecliptic respectively, starting from the winter solstice, divided into: 365 1/4 degrees, and each degree is divided into four squares. Solar radiation moves once a day on the ecliptic, so astronomical phenomena can be shown on the ball. In order to make the elephant rotate by itself, a gear is installed on the instrument based on the principle of dripping timing of the leaky kettle in ancient China, and the gear is started by dripping water from the leaky kettle to drive the elephant to rotate around the shaft. The elephant rotates once a day, leveling the ground with a big cabinet, so that the celestial sphere is half underground, and there are two Woodenhead on the ground. The bell and drum are placed in front, and the bell is rung every hour (two hours). The demonstration is controlled by gears in the cabinet.

Since the twelfth year of Kaiyuan, the delegation has organized astronomical geodesy at more than ten points in China, which is a pioneering work in the history of world science. The measurement task is mainly to measure the length of the sun shadow and the height of the North Pole at noon on the vernal equinox, autumnal equinox, summer solstice and winter solstice. In order to measure the length of the sun's shadow, an 8-foot-long benchmark (called a "watch" in ancient times) was erected on the ground to measure its shadow length. The height of the North Pole, that is, the angle formed by the connecting line between the observation point and the North Pole and the meridian circle tangent passing through the observation point, needs more complicated instruments to solve. In order to measure the height of the North Pole, we designed a measuring tool-complex moment, and drew 24 complex moment maps (possibly astronomical maps with complex moments). Moment is a drawing tool in ancient China, much like the "bending" ruler used by carpenters. "Complex moment" is to invert the moment, and install an indexer from 0 to 9 1.3 1 on the right angle of the moment (the degree here refers to an ancient unit of measurement, which is 365.25 of the circumference) as long as the right angle edge of the complex moment near 9 1.3 1 degree points to the North Pole. Complex moment is not only simple in structure, dexterous and easy to move, but also scientific in principle, which occupies a very important position in astronomical measurement at that time. The height of the North Pole at each observation point is measured by it, which is a contribution of this line in astronomical measurement.

In this survey, it is most important to take Nangong as an example to measure at four points in Henan Province today. These four points are Baima (now northeast of Hua County, Henan Province), Junyi (now Kaifeng, Henan Province), Fugou (now Fugou County, Henan Province) and Shangcai (now southwest of Shangcai County, Henan Province). The four observation points are on a meridian. They measured the height of the North Pole at each point, the shadow length of eight feet at noon from summer to Sunday, and the distance between the two points.

This survey completely overthrew the wrong statement that "the south, the north and the south are separated by thousands of miles, and the shadows are separated by one inch" in the Weekly Parallel Calculations. The survey team sent to Long Bian (the north bank of Dejiang, east of Hanoi) measured that the shadow of the summer solstice was three inches three points south of the table, and Yangcheng (southwest of Henan Shangshui) was one foot four inches nine points north of the table. If the linear distance between the two places is less than 5000 miles, the shadow difference is about 277 miles. Nangong said that the distance from Baima to Shangcai is 270 steps (Tang feet) in 526 miles, and the shadow difference from summer to the sun is two inches zero, and the shadow difference in 263 miles is about one inch, which proves that the shadow difference between the north and the south is not one inch, and the ratio of the shadow difference to the distance between the north and the south is not fixed with different places; It also proved that Li's views in Sui Dynasty and early Tang Dynasty were correct, which made the group completely give up the concept that the earth is thousands of miles apart and the shadows are one inch apart.

The most important achievement of this survey is that according to the data observed by Nangong Shuo at four points on the same meridian in the same plain area of Henan Province today, the calculated height of the North Pole differs by one degree, and the distance between the north and the south differs by 35 1 and 80 steps (Tang Dynasty scale). 129.22 km), this data is the arc length of the meridian of the earth, which is only11.2km away from 34.5 north latitude. It is the first measured meridian length in the world, which opens a way to understand the earth through actual measurement. Joseph Needham, a British scientist, has written many times that this is "an epoch-making pioneering work in the history of science".

After several years of observation and research, in the 13th year of Kaiyuan (725), a group set out to compile a new calendar, and in the 15th year of Kaiyuan (727), a draft of the new calendar was completed, named Dayan Calendar, and the group also died in that year. Later, you and Chen compiled the New Calendar Draft into a book, including: Kaiyuan Dayan Calendar Classic (1)7 articles, Seven Political Calendar (3 volumes), Calendar Discussion (10 volume), Li Licheng (12 volume), and so on. Among them, the full text of Jingjing is contained in the Book of the New Tang Dynasty Yi Li, and the simple examples are contained in the Book of the New Tang Dynasty. Since the 16th year of Kaiyuan, the almanac of the following year based on Dayan calendar has been issued every year. It has been proved that Dayan Calendar is more accurate than all previous calendars, with rigorous structure and logical calculation steps, which is learned by later calendars. The most outstanding achievement of "Dayan Calendar" is to correctly grasp the law of speed change in the annual apparent motion of the sun (in fact, it should be the law of speed change when the earth moves around the sun). It is pointed out that the daily journey from winter to around is the fastest, so the time between two solar terms is the shortest; Summer is the slowest from the day before to the day after, so the time between two solar terms is the longest; It is also measured that * * * from winter solstice to vernal equinox is 88.99 days, and from vernal equinox to summer solstice is ***9 1.73 days; The situation before and after the autumnal equinox is the same, which accords with the actual situation. For the first time, the calculation of solar eclipse in Dayan calendar takes into account the differences in all parts of the country. The calculation of five-star movement unevenness is also more scientific than the previous calendar. At that time, Dayan calendar was the most advanced calendar, so Shen Kuo, a scientist in the Song Dynasty, said, "Kaiyuan Dayan calendar is the most precise and has been used for generations." It took more than 800 years from the mid-Tang Dynasty to the late Ming Dynasty. In the 21st year of Kaiyuan, Dayan calendar was introduced to Japan, where it was widely used and had a great influence.

One line is also very helpful in math. In da Yan Li, he proposed a quadratic difference interpolation method with unequal independent variables. Absorb the sine function imported from India and use it to compile astronomical tables; An approximate interpolation formula of cubic difference is proposed.

Zhang Dasu, a great-uncle, wrote the Book of the Later Wei Dynasty, but he didn't finish his Tian. The bank continued to be two volumes. Later generations added these two volumes to Wei Shou's Wei Shu, which became the third and fourth volumes of astronomical records. Line also helped Jin Gangzhi translate Dalagni classics; Help India's Subhakara simha to translate 7 volumes of The Great Sun Sutra (save); And wrote 20 volumes of the Great Sun Classic (preserved); Feng Yi wrote Shi Family Records (Volume1); Author of "Photographing, Adjusting and Hiding" 10; Brahma Skyfire Luo Jiu Yao (volume 1 (save).

On August 25th, 1955, the Ministry of Posts and Telecommunications issued a commemorative stamp for ancient scientists, including a monk and his party, which affirmed his creative achievements and the status of ancient scientists.