One line. What?

Problem description:

One line is a monk with a name.

Analysis:

Monks and their entourage, whose real names are Zhang Sui, were born in Changle, Weizhou (now Nanle County, Puyang City, Henan Province) in the fourth year of Xianheng, Tang Gaozong (AD 673). Become a monk when you are young, and act in a legal name. As a teenager, he studied hard and mastered profound knowledge. He once went to Du Yuan, a city rich in books, to borrow books and read. Later, in order to learn mathematics knowledge, he traveled thousands of miles and visited celebrities for advice. This learning spirit made this group famous for its mastery of astronomy and calendars when it was young.

In the fifth year of Kaiyuan (AD 7 17), a group of people came to Chang 'an, Kyoto, from Dangyang Mountain Buddhist Temple, where Jingzhou lived in seclusion, to serve as a consultant to Emperor Xuanzong of the Tang Dynasty. This group of people lived in Chang 'an for ten years and died in the fifteenth year of Kaiyuan (AD 727). Over the past ten years, our party has devoted itself to astronomical research and calendar reform and made outstanding contributions.

In the ninth year of Kaiyuan (AD 72 1 year), Emperor Xuanzong of the Tang Dynasty ordered his party to preside over the revision of the new calendar. On the issue of calendar revision, the delegation inherited the fine tradition of astronomy in China, and advocated compiling a new calendar based on the measured operation of the sun, moon and five stars. To this end, together with Liang Lingzan, a mechanical expert, and relying on a group of craftsmen, he created large-scale astronomical observation instruments and demonstration instruments, such as the Zodiac Patrol Instrument and the Waterborne Astrologer, which prepared material and technical conditions for revising the new calendar.

Zodiac is an astronomical instrument used to observe the position and operation of the sun, moon and stars, and it is a kind of armillary sphere. The water-borne armillary sphere (elephant) is an instrument driven by water, which can imitate the movement of celestial bodies, similar to the modern celestial sphere. This kind of water transport almanac regularly demonstrates the movement of the sun, moon and stars, which is more delicate and complicated than Zhang Heng's water transport almanac. In addition, there are two wooden figures on the water-borne armillary sphere, driven by gears. One automatically beats the drum every moment (in ancient times, it was 100 minutes a day and night), and the other automatically rings the bell every morning (within two hours). It can be said that it is the ancestor of modern clocks, six centuries earlier than the wicker clock that appeared in the west in 1370, which fully shows the intelligence of the working people and scientists in ancient China.

After the instrument was made, in the 12th year of Kaiyuan (AD 724), the team initiated and organized a large-scale astronomical survey. The measurement contents include the length of the sun shadow at noon on the equinox (vernal equinox, autumnal equinox) and the second solstice (winter solstice, summer solstice), the height of the North Pole (elevation angle of the celestial pole), the length of day and night, and so on. In order to measure the elevation angle of the North Pole, we designed a measuring tool called "moment superposition" and drew 24 "moment superposition diagrams" according to the observed data. At the same time, according to the measured data, the line also calculates that the height difference of the North Pole is one degree, and the north-south distance is 35 1 80 steps, that is, 15 1.07 km. This data is essentially the length of the meridian of the earth (that is, the meridian). Although it is not very accurate, it is the beginning of large-scale meridian measurement in the world. In foreign countries, the earliest longitude measurement was carried out by * * * astronomer Al-Khwarizmi and others in 8 14, 90 years later than in China.

On the basis of large-scale field observation and absorption of previous research results, the group began to formulate a new calendar in the thirteenth year of Kaiyuan (AD 725), and completed the first draft in the fifteenth year of Kaiyuan, named Dayan Calendar. Unfortunately, in this year, the party passed away. His posthumous works were edited and arranged by Chen and others, with a total of 52 volumes.

The most outstanding contribution of Dayan Calendar is to correctly grasp the changing law of the apparent speed of the sun on the ecliptic. Ancient astronomers always thought that the speed of the sun was uniform. They divide the ecliptic into three degrees, six degrees, five degrees and twenty-five degrees, and think that the sun passes through one degree at a constant speed every day. Through calculation, it is pointed out that the sun runs fastest in winter solstice, then slows down gradually, and runs slowest in summer solstice. The situation after the summer solstice is opposite to that before the summer solstice. The understanding of lines is more realistic. According to the calculation of a group of people, from the winter solstice to the vernal equinox, the sun runs a quarter of 365.25 degrees, about 9 1.3 1 degree, and it takes six solar terms and * * * 89 days. From the vernal equinox to the summer solstice, the sun also passed 9 1.3 1 degree, which took * * * 93.37 days. The situation around the autumnal equinox is the same as that around the vernal equinox. This is illustrated by concrete data, which shows that the degree on the ecliptic between every two qi is the same, but the time interval is not equal. A line further creates a quadratic interpolation formula with unequal spacing, which is not only of great significance to astronomical calculation, but also of certain significance in the history of world mathematics development.

Dayan Calendar was compiled on the basis of a comprehensive study and summary of ancient calendars. It summarizes the China calendar without a unified format in the past into seven parts: one is to calculate the solar terms and the average time of the first month (step by step); Second, calculate the seventy-second phase (the first phase is calculated in five days, and the climate change is described by the change of bird and animal vegetation) (gradual convergence); Third, calculate the movement of the sun (step method) (sound entanglement, Chá n); Fourth, calculate the movement of the moon (step-moon separation); Fifth, calculate the time (track leakage); Six, the calculation of solar eclipse and lunar eclipse (step intersection); Seventh, calculate the five-element operation (step five-star technique). This writing method is systematic in content, reasonable in structure and strict in logic, so it has been used until the end of the Ming Dynasty. It can be seen that Dayan history plays an important role in the history of China. Although Dayan Calendar was the most superior calendar at that time, it was opposed by the old school soon after its promulgation. Later, it was calculated by Linde calendar, nine calendars introduced from India and Dayan calendar respectively. Results Dayan calendar was accurate seven or eight times, Linde calendar was accurate three or four times, and nine calendars were accurate only once or twice ten times. In the face of facts, the Dayan calendar can continue to be used.

In a word, he and his party have made great achievements in astronomy, calendar, instrument manufacturing, mathematics and so on, and are famous astronomers with outstanding achievements in the history of science and technology in China.