Leap-year
Leap year is an expression derived from the Latin "bis sextus dies ante calendas martii" ("repeated on the sixth day before the first day of the month of March"), which corresponded to an extra day inserted between February 23 and 24 by Julius Caesar.
February 24 was the sixth day before the Kalends (first day of the month) of March. The Romans did not count the days of the month from 1 to 31, but took three reference dates: "calendas", "nonas" and "idus" (see Roman calendar). To count, the reference day was included (in this case, March 1).
In the Gregorian calendar, which is the one used today, and which was established by Pope Gregory XIII from 1582, this extra day was placed at the end of the month of February, February 29.
Reason and definition of leap year
It is added to correct the gap that exists between the duration of the tropical year: 365 days 5 h 48 min 45.10 s (365.242189 days) and the calendar year of 365 days. This requires that every four years the calendar year be corrected by an unaccounted for accumulation of approximately 1/4 day per year equal to one extra day.
In the Julian calendar, years divisible by four were considered leap years, resulting in years of 365.25 days. This represents an advance of about 11.25 minutes per year compared to the tropical year. It may not sound like much, but just in 500 years it would be a lag of almost four days. It became necessary to shorten the year, and thus the Gregorian calendar establishes:
|
That is, two groups of years are determined: non-secular and secular. The first must be multiples of 4, while the second must be multiples of 400. In this way, 3 out of every 4 secular years are eliminated as leap years. In this way, the years 1800 and 1900, despite being divisible by 4, are not divisible by 400, so they were common years. For its part, the year 2000 is divisible by both 4 and 400, therefore it was a leap year.
The Julian cycle of 4 years gives way to a Gregorian one of 400 in which there are 97 leap years and 303 common ones, resulting in years of 365.2425 days. The difference with the tropical year is now reduced to less than half a minute per year (approximately 26.9 seconds).
Origin of leap year
Egyptian and Roman calendar
It was in the year 49 B.C. C., when Julius Caesar arrived in Egypt. Until then, the Roman calendar had centuries of lag due to its imprecision. Among other things, Julius found an excellent calendar in the lands of the Egyptian pharaoh Cleopatra. It was then that he delegated to Sosigenes of Alexandria, astronomer, mathematician, and philosopher, the task of designing a new calendar to the height and accuracy that the empire needed. Sosigenes gave Caesar his calendar between 48 and 46 BC. C., based mainly on the Egyptian calendar, but keeping the names of the Roman months. This calendar had a duration of 365 days and an additional day initially every four years, to compensate for a natural lag produced by the non-synchronous revolution of the Earth around the Sun.
The compensation for the gaps that the Roman calendar had accumulated forced the year 46 B.C. C. became the longest year in history, with 445 days to compensate and start again from scratch. This unusual year was called the "Julian year" or the "year of confusion".
The Egyptians already knew that every four years the heliacal rise of the star Sothis (Sirius) was delayed by one day, beginning the new year. However, two hundred years before, at the Council of Canopus, when they were able to make the reform, the Egyptians did not do it due to conflicts between the priestly castes and the political class.
Roughly six centuries earlier, King Numa Pompilius had added the months of Januarius and Februarius to the already battered Roman year, and it was to the latter, Februarius, that the extra day was added. The Romans used to call kalends (or kalendas) the first day of each month and counted backwards the days it took. The first day of March was called "calendas de marzo" or kalendas martias. In the Gregorian calendar, currently used, February 28 would be the day before (the second day before, inclusively reckoning, the March kalends, and February 27 would be the third day before these kalends (note that both the kalends and the day itself must be counted, since the Romans and the Jews practiced the inclusive reckoning of the days) and so on, so that February 24 would be the sixth day before the March kalends ( ante diem sextum kalendas martias). The reform of Julius Caesar added a day after February 24th the ante diem bis sextum kalendas martias. Over time it continued to be called Bi-sextum or leap year, even if the extra day was added after the last day of February.
This calendar was official in Rome for the following centuries, even at the Council of Nicea I it was warned that there was an error by Sosigenes, but they did nothing to correct it, until 1582, when the Gregorian calendar was adopted.
Gregorian Reform
Pope Gregory XIII, advised by the Jesuit astronomer Christopher Clavius, promulgated the bull Inter Gravissimas on February 24, 1582, in which he established that after Thursday, October 4, 1582, Friday, October 15, 1582 would follow.
With the elimination of these ten days the gap with the solar year disappeared. So that it would not happen again, in the new calendar three leap years were eliminated every four centuries. With the above, October 4, 1582 was the last day of the Julian calendar and October 15, 1582 was the first day of the Gregorian calendar. For this reason, the dates from October 5 to 14 of that year did not exist.
If current methods are used, calculating dates prior to October 15, 1582 will always be in error, since they should be used exclusively in retrospect to this date and switch to Julian date calculation after October 4, 1582, without forgetting these non-existent 10 days.
Computational algorithm
A year is leap year if it is:
- Divisible between 4.
- Not divisible 100.
- Divisible between 400. (2000 and 2400 are biscuits since still divisible between 100 are also between 400. But the years 1900, 2100, 2200 and 2300 are not because they are only divisible between 100).
From an algorithmic approach, the following logical propositions or statements are considered:
- p: It is divisible between 4
- q: It is divisible between 100 (¬q then means Not divisible 100)
- r: It is divisible between 400
Then the logical formula is used p∧ ∧ (¬ ¬ q r){displaystyle pland left(lnot qlor rright)} to establish if a given year is bisy: it is bisy if it is divisible between four and (it is not divisible between 100 or is divisible between 400).
Calendars
- Bite year started on Monday
- Bite year started on Tuesday
- Big Year Started on Wednesday
- Bite year started on Thursday
- Bite year started on Friday
- Bite year started on Saturday
- Bite year started on Sunday