Common year starting on Tuesday

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A common year starting on Tuesday is any non-leap year (i.e. a year with 365 days) 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.

Contents

Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths: those two in this common year occur 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 (14 months) 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.

In this common year, Martin Luther King Jr. Day is on its latest possible date, January 21, Valentine's Day is on a Thursday, Presidents Day is on February 18, Saint Patrick's Day is on a Sunday, Memorial Day is on May 27, U.S. Independence Day and Halloween are on a Thursday, Labor Day is on September 2, Columbus Day is on its latest possible date, October 14, Election Day in the USA is on November 5th, Veterans Day is on a Monday, Thanksgiving is on its latest possible date, November 28, and Christmas is on a Wednesday.

Calendars

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

January
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
February
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
2425262728
 
March
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
April
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
282930 
 
May
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
June
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
July
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
August
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
September
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
October
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
November
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
December
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 

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

January
WkMoTuWeThFrSaSu
01010203040506
0207080910111213
0314151617181920
0421222324252627
0528293031 
  
February
WkMoTuWeThFrSaSu
05010203
0604050607080910
0711121314151617
0818192021222324
0925262728
  
March
WkMoTuWeThFrSaSu
09010203
1004050607080910
1111121314151617
1218192021222324
1325262728293031
  
April
WkMoTuWeThFrSaSu
1401020304050607
1508091011121314
1615161718192021
1722232425262728
182930 
  
May
WkMoTuWeThFrSaSu
180102030405
1906070809101112
2013141516171819
2120212223242526
222728293031 
  
June
WkMoTuWeThFrSaSu
220102
2303040506070809
2410111213141516
2517181920212223
2624252627282930
  
July
WkMoTuWeThFrSaSu
2701020304050607
2808091011121314
2915161718192021
3022232425262728
31293031 
  
August
WkMoTuWeThFrSaSu
3101020304
3205060708091011
3312131415161718
3419202122232425
35262728293031 
  
September
WkMoTuWeThFrSaSu
3501
3602030405060708
3709101112131415
3816171819202122
3923242526272829
4030 
October
WkMoTuWeThFrSaSu
40010203040506
4107080910111213
4214151617181920
4321222324252627
4428293031 
  
November
WkMoTuWeThFrSaSu
44010203
4504050607080910
4611121314151617
4718192021222324
48252627282930
  
December
WkMoTuWeThFrSaSu
4801
4902030405060708
5009101112131415
5116171819202122
5223242526272829
013031 

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, along with Thursday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Tuesday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Tuesday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
17th century 1602 1613 1619 1630 1641 1647 1658 1669 1675 1686 1697
18th century 1709 1715 1726 1737 1743 1754 1765 1771 1782 1793 1799
19th century 1805 1811 1822 1833 1839 1850 1861 1867 1878 1889 1895
20th century 1901 1907 1918 1929 1935 1946 1957 1963 1974 1985 1991
21st century 2002 2013 2019 2030 2041 2047 2058 2069 2075 2086 2097
22nd century 2109 2115 2126 2137 2143 2154 2165 2171 2182 2193 2199
23rd century 2205 2211 2222 2233 2239 2250 2261 2367 2278 2289 2295
24th century 2301 2307 2318 2329 2335 2346 2357 2363 2374 2385 2391

400 year cycle

century 1: 2, 13, 19, 30, 41, 47, 58, 69, 75, 86, 97

century 2: 109, 115, 126, 137, 143, 154, 165, 171, 182, 193, 199

century 3: 205, 211, 222, 233, 239, 250, 261, 267, 278, 289, 295

century 4: 301, 307, 318, 329, 335, 346, 357, 363, 374, 385, 391

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 in the Church of England as 29 February has no letter). Each of the seven two-letter sequences occurs 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 7, 18 and 24 of the cycle are common years beginning on Tuesday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Tuesday.

Julian common years starting on Tuesday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1409 1415 1426 1437 1443 1454 1465 1471 1482 1493 1499
16th century 1510 1521 1527 1538 1549 1555 1566 1577 15831594
17th century16051611162216331639165016611667167816891695
18th century1706171717231734174517511762177317791790
19th century18011807181818291835184618571863187418851891
20th century19021913191919301941194719581969197519861997
21st century20032014202520312042205320592070208120872098

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, 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. The current year, 2021, is a common year starting on 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.

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, 2019 and 2030 in the 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.

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.

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 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. Most recently this occurred in 2000; the next such occurrence 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.

Zimmer tower

The Zimmer tower is a tower in Lier, Belgium, also known as the Cornelius tower, that was originally a keep of Lier's 14th-century city fortifications. In 1930, astronomer and clockmaker Louis Zimmer (1888–1970) built the Jubilee Clock, which is displayed on the front of the tower, and consists of 12 clocks encircling a central one with 57 dials. These clocks showed time on all continents, phases of the moons, times of tides and many other periodic phenomena.

A century leap year is a leap year in the Gregorian calendar that is evenly divisible by 400.

References

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