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, 2019 and 2030 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on and occurs in century years that yield a remainder of 300 when divided by 400. The most recent such year was 1900 and the next one will be 2300.

Contents

Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths: those two in this common year occur in April and July. Leap years starting on Sunday share this characteristic, but also have another in January.

In this common year, Martin Luther King Jr. Day is on its earliest possible date, January 15, Valentine's Day, U.S. Independence Day, and Halloween fall on a Wednesday, President's Day is on February 19, Saint Patrick's Day is on a Saturday, Memorial Day is on May 28, Labor Day is on September 3, Columbus Day is on its earliest possible date, October 8, Veterans Day is on a Sunday, Thanksgiving is on its earliest possible date, November 22, and Christmas is on a Tuesday.

The Election Day in the USA is on November 6th, as well in leap years starting on Sunday.

Calendars

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

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07080910111213
14151617181920
21222324252627
28293031 
 
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04050607080910
11121314151617
18192021222324
252627282930
 
01
02030405060708
09101112131415
16171819202122
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3031 

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

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08091011121314
15161718192021
22232425262728
293031 
 
01020304
05060708091011
12131415161718
19202122232425
262728 
 
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
010203
04050607080910
11121314151617
18192021222324
252627282930
 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
01020304
05060708091011
12131415161718
19202122232425
2627282930 
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 

Applicable years

Gregorian calendar

In the (currently used) Gregorian calendar, along with Sunday, Wednesday, Friday or Saturday, 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 only spans 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
22nd century 2103 2114 2125 2131 2142 2153 2159 2170 2181 2187 2198
23rd century 2210 2221 2227 2238 2249 2255 2266 2277 2283 2294 2300
24th century 2306 2317 2323 2334 2345 2351 2362 2373 2379 2390

400 year cycle (add any multiple of 400 to a number in the following list to get a year with this calendar.)

century 1: 1, 7, 18, 29, 35, 46, 57, 63, 74, 85, 91

century 2: 103, 114, 125, 131, 142, 153, 159, 170, 181, 187, 198

century 3: 210, 221, 227, 238, 249, 255, 266, 277, 283, 294, 300

century 4: 306, 317, 323, 334, 345, 351, 362, 373, 379, 390

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.

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

Week Time unit equal to seven days

A week is a time unit equal to seven days. It is the standard time period used for cycles of rest days in most parts of the world, mostly alongside—although not strictly part of—the Gregorian calendar.

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, 2007, 2018 and 2029 in the obsolete Julian calendar, see below for more.

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. 2021, the current year, is a common year starting on a Friday in the Gregorian calendar. The last such year was 2010 and the next such year will be 2027 in the Gregorian calendar, or, likewise, 2005, 2011 and 2022 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 100 when divided by 400. The most recent such year was 1700 and the next one will be 2100.

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.

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. The most recent year of such kind was 2012 and the next one will be 2040 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 most recent year of such kind was 2019 and the next one will be 2030, or, likewise, 2014 and 2025 in the obsolete Julian calendar, see below for more.

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. The most recent year of such kind was 1996 and the next one will be 2024 in the Gregorian calendar or, likewise, 2008, and 2036 in the obsolete Julian calendar.

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 Gregorian calendar or, likewise, 2009, 2015 and 2026 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 200 when divided by 400. The most recent such year was 1800 and the next one will be 2200.

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. The most recent year of such kind was 2008 and the next one will be 2036 in the Gregorian calendar or, likewise 2020 and 2048 in the obsolete Julian calendar.

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, 2006, 2017 and 2023 in the obsolete Julian calendar. See below for more.

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.

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. The most recent year of such kind was 2000 and the next one will be 2028 in the Gregorian calendar or, likewise, 2012 and 2040 in the obsolescent Julian calendar. In the Gregorian calendar, years divisible by 400 are always leap years starting on Saturday. The most recent such year was 2000 and the next one 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. The most recent year of such kind was 2016 and the next one will be 2044 in the Gregorian calendar or, likewise, 2000 and 2028 in the obsolete Julian calendar.

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. The most recent year of such kind was 2004 and the next one will be 2032 in the Gregorian calendar or, likewise, 2016 and 2044 in the obsolete Julian calendar.

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. The most recent year of such kind was 2020 and the next one will be 2048, or likewise, 2004 and 2032 in the obsolete Julian calendar, see below for more.

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 algorithm for mental calculation was devised by John Conway in 1973, drawing inspiration from Lewis Carroll's perpetual calendar algorithm. It takes advantage of each year having a certain day of the week upon which certain easy-to-remember dates, called the doomsdays, fall; for example, the last day of February, 4/4, 6/6, 8/8, 10/10, and 12/12 all occur on the same day of the week in any year. Applying the Doomsday algorithm involves three steps: Determination of the anchor day for the century, calculation of the anchor day for the year from the one for the century, and selection of the closest date out of those that always fall on the doomsday, e.g., 4/4 and 6/6, and count of the number of days between that date and the date in question to arrive at the day of the week. The technique applies to both the Gregorian calendar and the Julian calendar, although their doomsdays are usually different days of the week.

The solar cycle is a 28-year cycle of the Julian calendar, and 400-year cycle of the Gregorian 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.

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.

The Gregorian calendar is the calendar used in most of the world. It was introduced in October 1582 by Pope Gregory XIII as a minor modification of the Julian calendar, reducing the average year from 365.25 days to 365.2425 days, and adjusting for the drift in the 'tropical' or 'solar' year that the inaccuracy had caused during the intervening centuries.

References

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