What do you mean by the nine blessings in history?

Classification: society/culture >> ethnic groups

Problem description:

This word often appears in ancient Chinese and history classes, but I still don't understand it. Can you give me a good explanation?

Analysis:

Nine-service shadow algorithm in Dayan Calendar and its tangent function table

Since the calendar of the Eastern Han Dynasty, there have been observation records of the length of the sundial and the number of solar poles at the beginning of each solar term, and the missing and sundial have become important calculation items in ancient calendars. After the invention of the quadratic equidistant interpolation method in Sui Dynasty, Li first introduced the quadratic interpolation method into the calculation of leakage, and calculated the number of leakage and shadow every day from the number of leakage and shadow on the first day of each gas. However, most of the missing shadows recorded and calculated in various calendars are the values of Yangcheng (now Gaocheng Town, southeast of Dengfeng, Henan Province). When compiling The Great Yan Li, a group made a large-scale astronomical survey. Through observation, we know that the shadow length that changes dramatically with the passage of time varies from place to place, but it has a fixed corresponding relationship with the zenith distance of the sun. In Yan Li, a group of people invented a method to calculate the length and extreme value of the sun shadow at any place, which is called "Nine Clothes Shadow".

The ancients took Yangcheng as the standard location for shadow measurement, which was called the middle of the earth. If NP is the north pole height of Yangcheng, and S 1, S2, PS3………… ................................................................................................................................................ And this difference is equal to the corresponding season everywhere.

If the height of the North Pole is NP', the transit positions of the sun on the summer solstice, slight heat and great heat are S' 1, S'2 and S' 3. Obviously there is.

a 1 = PS′2-PS′ 1，a2 = PS′3-PS′2 .

The solar zenith distance in summer solstice, light summer and heavy summer in Yangcheng is ZS 1, ZS2 and ZS3 respectively.

a 1=ZS2-ZS 1，a2=ZS3-ZS2，

Similarly, there are also

a 1 = ZS 2-ZS 2，a2 = ZS 3-ZS 2。

The solar depolarization of various gases in Yangcheng is given in the calendar, so we know the solar zenith distance difference of various gases, which is equal to anywhere. In this way, for any place, as long as we know the solar zenith distance of a solar term (such as summer solstice), we can calculate the solar zenith distance of other gases by adding and subtracting this difference. The remaining two problems need to be solved: first, how to find the solar zenith distance of a certain summer solstice (or winter solstice); Secondly, it is known how zenith distance transforms the shadow length. These two problems can be solved by establishing a table corresponding to the shadow length of the sun and the zenith distance.

If we list a numerical table with zenith distance as the independent variable and the shadow length every other degree, we can solve the above two problems: firstly, measure the shadow length of the measured site from summer solstice to the sun (this measurement is carried out everywhere in the geodetic survey led by a line), get the sun zenith distance from the shadow length look-up table, and then add and subtract a difference ai as mentioned above to get the zenith distance of each gas in the site, and then look up the table again. A line in Da Yan Li's "Step Leakage" established such a corresponding table between the shadow length of each degree from 0 to 80 degrees and the zenith distance of the sun, which is the earliest tangent function table in the history of mathematics in the world.

Abroad, around 920, al-Battani (about 858-929), a scholar of * *, compiled a table of the shadow length of 12 foot pole, with an interval of 0-90 degrees, which was actually a table of 12ctga. Another * * * scholar, Aboul Waha (940-998), compiled a tangent cotangent function table of about 980, and gave a value every 15 degree and 10 degree. He also introduced secant and cotangent function for the first time. The method of compiling a line into tangent and cotangent function tables is almost the same as that of Al Batani. A line uses the zenith distance of the sun, and Al Albatani uses the elevation angle of the sun. They are complementary angles, so their findings are the same. The tangent function table of a line is nearly 200 years earlier than that of Al Albatani and 250 years earlier than that of Al Weaver. Although the tangent function table of a row is only from 0 degrees to 80 degrees, and the error is relatively large, it is the earliest tangent function table in the world after all.