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A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) added to keep the calendar year synchronized with the astronomical year or seasonal year.Because astronomical events and seasons do not repeat in a whole number of days, calendars that have the same number of days in each year drift over time with respect to the event that the year is supposed to track. By inserting (called intercalating in technical terminology) an additional day or month into the year, the drift can be corrected. A year that is not a leap year is a common year.
For example, in the Gregorian calendar, each leap year has 366 days instead of 365, by extending February to 29 days rather than the common 28. These extra days occur in each year which is an integer multiple of 4 (except for years evenly divisible by 100, which are not leap years unless evenly divisible by 400). Similarly, in the lunisolar Hebrew calendar, Adar Aleph, a 13th lunar month, is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Bahá'í Calendar, a leap day is added when needed to ensure that the following year begins on the March equinox.
The term leap year probably comes from the fact that a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, but the day of the week in the 12 months following the leap day (from March 1 through February 28 of the following year) will advance two days due to the extra day, thus leaping over one day in the week.For example, Christmas Day (December 25) fell on a Sunday in 2016, Monday in 2017, Tuesday in 2018 and Wednesday in 2019, but then will leap over Thursday to fall on a Friday in 2020.
The length of a day is also occasionally corrected by inserting a leap second into Coordinated Universal Time (UTC) because of variations in Earth's rotation period. Unlike leap days, leap seconds are not introduced on a regular schedule because variations in the length of the day are not entirely predictable.
Leap years can present a problem in computing, known as the leap year bug, when a year is not correctly identified as a leap year or when February 29 is not handled correctly in logic that accepts or manipulates dates.
In the Gregorian calendar, the standard calendar in most of the world, most years that are multiples of 4 are leap years. In each leap year, the month of February has 29 days instead of 28. Adding one extra day in the calendar every four years compensates for the fact that a period of 365 days is shorter than a tropical year by almost 6 hours.Some exceptions to this basic rule are required since the duration of a tropical year is slightly less than 365.25 days. The Gregorian reform modified the Julian calendar's scheme of leap years as follows:
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are.
Over a period of four centuries, the accumulated error of adding a leap day every four years amounts to about three extra days. The Gregorian calendar therefore drops three leap days every 400 years, which is the length of its leap cycle. This is done by dropping February 29 in the three century years (multiples of 100) that cannot be exactly divided by 400. + 1⁄4 − 1⁄100 + 1⁄400 = 365.2425. The rule can be applied to years before the Gregorian reform (the proleptic Gregorian calendar), if astronomical year numbering is used.The years 1600, 2000 and 2400 are leap years, while 1700, 1800, 1900, 2100, 2200 and 2300 are not leap years. By this rule, the average number of days per year is 365
This graph shows the variations in date and time of the June Solstice due to unequally spaced "leap day" rules. Contrast this with the Iranian Solar Hijri calendar, which generally has 8 leap year days every 33 years.
The Gregorian calendar was designed to keep the vernal equinox on or close to March 21, so that the date of Easter (celebrated on the Sunday after the ecclesiastical full moon that falls on or after March 21) remains close to the vernal equinox.The "Accuracy" section of the "Gregorian calendar" article discusses how well the Gregorian calendar achieves this design goal, and how well it approximates the tropical year.
The following pseudocode determines whether a year is a leap year or a common year in the Gregorian calendar (and in the proleptic Gregorian calendar before 1582). The year variable being tested is the integer representing the number of the year in the Gregorian calendar.
if (year is not divisible by 4) then (it is a common year)
else if (year is not divisible by 100) then (it is a leap year)
else if (year is not divisible by 400) then (it is a common year)
else (it is a leap year)
The algorithm applies to proleptic Gregorian calendar years before 1, but only if the year is expressed with astronomical year numbering. It is not valid for the BC or BCE notation. The algorithm is not necessarily valid for years in the Julian calendar, such as years before 1752 in the British Empire. The year 1700 was a leap year in the Julian calendar, but not in the Gregorian calendar.
February 29 is a date that usually occurs every four years, and is called the leap day. This day is added to the calendar in leap years as a corrective measure, because the Earth does not orbit the sun in precisely 365 days.
The Gregorian calendar is a modification of the Julian calendar first used by the Romans. The Roman calendar originated as a lunisolar calendar and named many of its days after the syzygies of the moon: the new moon (Kalendae or calends, hence "calendar") and the full moon (Idus or ides). The Nonae or nones was not the first quarter moon but was exactly one nundina or Roman market week of nine days before the ides, inclusively counting the ides as the first of those nine days. This is what we would call a period of eight days. In 1825, Ideler believed that the lunisolar calendar was abandoned about 450 BC by the decemvirs, who implemented the Roman Republican calendar, used until 46 BC. The days of these calendars were counted down (inclusively) to the next named day, so February 24 was ante diem sextum Kalendas Martias ("the sixth day before the calends of March") often abbreviated a. d. VI Kal. Mart. The Romans counted days inclusively in their calendars, so this was actually the fifth day before March 1 when counted in the modern exclusive manner (not including the starting day).
The Republican calendar's intercalary month was inserted on the first or second day after the Terminalia (a. d. VII Kal. Mar., February 23). The remaining days of Februarius were dropped. This intercalary month, named Intercalaris or Mercedonius, contained 27 days. The religious festivals that were normally celebrated in the last five days of February were moved to the last five days of Intercalaris. Because only 22 or 23 days were effectively added, not a full lunation, the calends and ides of the Roman Republican calendar were no longer associated with the new moon and full moon.
The Julian calendar, which was developed in 46 BC by Julius Caesar, and became effective in 45 BC, distributed an extra ten days among the months of the Roman Republican calendar. Caesar also replaced the intercalary month by a single intercalary day, located where the intercalary month used to be. To create the intercalary day, the existing ante diem sextum Kalendas Martias (February 24) was doubled, producing ante diem bis sextum Kalendas Martias. Hence, the year containing the doubled day was a bissextile (bis sextum, "twice sixth") year. For legal purposes, the two days of the bis sextum were considered to be a single day, with the second half being intercalated; but in common practice by 238, when Censorinus wrote, the intercalary day was followed by the last five days of February, a. d. VI, V, IV, III and pridie Kal. Mart. (the days numbered 24, 25, 26, 27, and 28 from the beginning of February in a common year), so that the intercalated day was the first half of the doubled day. Thus the intercalated day was effectively inserted between the 23rd and 24th days of February. All later writers, including Macrobius about 430, Bede in 725, and other medieval computists (calculators of Easter), continued to state that the bissextum (bissextile day) occurred before the last five days of February.
Until 1970, the Roman Catholic Church always celebrated the feast of Saint Matthias on a. d. VI Kal. Mart., so if the days were numbered from the beginning of the month, it was named February 24 in common years, but the presence of the bissextum in a bissextile year immediately before a. d. VI Kal. Mart. shifted the latter day to February 25 in leap years, with the Vigil of St. Matthias shifting from February 23 to the leap day of February 24. This shift did not take place in pre-Reformation Norway and Iceland; Pope Alexander III ruled that either practice was lawful (Liber Extra, 5. 40. 14. 1). Other feasts normally falling on February 25–28 in common years are also shifted to the following day in a leap year (although they would be on the same day according to the Roman notation). The practice is still observed by those who use the older calendars.
The Revised Bengali Calendar of Bangladesh and the Indian National Calendar organise their leap years so that the every leap day is close to a February 29 in the Gregorian calendar and vice versa. This makes it easy to convert dates to or from Gregorian.
The Thai solar calendar uses the Buddhist Era (BE), but has been synchronized with the Gregorian since AD 1941.
The Julian calendar was instituted in 45 BC at the order of Julius Caesar, and the original intent was to make every fourth year a leap year, but this was not carried out correctly. Augustus ordered some leap years to be omitted to correct the problem, and by AD 8 the leap years were being observed every fourth year, and the observances were consistent up to and including modern times.
From AD 8 the Julian calendar received an extra day added to February in years that are multiples of 4 (although the AD year numbering system was not introduced until AD 525).
The Coptic calendar and Ethiopian calendar also add an extra day to the end of the year once every four years before a Julian 29-day February.
This rule gives an average year length of 365.25 days. However, it is 11 minutes longer than a tropical year. This means that the vernal equinox moves a day earlier in the calendar about every 131 years.
The Revised Julian calendar adds an extra day to February in years that are multiples of four, except for years that are multiples of 100 that do not leave a remainder of 200 or 600 when divided by 900. This rule agrees with the rule for the Gregorian calendar until 2799. The first year that dates in the Revised Julian calendar will not agree with those in the Gregorian calendar will be 2800, because it will be a leap year in the Gregorian calendar but not in the Revised Julian calendar.
This rule gives an average year length of 365.242222 days. This is a very good approximation to the mean tropical year, but because the vernal equinox year is slightly longer, the Revised Julian calendar for the time being does not do as good a job as the Gregorian calendar at keeping the vernal equinox on or close to March 21.
The Chinese calendar is lunisolar, so a leap year has an extra month, often called an embolismic month after the Greek word for it. In the Chinese calendar the leap month is added according to a rule which ensures that month 11 is always the month that contains the northern winter solstice. The intercalary month takes the same number as the preceding month; for example, if it follows the second month (二月) then it is simply called "leap second month" i.e. simplified Chinese :闰二月; traditional Chinese :閏二月; pinyin :rùn'èryuè.
The Hebrew calendar is lunisolar with an embolismic month. This extra month is called Adar Alef (first Adar) and is added before Adar , which then becomes Adar Bet (second Adar). According to the Metonic cycle, this is done seven times every nineteen years (specifically, in years 3, 6, 8, 11, 14, 17, and 19). This is to ensure that Passover (Pesah) is always in the spring as required by the Torah (Pentateuch) in many versesrelating to Passover.
In addition, the Hebrew calendar has postponement rules that postpone the start of the year by one or two days. These postponement rules reduce the number of different combinations of year length and starting days of the week from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath. In particular, the first day of the Hebrew year can never be Sunday, Wednesday or Friday. This rule is known in Hebrew as "lo adu rosh" (לא אד״ו ראש), i.e., "Rosh [ha-Shanah, first day of the year] is not Sunday, Wednesday or Friday" (as the Hebrew word adu is written by three Hebrew letters signifying Sunday, Wednesday and Friday). Accordingly, the first day of Passover is never Monday, Wednesday or Friday. This rule is known in Hebrew as "lo badu Pesah" (לא בד״ו פסח), which has a double meaning — "Passover is not a legend", but also "Passover is not Monday, Wednesday or Friday" (as the Hebrew word badu is written by three Hebrew letters signifying Monday, Wednesday and Friday).
One reason for this rule is that Yom Kippur, the holiest day in the Hebrew calendar and the tenth day of the Hebrew year, now must never be adjacent to the weekly Sabbath (which is Saturday), i.e., it must never fall on Friday or Sunday, in order not to have two adjacent Sabbath days. However, Yom Kippur can still be on Saturday. A second reason is that Hoshana Rabbah, the 21st day of the Hebrew year, will never be on Saturday. These rules for the Feasts do not apply to the years from the Creation to the deliverance of the Hebrews from Egypt under Moses. It was at that time (cf. Exodus 13) that the God of Abraham, Isaac and Jacob gave the Hebrews their "Law" including the days to be kept holy and the feast days and Sabbaths.
Years consisting of 12 months have between 353 and 355 days. In a k'sidra ("in order") 354-day year, months have alternating 30 and 29 day lengths. In a chaser ("lacking") year, the month of Kislev is reduced to 29 days. In a malei ("filled") year, the month of Marcheshvan is increased to 30 days. 13-month years follow the same pattern, with the addition of the 30-day Adar Alef, giving them between 383 and 385 days.
The observed and calculated versions of the Islamic calendar do not have regular leap days, even though both have lunar months containing 29 or 30 days, generally in alternating order. However, the tabular Islamic calendar used by Islamic astronomers during the Middle Ages and still used by some Muslims does have a regular leap day added to the last month of the lunar year in 11 years of a 30-year cycle.This additional day is found at the end of the last month, Dhu 'l-Hijja, which is also the month of the Hajj.
The Hijri-Shamsi calendar, also adopted by the Ahmadiyya Community, is based on solar calculations and is similar to the Gregorian calendar in its structure with the exception that the first year starts with Hijra.
The Bahá'í calendar is a solar calendar composed of 19 months of 19 days each (361 days). Years begin at Naw-Rúz, on the vernal equinox, on or about March 21. A period of "Intercalary Days", called Ayyam-i-Ha, are inserted before the 19th month. This period normally has 4 days, but an extra day is added when needed to ensure that the following year starts on the vernal equinox. This is calculated and known years in advance.
The Iranian calendar is an observational calendar that starts on the spring equinox and adds a single intercalated day to the last month (Esfand) once every four or five years; the first leap year occurs as the fifth year of the typical 33-year cycle and the remaining leap years occur every four years through the remainder of the 33-year cycle. This system has less periodic deviation or jitter from its mean year than the Gregorian calendar, and operates on the simple rule that the vernal equinox always falls in the 24-hour period ending at noon on New Year's Day.The 33-year period is not completely regular; every so often the 33-year cycle will be broken by a cycle of 29 years. A similar rule has been proposed to simplify the Gregorian calendar. The centennial leap years would be spaced so that in years giving remainder 3 on division by 100 the dynamic mean sun passes through the equinox in the 24-hour period ending at 1 PM GMT on 19 March. The system would be introduced when for the first time the dynamic mean sun is due to pass through the equinox before 1 PM GMT on 18 March in a year giving remainder 3 on division by 400. The immediately preceding centennial leap year will be cancelled. The first cancellation will probably be AD 8400 and the next two centennial leap years thereafter will probably be AD 8800 and AD 9700.
In Ireland and Britain, it is a tradition that women may propose marriage only in leap years. While it has been claimed that the tradition was initiated by Saint Patrick or Brigid of Kildare in 5th century Ireland, this is dubious, as the tradition has not been attested before the 19th century.Supposedly, a 1288 law by Queen Margaret of Scotland (then age five and living in Norway), required that fines be levied if a marriage proposal was refused by the man; compensation was deemed to be a pair of leather gloves, a single rose, £1 and a kiss. In some places the tradition was tightened to restricting female proposals to the modern leap day, February 29, or to the medieval (bissextile) leap day, February 24.
According to Felten: "A play from the turn of the 17th century, 'The Maydes Metamorphosis,' has it that 'this is leape year/women wear breeches.' A few hundred years later, breeches wouldn't do at all: Women looking to take advantage of their opportunity to pitch woo were expected to wear a scarlet petticoat — fair warning, if you will."
In Finland, the tradition is that if a man refuses a woman's proposal on leap day, he should buy her the fabrics for a skirt.
In France, since 1980, a satirical newspaper entitled La Bougie du Sapeur is published only on leap year, on February 29.
In Greece, marriage in a leap year is considered unlucky.One in five engaged couples in Greece will plan to avoid getting married in a leap year.
In February 1988 the town of Anthony in Texas, declared itself "leap year capital of the world", and an international leapling birthday club was started.
A person born on February 29 may be called a "leapling" or a "leaper".In common years, they usually celebrate their birthdays on February 28. In some situations, March 1 is used as the birthday in a non-leap year, since it is the day following February 28.
Technically, a leapling will have fewer birthday anniversaries than their age in years. This phenomenon is exploited when a person claims to be only a quarter of their actual age, by counting their leap-year birthday anniversaries only: for example, in Gilbert and Sullivan's 1879 comic opera The Pirates of Penzance , Frederic the pirate apprentice discovers that he is bound to serve the pirates until his 21st birthday (that is, when he turns 88 years old, since 1900 was not a leap year) rather than until his 21st year.
For legal purposes, legal birthdays depend on how local laws count time intervals.
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The Civil Code of the Taiwan since October 10, 1929,implies that the legal birthday of a leapling is February 28 in common years:
If a period fixed by weeks, months, and years does not commence from the beginning of a week, month, or year, it ends with the ending of the day which precedes the day of the last week, month, or year which corresponds to that on which it began to commence. But if there is no corresponding day in the last month, the period ends with the ending of the last day of the last month.
Since 1990 non-retroactively, Hong Kong considers the legal birthday of a leapling March 1 in common years:
- The time at which a person attains a particular age expressed in years shall be the commencement of the anniversary corresponding to the date of [their] birth.
- Where a person has been born on February 29 in a leap year, the relevant anniversary in any year other than a leap year shall be taken to be March 1.
- This section shall apply only where the relevant anniversary falls on a date after the date of commencement of this Ordinance.
A calendar is a system of organizing days for social, religious, commercial or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single, specific day within such a system. A calendar is also a physical record of such a system. A calendar can also mean a list of planned events, such as a court calendar or a partly or fully chronological list of documents, such as a calendar of wills.
Generally speaking, a calendar year begins on the New Year's Day of the given calendar system and ends on the day before the following New Year's Day, and thus consists of a whole number of days. A year can also be measured by starting on any other named day of the calendar, and ending on the day before this named day in the following year. This may be termed a "year's time", but not a "calendar year". To reconcilie the calendar year with the astronomical cycle certain years contain extra days.
February 29, also known as leap day or leap year day, is a date added to most years that are divisible by 4, such as 2016, 2020, and 2024. A leap day is added in various solar calendars, including the Gregorian calendar standard in most of the world. Lunisolar calendars instead add a leap or intercalary month.
The Hebrew or Jewish calendar is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits, and daily Psalm readings, among many ceremonial uses. In Israel, it is used for religious purposes, provides a time frame for agriculture and is an official calendar for civil purposes, although the latter usage has been steadily declining in favor of the Gregorian calendar.
Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.
The Julian calendar, proposed by Julius Caesar in 708 Ab urbe condita (AUC) (46 BC), was a reform of the Roman calendar. It took effect on 1 January 709 AUC (45 BC), by edict. It was designed with the aid of Greek mathematicians and Greek astronomers such as Sosigenes of Alexandria.
A lunisolar calendar is a calendar in many cultures whose date indicates both the Moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.
A month is a unit of time, used with calendars, which is approximately as long as a natural period related to the motion of the Moon; month and Moon are cognates. The traditional concept arose with the cycle of Moon phases; such months (lunations) are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth-Sun line, are still the basis of many calendars today, and are used to divide the year.
A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as standard in the world, is an example of a solar calendar. The main other type of calendar is a lunar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of Moon phase.
The Badíʻ calendar used in the Baháʼí Faith is a solar calendar consisting of 19 months and 4-5 Intercalary Days, with new year at the northern spring equinox. Each month is named after virtues, as are the days of the week. The first year is dated from 1844 CE, the year in which the Báb began teaching.
The Swedish calendar or Swedish style was a calendar in use in Sweden and its possessions from 1 March 1700 until 30 February 1712. It was one day ahead of the Julian calendar and ten days behind the Gregorian calendar. Easter was calculated nominally astronomically from 1740 to 1844.
Calendar reform or calendrical reform, is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design.
Birkat Hachama refers to a rare Jewish blessing that is recited to the Creator, thanking Him for creating the sun. The blessing is recited when the sun completes its cycle every 28 years on a Tuesday at sundown. Jewish tradition says that when the Sun completes this cycle, it has returned to its position when the world was created. Because the blessing needs to be said when the sun is visible, the blessing is postponed to the following day, on Wednesday morning.
The Buddhist calendar is a set of lunisolar calendars primarily used in mainland Southeast Asian countries of Cambodia, Laos, Myanmar and Thailand as well as in Sri Lanka and Chinese populations of Malaysia and Singapore for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunisolar calendar and by the Thai solar calendar.
Bissext, or bissextus is the day which is added to the Gregorian calendar every fourth year to compensate for the six-hour difference in length between the common 365-day year and the actual length of the solar year.
In the Gregorian calendar, a year ending in "00" that is divisible by 400 is a century leap year, with the intercalation of February 29 yielding 366 days instead of 365. Century years that are not divisible by 400 are not leap years but common years of 365 days. For example, the years 1600, 2000, and 2400 are century leap years since those numbers are divisible by 400, while 1700, 1800, 1900, 2100, 2200, and 2300 are not leap years despite being divisible by 4. Leap years divisible by 400 always start on a Saturday; thus the leap day February 29 in those years always falls on a Tuesday.
The Gregorian calendar is the calendar used in most of the world. It is named after Pope Gregory XIII, who introduced it in October 1582.
Tishri-years, often called the Jewish Civil Calendar, is an ancient calendar system used in Israel/Judea, and the Jewish diaspora. It is based on, and is a variation of, the Nisan-years, which is often called the Jewish Religious Calendar. Tishri-years is similar to, and sometimes equivalent to, the Ancient Macedonian calendar used by the Hellenistic empires. They are all lunisolar years beginning from Autumn, but could differ by a month.
The Jewish Talmudic Calendar is a lunisolar calendar using Tishri-years, observed by the Jewish people since Late Antiquity. While it is based on Nisan-years, which began from the prebiblical Babylonian times, and the Tishri-years was formed in the time of David, the full formation of the Jewish Talmudic Calendar was during the time of the writing of Talmud, usually attributed to Hillel II.
The Solar Hijri calendar, also called the Iranian Hijri calendar or Shamsi Hijri calendar, and abbreviated as SH, is the official calendar of Iran and Afghanistan. It begins on the March equinox (Nowruz) as determined by astronomical calculation for the Iran Standard Time meridian and has years of 365 or 366 days.