Common year starting on Monday

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A common year starting on Monday is any non-leap year (i.e., a year with 365 days) 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 (the current year) 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 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.

Monday day of the week

Monday is the day of the week between Sunday and Tuesday. According to the international standard ISO 8601 it is the first day of the week. The name of Monday is derived from Old English Mōnandæg and Middle English Monenday, originally a translation of Latin dies lunae "day of the Moon".

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 common year starting on Monday,
presented as common in many English-speaking areas

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.

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ISO 8601-conformant calendar with week numbers for
any common year starting on Monday (dominical letter G)

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

In the (currently used) Gregorian calendar, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Monday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Monday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1590
17th century 1601 1607 1618 1629 1635 1646 1657 1663 1674 1685 1691
18th century 1703 1714 1725 1731 1742 1753 1759 1770 1781 1787 1798
19th century 1810 1821 1827 1838 1849 1855 1866 1877 1883 1894 1900
20th century 1906 1917 1923 1934 1945 1951 1962 1973 1979 1990
21st century 2001 2007 2018 2029 2035 2046 2057 2063 2074 2085 2091

Julian calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters (one for January and February and the other for March to December, as 29 February has no letter). This sequence occurs exactly once within a cycle, and every common letter thrice.

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.

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). Years 6, 12 and 23 of the cycle are common years beginning on Monday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Monday.

Julian common years starting on Monday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1403 1414 1425 1431 1442 1453 1459 1470 1481 1487 1498
16th century 1509 1515 1526 1537 1543 1554 1565 1571 1582 15931599
17th century1610162116271638164916551666167716831694
18th century17051711172217331739175017611767177817891795
19th century1806181718231834184518511862187318791890
20th century19011907191819291935194619571963197419851991
21st century20022013201920302041204720582069207520862097

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 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, 2009, 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 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.

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.

A leap year starting on Wednesday is any year with 366 days 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 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.

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.

Perpetual calendar calendar valid for many years

A perpetual calendar is a calendar valid for many years, usually designed to allow the calculation of the day of the week for a given date in the future.

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.

References

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