Leap year starting on Wednesday

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A leap year starting on Wednesday is any year with 366 days (i.e. it includes 29 February) that begins on Wednesday, 1 January, and ends on Thursday, 31 December. Its dominical letters hence are ED, such as the years 1908, 1936, 1964, 1992, 2020, 2048, 2076, and 2116 in the Gregorian calendar [1] or, likewise, 2004 and 2032 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in March and November. Common years starting on Thursday share this characteristic, but also have another in February.

Wednesday is the day of the week between Tuesday and Thursday. According to international standard ISO 8601 it is the third day of the week. In countries that use the Sunday-first convention and in the Jewish Hebrew calendar Wednesday is defined as the fourth day of the week. The name is derived from Old English Wōdnesdæg and Middle English Wednesdei, "day of Woden", reflecting the pre-Christian religion practiced by the Anglo-Saxons, a variation of the Norse god Odin. In other languages, such as the French mercredi or Italian mercoledì, the day's name is a calque of dies Mercurii "day of Mercury". It has the most letters out of all the Gregorian calendar days.

Thursday is the day of the week between Wednesday and Friday. According to the ISO 8601 international standard, it is the fourth day of the week.

Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter depending on which day of the week the year starts on.

Contents

Calendars

Calendar for any leap year starting on Wednesday,
presented as common in many English-speaking areas

A leap year is a calendar year containing one additional day added to keep the calendar year synchronized with the astronomical or seasonal year. Because seasons and astronomical events 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 an additional day or month into the year, the drift can be corrected. A year that is not a leap year is called a common year.

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ISO 8601-conformant calendar with week numbers for
any leap year starting on Wednesday (dominical letter ED)

ISO 8601Data elements and interchange formats – Information interchange – Representation of dates and times is an international standard covering the exchange of date- and time-related data. It was issued by the International Organization for Standardization (ISO) and was first published in 1988. The purpose of this standard is to provide an unambiguous and well-defined method of representing dates and times, so as to avoid misinterpretation of numeric representations of dates and times, particularly when data are transferred between countries with different conventions for writing numeric dates and times.

The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.

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Applicable years

Gregorian Calendar

Leap years that begin on Wednesday, like those that start on Tuesday, occur at a rate of approximately 14.4% (14 out of 97) of all total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is thus 3.5% (14 out of 400).

A leap year starting on Tuesday is any year with 366 days that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE, such as the years 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, and 2104 in the Gregorian calendar or, likewise, 1964, 1992, and 2020 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this leap year occurs in June. Common years starting on Wednesday share this characteristic.

The Gregorian calendar is the most widely used civil calendar in the world. It is named after Pope Gregory XIII, who introduced it in October 1582. The calendar spaces leap years to make the average year 365.2425 days long, approximating the 365.2422-day tropical year that is determined by the Earth's revolution around the Sun. The rule for leap years is:

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 year 2000 is.

For this kind of year, the corresponding ISO year has 53 weeks, and the ISO week 10 (which begins March 2) and all subsequent ISO weeks occur earlier than in all other years. That means, moveable holidays may occur one calendar week later than otherwise possible.

Gregorian leap years starting on Wednesday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
17th century 1620 1648 1676
18th century 1716 1744 1772
19th century 1812 1840 1868 1896
20th century 1908 1936 1964 1992
21st century 2020 2048 2076
22nd century 2116 2144 2172

Julian Calendar

Like all leap year types, the one starting with 1 January on a Wednesday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1).

Solar cycle periodic change in the Suns activity

The solar cycle or solar magnetic activity cycle is the nearly periodic 11-year change in the Sun's activity and appearance.

Julian leap years starting on Wednesday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1416 1444 1472 1500
16th century 1528 1556 1584
17th century 1612 1640 1668 1696
18th century172417521780
19th century1808183618641892
20th century192019481976
21st century2004203220602088
22nd century2116214421722200

Related Research Articles

A common year starting on Sunday is any non-leap year that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2017 and the next one will be 2023 in the Gregorian calendar, or, likewise, 2018 and 2029 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in January and October.

A common year starting on Friday is any non-leap year that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2010 and the next one will be 2021 in the Gregorian calendar, or, likewise, 2011 and 2022 in the obsolete Julian calendar. The century year, 2100, will also be a common year starting on Friday in the Gregorian calendar. See below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.

A common year starting on Monday is any non-leap year that begins on Monday, 1 January, and ends on Monday, 31 December. Its dominical letter hence is G. The most recent year of such kind was 2018 and the next one will be 2029 in the Gregorian calendar, or likewise, 2013 and 2019 in the obsolete Julian calendar. The century year, 1900, was also a common year starting on Monday in the Gregorian calendar. See below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year of this type contains two Friday the 13ths in April and July. Leap years starting on Sunday share this characteristic, but also have another in January.

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar,, employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

A leap year starting on Sunday is any year with 366 days that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG, such as the years 1888, 1928, 1956, 1984, 2012, 2040, 2068, 2096, 2108, 2136, 2164, and 2192 in the Gregorian calendar or, likewise, 1996 and 2024 in the obsolete Julian calendar.

A common year starting on Tuesday is any non-leap year that begins on Tuesday, 1 January, and ends on Tuesday, 31 December. Its dominical letter hence is F. The current year, 2019, is a common year starting on Tuesday in the Gregorian calendar. The last such year was 2013 and the next such year will be 2030, or, likewise, 2014 and 2025 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in September and December. Leap years starting on Monday share this characteristic. From July of the year that precedes this year until September in this type of year is the longest period that occurs without a Friday the 13th. Leap years starting on Saturday share this characteristic, from August of the common year that precedes it to October in that type of year.

A leap year starting on Monday is any year with 366 days that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF, such as the years 1912, 1940, 1968, 1996, 2024, 2052, 2080, and 2120 in the Gregorian calendar or, likewise, 2008, 2036, and 2064 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in September and December. Common years starting on Tuesday share this characteristic.

A common year starting on Wednesday is any non-leap year that begins on Wednesday, 1 January, and ends on Wednesday, 31 December. Its dominical letter hence is E. The most recent year of such kind was 2014, and the next one will be 2025 in the in the Gregorian calendar or, likewise, 2015 and 2026 in the obsolete Julian calendar. The century year, 1800, was also a common year starting on Wednesday in the Gregorian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in June. Leap years starting on Tuesday share this characteristic.

A common year starting on Saturday is any non-leap year that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2011 and the next one will be 2022 in the Gregorian calendar or, likewise, 2017 and 2023 in the obsolete Julian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in May. Leap years starting on Friday share this characteristic.

A common year starting on Thursday is any non-leap year that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar or, likewise, 2010 and 2021 in the obsolete Julian calendar, see below for more. This common year contains the most Friday the 13ths; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic. From February until March in this type of year is also the shortest period that occurs within a Friday the 13th.

A leap year starting on Saturday is any year with 366 days that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA, such as the years 1916, 1944, 1972, 2000, and 2028 in the Gregorian calendar or, likewise, 2012 and 2040 in the obsolete Julian calendar. In the Gregorian calendar all centennial leap years start on Saturday; the next such year will be 2400, see below for more.

A leap year starting on Friday is any year with 366 days that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB, such as the years 1808, 1836, 1864, 1892, 1904, 1932, 1960, 1988, 2016, 2044, 2072, and 2112 in the Gregorian calendar or, likewise, 2000 and 2028 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this leap year occurs in May. Common years starting on Saturday share this characteristic.

A leap year starting on Thursday is any year with 366 days that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC, such as the years 1880, 1920, 1948, 1976, 2004, 2032, 2060, and 2088, in the Gregorian calendar or, likewise, 1988, 2016, and 2044 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in February and August.

The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the day of the week on which someone was born or a specific event occurred.

Doomsday rule way of calculating the day of the week of a given date

The Doomsday rule is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years.

The solar cycle is a 28-year cycle of the Julian calendar with respect to the week. It occurs because leap years occur every 4 years and there are 7 possible days to start a leap year, making a 28-year sequence.

References

  1. 1 2 3 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.