Leap Year Logistics
A leap year means that the year has 366 days, which is one day more than a normal year. Leap years were established to make up for the gap between the annual number of 365 days prescribed by the artificial calendar and the average tropical year of approximately 365.24219 days. Different calendars have different methods of setting leaps . The Julian calendar has a leap day every four years, and the average year is 365.25 days. The Gregorian calendar misses three leap days every 400 years, with an average of 365.2425. The extra day is February 29th.
leap rule
The Julian calendar was used on October 4, 1582, 442 years ago . After the announcement of October 5, the calendar was changed to the Gregorian Gregorian calendar, which has been in use since October 15. The rules for leap years under the calendar are as follows (AD here refers to the year after AD, please refer to subsequent chapters for modification of the rules for leap years after BC, for example: therefore 1700 , 1800 , 1900 , 2100 , 2200 , 2300 Years without leap days are ordinary years, except for 1600 , 2000 and 2400 , which are leap years, etc.)
Calculate whether a year in the Gregorian calendar is an ordinary year or a leap year
AD years are not multiples of 4, they are 365 celestial years.
AD years are multiples of 4 but not 100, and are leap years with 366 days.
AD years are multiples of 100 but not multiples of 400, ( 1700 , 1800 and 1900 ) are ordinary years.
AD years are multiples of 400, and ( 1600 and 2000 ) are leap years.
Every leap year, there is a leap day on February 29th.
Therefore, 1979 , 2018 , and 2021 are ordinary years, and the multiples of 4 in 1980 and 2020 are leap years. There is no way to set leap years in 300 years such as 1700 , 1800 , 1900, and 2100 , and there are no 400 years. The multiples and the multiples of once every 100 years are not the multiples of once every 400 years. Therefore, there is no multiple of 400 years from 2100. It is a leap year but an ordinary year. From 1600 and 2000 , there are also leap years that occur every 400 years.
There is still an error in the length of the Gregorian calendar and the solar year, about 3200, which is about one day off. Therefore, John Herschel proposed that there should be no leaps in every multiple of 3200, such as 3200 AD . However, it is still 1176 years away from this year, so it has not been truly included in the rules or implemented. In addition, due to the instability of the earth's revolution speed and many influencing factors, whether this rule needs to be incorporated into the new calendar is yet to be discussed.
Sequence ( OEIS Sequence A189917 ): 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 , 40 , 44 , 48 , 52 , 56 , 60 , 64 , 68 …
Julian calendar§ Rome loses leap years
Leap years in BC appear in BC 1, BC 5, BC 9, BC 13,..., or are recorded as 1 BC, 5 BC, 9 BC, 13 BC,..., or are recorded as 0 on the number line, - 4,-8,-12,…. To determine whether it is a leap year, you must subtract 1 from the year value and then calculate it by "dividing by 4", or calculate it directly when expressed in number line notation (the sign does not affect whether it is divisible). (Because there is no year 0 AD (unless temporarily agreed and the corresponding equation is noted), 1, 2, 3, 4, ... years BC should correspond to the mathematical number axis (but not, or not It should be called AD 0, -1, -2, -3,... years on the calendar, while BC 1, 5, 9, 13,... years corresponds to 0, -4, - on the mathematical number axis. 8, -12, ... years, multiples of 4).
Leap years in various calendars
"Leap Year" in the Gregorian Calendar
A year with a leap day in the Gregorian calendar is called a leap year. On the contrary, it is an ordinary year . An ordinary year has 365 days and a leap year has 366 days (excluding leap months with 383, 384 or 385 days). In the Gregorian calendar and Gregorian calendar , ordinary years February in February has 28 days, and February in leap years has 29 days. February 29th in a leap year is leap day .
"Leap year" or leap month in the lunar calendar
The lunar calendar is a lunisolar calendar . The number and sum of the days in each month are determined according to the waning moon. The time of a year is based on 12 months. An ordinary year is about 11 days shorter than a tropical year. In order to match the period of the Earth's orbit around the sun, which is the tropical year, one month is added every 2 to 3 years, and the added month is a leap month. The month to which a leap month is added is inferred according to the rules of the lunar calendar, and is mainly determined based on the consistency with the twenty-four solar terms of the lunar calendar. In a year with a leap month, there are 13 months. The length of the calendar year is 383, 384 to 385 days, and the total number of leap months is only 18, 19, and 20 days. This year is also called a leap year. For example, in the lunar calendar of 2023, the Year of the Rabbit, there are two Februarys, usually called the first two months and the last two months (i.e., leap months). The calculation of leap months in leap years of the lunar calendar includes one leap every three years, two leaps every five years, and seven leaps every nineteen years. The 19-year cycle of the lunar calendar basically corresponds to the same time in the Gregorian calendar, but there are some exceptions. For example, in the Gregorian calendar, May 27, 1963, May 27, 1982, May 27, 2001, May 27, 2020 and May 27, 2058 are all leap days on the fifth day of April. Later, however, The exception is May 27, 2039, which is also the fifth day of May ( Dragon Boat Festival ), and June 26, 2039, which is the fifth day of the leap fifth month of the lunar calendar.