What is the Shang Yuan Chronology?

I hope it will help you to explain the accumulated years of Shangyuan.

1. Calendar needs to specify a start time. Ancient calendar mathematicians in China called this starting point "Era" or "Shangyuan", and the cumulative time from the era to the calendar year was called "Shangyuan cumulative year".

2. The calculation of shangyuan cumulative year needs to solve a group of one-time congruences. Take Jing promoted by Wei in the Three Kingdoms period in the 3rd century A.D. as an example. This calendar stipulates that the time when the winter solstice, the new moon (midnight of the new moon) and Jiazi meet at 0: 00 is the era. Let A be the number of days in the tropic year and B be the number of days in the first month of the lunar calendar. When the winter solstice is Jiazi day R 1 and Pingshuo is R2 day, the number of elements n in the Jingchu calendar is a congruence group.

An ri (mod 60)R2(modb)

The solution of. In the Northern and Southern Dynasties, Zu Chongzhi's Da Li Ming (AD 462) required that the era should be the beginning of Jiazi year at the same time, and the moon should pass through its perigee and ascending intersection. Under such conditions, calculating the cumulative year of the last element is equivalent to finding the solution of ten congruences. Astronomical calendar data are generally very complicated. Therefore, in the Wei, Jin, Southern and Northern Dynasties before and after the book Sunzi Suanjing, the astronomers in China were undoubtedly able to work out a congruence formula that was much more complicated than the problem of "unknown things" in Sunzi Suanjing, so they must have mastered the method of calculating a congruence formula according to certain procedures. This fact is summarized and reflected in the form of proportional problem in Sun Zi Shu Jing. In the future, astronomers will use Sun Tzu's algorithm to calculate the cumulative year of the last element for a long time, which will surely lead to more in-depth discussions. In the13rd century, the great mathematician Qin finally made brilliant achievements in the study of congruence.

3. In practical use, it is precise, but it is gradually eliminated.

I won't relive it.

1. In the ancient calendar, the era was generally set as the starting point of calculation. This starting point is usually an ideal moment.

2. It is usually based on midnight of Jiazi Day, which is a new moon and a winter solstice solar term.

3. Push up from the epoch, and find a moment when the celestial phenomena of "the sun and the moon meet and the five stars meet the pearl" appear. The latitude and longitude of the current moon are exactly the same, and the five planets gather in the same direction. This moment is called Shangyuan.

4. The number of years from Shangyuan to calendar year is called cumulative year, commonly known as Shangyuan cumulative year. Shangyuan is actually the same starting point of several astronomical cycles.

With shangyuan and shangyuan cumulative years, it is more convenient for a calendar to calculate the movements and positions of the sun, the moon and the five stars.

6. China began to calculate the cumulative years of Shangyuan in Liu Xin at the end of the Western Han Dynasty. Liu Xin's Three thomas lee takes 19 as 1 chapter, 8 1 chapter as 1 series, and 3 series as 1 yuan. 1 After reunification, that is, 1 539, Shuodan and the Winter Solstice Day were in the middle of the night, but they did not return to Jiazi Day. It took three years, that is, 4,665,438+07, to return to the original Jiazi Day. At this point, the main branches of the year could not be recovered. The "three calendars" also take 135 moons (see the moon) as the eclipse cycle, which is called "the meeting of the moon". There are exactly 1 41meetings in1series. Therefore, mating also takes 1 series as a big cycle. These all started in the first year of Taichu 1 1 midnight. In order to get the conditions of the combination of the sun and the moon and the five-star connection, Liu Xin has also set a large period of 5 120 yuan, 23,639,040 years. The starting point of this great cycle is called Tai Chi Shang Yuan. From Shangyuan to the first year of Taiji, it was 143 and 127. After Liu Xin, with the discovery of periods such as the node month and the perigee month, historians added these factors to the ideal elements.

6. The sun, the moon and the five stars each have their own movement cycles and their own ideal starting points, such as the winter solstice, the new moon, the perigee, the yellow and white intersection of the moon's movement and so on. The positions of the sun, the moon and the five stars measured from a certain moment are different from their respective starting points. It is a congruence problem in integer theory to calculate the integer year of the upper element with various periods and corresponding differences.

7. As the observation becomes more and more accurate, it becomes more and more difficult to solve the linear congruence formula, the mathematical operation is quite heavy, and the accumulated years are also very large. This is of little practical significance to calendar work, but has become a burden. After Cao Shi? Yang Zhongfu, etc. In the Yuan Dynasty, Guo Shoujing abolished the "chronograph calendar" created in the first year of last year.