How to get the corresponding Dry Branch and Day from known years and dates
Text / Ge Minqin
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Summary:
It is very simple to calculate the dry branch of the year: the number of years is reduced, and the remainder of 10 is dry, and the remainder of 12 is
support.
From the known date, the formula and the Caile formula are very similar, as follows:
G = 4C [C / 4] 5Y [Y / 4] [3 * (M 1) / 5] D - 3
Z = 8C [C / 4] 5Y [Y / 4] [3 * (M 1) / 5] D 7 I (odd month i = 0, even month I = 6)
Where c is the number of centuries, Y is two after the year, M is the month, D is the number of days. From January and February to 13 months in the previous year and
Come on 14 months. g from the remainder of 10 is dry, and Z divided by 10 remaining.
Several computing formulas related to the use of the dry support, can also calculate the dryness of the ancient book without a long-year-old
The question date corresponding to the branch day.
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The Dry Budget, starting from Xia Dynasty. According to the eclipse recorded in the "Spring and Autumn" in ancient Chinese historical classics
Study, the date of the Diji of my country, starting from Lu Hougong, February, February 10, January 10, 720 BC, has been
Today, I have never been broken. The emergence of the Dissaudi New Year is slightly late until the Eastern Han Dynasty and the Second Year (AD 85)
Ordered to be implemented nationwide, has not been interrupted. Therefore, anyone who needs to contact Chinese history should not be encountered.
The dry branch of a certain year or a certain day, as well as the annual daughter support and the day dry, or which day. through
Often, this type of conversion can be resolved by the vectors. But since the dry support is also a circulatory system, naturally there is from the year and
Date asks the formula of the dry branch.
Introducing the characteristics of the dryers before introducing the formula of the year, the day of the day. Dry support is a day of dry and land
combination. There are ten days, namely, B, B, C, Ding, Ples, Heng, Geng, Xin,,; there are twelve, namely
Son, ugly, 寅,,,, 午, 未,, 酉,, 亥. Tian dry and land support start from "Jiazi", press smooth
The sequence is each matching, and when each time it is used, it will continue to match from the first one, and sixty dried support is formed.
"十 花". Why is it sixty dried? This is easy to answer from mathematics. According to the composition of the dry support
Parts, its cycle cycle is inevitably the minimum common multiple of the number of dry days and dry number. And 60 is the least common multiple of 10 and 12.
If we compose "Jiazi" into No. 1, "B is" is 2, so you can get a dry support.
The comparison table of the serial number is as follows:
1. Beeth 2. B is now 3. 寅 4. Ding Wei 5. 辰 6. 巳 7. 午 8 8. 未
9. 申 10. 酉 11. 12. 13. 14. Ding Mun 15. 寅 16.
17. Geng Chen 18. Xin Xin 19. 壬 午 20. 未 21. 申 22. 酉 23. 戌 24. 丁海
25. 子 26. Has you want 27. Gengzi 28. Xin Jun 29. 辰 30. 巳 31. Amate 32.
33. App IS 34. Ding Wei 35. 戌 36. 海 37. Gengzi 38. Xin ug 39. 寅 40. 卯
41. Jiachen 42. 43. 午 44. Ding did not 45. 申 46. 酉 47. 戌 48. Xin Hai 49. 子 50. 丑 51. 52. 53. 辰54. Ding Wei 55. Whely 56.
57. Geng Shen 58. Xin Wei 59. 60. 海
Keep carefully observed this table, it is not difficult to find that the corresponding dry support by the serial number is easy, and the number of serial numbers is divided by the remainder of 10.
It is the number of days (if the remainder is 0, the last day dry), the number of sequence numbers is the order of the remaining number of 12
Number (if the remainder is 0, the last place is the last place. For example, dry branch of 37, because 37 mod 10 = 7 (MOD said
Take the lifetime), the corresponding day dry is Geng, 37 mod 12 = 1, the corresponding land branch is a child, so the three-day dry support is the Gengzi.
Obviously, an integer is divided by 10, which is more convenient to make the day.
It is not difficult to push it from the dry support. This is actually a problem of solving the same equation group, we use the first
China's remaining theorem can be solved. For example, how much is the serial number of the wurto, it is obtained from the serial number above.
It is easy to get the following equation group for the principle of the corresponding dry support:
{X MOD 10 = 5
{x MOD 12 = 7.
Where X is the dry branch number of the treated. According to China's remaining theorem, there are:
X ≡ 6 * 5 - 5 * 7 (MOD 60) = 55,
That is, the trenu is 55. This is consistent with the above comparison table. Generally, if the dry serial number is m, the ground
The serial number is N, and the serial number of the dryer is:
X ≡ 6M - 5N (MOD 60) (1)
Simply said that if the result of 6M-5N is a positive number, this is the serial number of the dryer; if it is a negative number, put it with 60
It is the serial number of the dry branch.
Understand the mutual estimate of the dry and its serial number, let's first introduce the annual daughter support. It should be noted,
The boss is the age of the lunar calendar, not the Queen Year of the Calendar. But because the age of the age of the Lunar Year and the age of the Queen Calenday is close,
Missing the Lunar Year of the Lunar New Year, there is usually the annual representation of the Physical Calendar Year, most of them.
The year of the lunar calendar. In this way, we will easily give the number of dry bodies in the Lunar New Year:
X = (Y-3) MOD 60, (2)
Where Y is the year. The dry branch number X is obtained, and the corresponding dry boss can be obtained. For example, 2004 Dry Dissipation Series:
X = (2004-3) MOD 60 = 2001 MOD 60 = 21,
21 MOD 10 = 1, the day is A, 21 MOD 12 = 9, the ground is the application, so 2004 is the year of the 1st.
Attentive observation, we can find that in addition to using Y-3, you can get the dry dry, and use Y-3 to divide
12, you can get the ground. This is because
x = (Y-3) MOD 60
Equivalent to
Y-3 = 60 * n X,
Where N is the number of Y-3 divided by 60. Also divided by 10, the remainder is inevitable. And the first item is 60
The multiple, natural is also a multiple of 10, can be 10 integers, so Y-3 is inevitably equal to the remainder of X in 10 by the remainder of 10.
Therefore, in fact, we don't use the serial number of the dry and support, and you can ask for the day and the land, and it is dry.
Branch, this reduces a step. And for the day of the year, the same is only one at the end. The end of 4 years
The day of the day, the day of the year, the end of 5 years, is always B ...
Let's see the date of date. We can simulate the week's consume, get a comparative computational day-dry
The formula is as follows:
G = (Y-1) * 5 [(Y-1) / 4] - [(Y-1) / 100] [(Y-1) / 400] D 15, (3)
Where Y is the year, D is accumulated days, [...] means the number of orders, that is, only the integer part of the calculation result. Except
Take 60, the remainder is the serial number of the dry branch. Or remove the G at 10 or 12, you can directly get a day dry and day. Do not
In the same formula, this formula is still not simple enough, especially the first item (Y-1) * 5, in the formula.
When Y is four-digit years, the calculated result is a larger four-digit or five digits, and the mouth is very inconvenient.
We can improve this formula with the way to derive the Caile formula. First come to see the improvements related to the year.
We know that according to the rules of the public calendar, the total number of days in a century may be 36524 days, or 36525 days. If this
The year of 00 at the end of the century is a leap year. This century is only 36,525 days; otherwise only 36524 days. We may wish to
The 36524-day century is "flat century", with a 36525-day century as "leap". For the flat century, because
36524 MOD 60 = 44,
Therefore, every time a flat century, the same day's dry support will advance 44 serial numbers. Similarly, every time a trick, the same
The day's dry support will advance 45 serial numbers. This makes us easy to get a calculation of each century (year
The end of 01) March 1st formula:
G = 44c [c / 4] 15, (4)
Where C is a minus one.
The formula for calculating the dried on March 1, can also be obtained:
G = 44c [c / 4] 5 (Y-1) [Y / 4] 15,
which is
G = 44c [c / 4] 5Y [Y / 4] 10, (5)
Where Y is the two digits after the year.
Below we will list the number of days per month:
Month, January, April April, September, September, September, September
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Day 31 28 (29) 31 30 31 30 31 31 30 31 30 31
Subtle
Remaining days 1 -2 (-1) 1 0 1 0 1 1 0 1 0 1
If you think in January and February is the next year and 14 months, you can also get the following:
D '[3 * (M 1) / 5] D - 2 (MOD 10) (6) and
D '≡ [3 * (m 1) / 5] D - 2 I (MOD 12) (odd month i = 0, even month I = 6), (7)
Among them, D 'is the cumulative number of days since March 1, and M is month, and D is the number of days. Put (6) (7) two or (5)
Get up, then make appropriate levels, you get the formula of the day and floor branch of any day of the case:
G = 4C [C / 4] 5Y [Y / 4] [3 * (M 1) / 5] D - 3; (8)
Z = 8C [C / 4] 5Y [Y / 4] [3 * (M 1) / 5] D 7 I (odd month i = 0, even month I = 6)
(9)
If you get G, then
Z = G 4C 10 I (odd month I = 0, even month i = 6). (10)
The number of gs is the day dry serial number, and Z divided by 12 remaining number. Here you need to emphasize: January and February
When doing the previous year and 14 months, C and Y are also values the previous year.
We can compare (8) (9) and the Caile formula:
W = -2c [c / 4] y [y / 4] [13 * (m 1) / 5] D - 1,
It can be seen that their form is very similar, and the difference is only a few constants.
Although China is now not having to pay for the date of the date, but sometimes it needs to calculate daily dry. For example, calendar
It is said that "three volts" and "into the plum" "Eutei", all related to the day dry branch. Three volts include the ambiguo, among the end, refers to the summer
The hottest period of the sky, into the plum and essay refers to the beginning and end of the Jiangnan, the beginning of the rain season, which is related to the climate.
The term. However, because there is no accurate weather forecast for ancient times, it is not possible to accurately predict the time of Santui and the Mei, so it is
The hardships of the calendar have several days as a day of three rows and into the messenger, which determines a general date to prepare
test. Now, although there is a relatively accurate weather forecast, it is still a traditional calendar as a traditional calendar.
Come.
The third Geng Day after the summer solstice is beginning to start, and the fourth Geng Day begins, ten days.
Or twenty days; the first Geng Day after the autumn begins to start, a total of ten days. The reason why the length of Zhongd is not fixed, it is because
For the summer solstice, the date of the autumn and the date of Geng Day is floating year by year, and the first Geng Day after the autumn may be the summer solstice.
The fifth Geng Day may also be the sixth Geng Day. If the former, there is only ten days in 200; if it is the latter,
It will last twenty days. Note If the summer solstice is Geng Day, the first Geng Day after the summer solstice refers to the tenth day after the summer is.
Not summer until the day, at this time, the first day of the first day is the thirtieth day after the summer. Similarly, if the autumn is the day, the end of Geng Day, at the end
The first day of the volush is the tenth day after the autumn, not the day of the autumn. Intimi is the first Custan after the mango.
Mei refers to the first short day after the summer, and there is also the same provisions.
I know these, we can count the ambiguo, among the ambiguo, among the last days. This needs to first know the day of summer sushine and autumn. If you know that summer is June 21, Li Qiu is on August 7th, then uses formula (8), summer
The G is:
g = 4 * 20 [20/4] 5 * 4 [4/4] [3 * (6 1) / 5] 21 - 3
= 80 5 20 1 4 21 - 3
= 128,
The number of digits is 8, and the day is dry. The third Geng Day after the summer solstice is the 29th day after the summer, that is, July 20th, this day
That is, the first day of the first day. The first day of China is July 30. Also calculate the G is:
g = 4 * 20 [20/4] 5 * 4 [4/4] [3 * (8 1) / 5] 7 - 3
= 80 5 20 1 5 7 - 3
= 115,
It is a helle. After the autumn, the first Geng Day is the second day after the autumn, that is, on August 9th, this day is the end of the last
day. It can also be seen that in 2004, only ten days in 2004. It can also be calculated by the dates of mamns and small heats.
In 2004, the Mei and East Mei Day were June 6 and July 15.
In turn, I know that year dry boss and daily daughter are concerned, and I have a relatively trouble of seeking a corresponding year and date. Because of dry
The support is cycled, so you must first know which time you want to ask for the year and the date. such as
We prepare 1864, 1924, 1984 in 1984, and 1984, if you want to know what the 18998 is
One year, first, it is necessary to determine that it is the end of the 19th century, that is, this cycle began in 1864. that
, We can use the formula (1) to calculate the number of Wuxu is 35, so the year of the 1864-1) 35 = 1898.
The reason is to be minimized first, because the serial number of the armor is 1, you need to subtract this serial number first.
As for the day dry, because the daily car of the ancient book is always used in conjunction with the year, it is not difficult to determine it belongs.
Which cycle. For example, "Ming History · Zhuang Lie" records that Ming Chongzhen Emperor Zhu Yushen is Chongzhen's days.
Ding Ding, September 16 Chongzhen is 1644 AD 1644. Although March is the lunar calendar, we know farmers
Although the calendar is floating in the question, it does not have a certain range, such as the first day of the lunar calendar, always
The calendar floats between March 22nd to April 19. Therefore, first come to the dry budget on March 22, 1644. We have:
g = 4 * 16 [16/4] 5 * 44 [44/4] [3 * (3 1) / 5] 22 - 3
= 64 4 220 11 2 22 - 3
= 320,
The number of digits is 0,
Z = g 4C 10
= 320 64 10
= 394,
Remove more than 12 10, the dry branch of this day is a sequential, and its number is 6 * 0-5 * 10 60 = 10. And the Dan Di's serial number is
6 * 4-5 * 8 60 = 44, in 34 days after the arrival, the March Ding is not sure to be 34 days after March 22, that is, April 25
day. That is to say, Chongzhen self-sufficiency is April 25, 1644, which is consistent with the results of the Valentine's Day. May 4, 2004
