Leap year starting on Tuesday

Last updated

A leap year starting on Tuesday is any year with 366 days (i.e. it includes 29 February) 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 [1] or, likewise 2020 and 2048 in the obsolete Julian calendar.

Contents

Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; the only one in this leap year occurs in June. Common years starting on Wednesday share this characteristic.

From August of the common year preceding that year until October in this type of year is also the longest period (14 months) that occurs without a Friday the 17th, as in 2007-08 or 2035-36. Common years starting on Friday share this characteristic, from July of the year that precedes it to September in that type of year.

Calendars

Calendar for any leap 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
242526272829
 
March
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
April
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
27282930 
 
May
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
June
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
July
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
August
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
September
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
282930 
 
October
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
November
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
December
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
ISO 8601-conformant calendar with week numbers for
any leap year starting on Tuesday (dominical letter FE)
January
WkMoTuWeThFrSaSu
01010203040506
0207080910111213
0314151617181920
0421222324252627
0528293031 
  
February
WkMoTuWeThFrSaSu
05010203
0604050607080910
0711121314151617
0818192021222324
092526272829
  
March
WkMoTuWeThFrSaSu
090102
1003040506070809
1110111213141516
1217181920212223
1324252627282930
1431 
April
WkMoTuWeThFrSaSu
14010203040506
1507080910111213
1614151617181920
1721222324252627
18282930 
  
May
WkMoTuWeThFrSaSu
1801020304
1905060708091011
2012131415161718
2119202122232425
22262728293031 
  
June
WkMoTuWeThFrSaSu
2201
2302030405060708
2409101112131415
2516171819202122
2623242526272829
2730 
July
WkMoTuWeThFrSaSu
27010203040506
2807080910111213
2914151617181920
3021222324252627
3128293031 
  
August
WkMoTuWeThFrSaSu
31010203
3204050607080910
3311121314151617
3418192021222324
3525262728293031
  
September
WkMoTuWeThFrSaSu
3601020304050607
3708091011121314
3815161718192021
3922232425262728
402930 
  
October
WkMoTuWeThFrSaSu
400102030405
4106070809101112
4213141516171819
4320212223242526
442728293031 
  
November
WkMoTuWeThFrSaSu
440102
4503040506070809
4610111213141516
4717181920212223
4824252627282930
  
December
WkMoTuWeThFrSaSu
4901020304050607
5008091011121314
5115161718192021
5222232425262728
01293031 
  

Applicable years

Gregorian Calendar

Leap years that begin on Tuesday, along with those starting on Wednesday, occur at a rate of approximately 14.43% (14 out of 97) of all total leap years in a 400-year cycle of the Gregorian calendar. Thus, their overall occurrence is 3.5% (14 out of 400).

Gregorian leap years starting on Tuesday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
17th century 1608 1636 1664 1692
18th century 1704 1732 1760 1788
19th century 1828 1856 1884
20th century 1924 1952 1980
21st century 2008 2036 2064 2092
22nd century 2104 2132 2160 2188
23rd century 2228 2256 2284
24th century 2324 2352 2380
25th century 2408 2436 2464 2492
26th century 2504253225602588
400-year cycle
0–998366492
100–199104132160188
200–299228256284
300–399324352380

Julian Calendar

Like all leap year types, the one starting with 1 January on a Tuesday 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).

Julian leap years starting on Tuesday
Decade1st2nd3rd4th5th6th7th8th9th10th
14th century 1320 1348 1376
15th century 1404 1432 1460 1488
16th century 1516 1544 1572 1600
17th century 1628 1656 1684
18th century1712174017681796
19th century182418521880
20th century1908193619641992
21st century202020482076
22nd century2104213221602188

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States


Related Research Articles

<span class="mw-page-title-main">Week</span> Time unit equal to seven days

A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are often mapped against yearly calendars, but are typically not the basis for them, as weeks are not based on astronomy.

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 2023 and the next one will be 2034 in the Gregorian calendar, or, likewise, 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 most recent year of such kind was 2021 and the next one will be 2027 in the Gregorian calendar, or, likewise, 2022 and 2033 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, 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.

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 2024 and 2052 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 current year, 2024, is a leap year starting on Monday in the Gregorian calendar. The last such year was 1996 and the next such year will be 2052 in the Gregorian calendar or, likewise, 2008 and 2036 in the obsolete Julian calendar. 29 February falls on Thursday.

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, 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 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 2022 and the next one will be 2033 in the Gregorian calendar or, likewise, 2023 and 2034 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, 2021 and 2027 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 occurrence 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 in the Gregorian calendar, 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.

<span class="mw-page-title-main">Doomsday rule</span> Way of calculating the day of the week of a given date

The Doomsday rule, Doomsday algorithm or Doomsday method 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.

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.

<span class="mw-page-title-main">Fasting and abstinence of the Coptic Orthodox Church</span> Coptic Orthodox fasts

The Copts, who belong mostly to the Coptic Orthodox Church, observe fasting periods according to the Coptic calendar. In Coptic Orthodox Christianity, fasting is defined as going without water and food from midnight to sunset; after that time, the consumption of water and one vegetarian meal is permitted. The fasting periods of Coptic Christians are exceeded by no other Christian denomination except the Orthodox Tewahedo. Out of the 365 days of the year, Copts often fast between 210 and 240 days. This means that Copts abstain from all animal products for up to two-thirds of each year. Coptic Orthodox fasts have evolved over time to become more lengthy and severe. A lifestyle involving such fasts may have contributed to the pacifist mindset of the Coptic people for centuries. Married couples refrain from sexual relations during Lent "to give themselves time for fasting and prayer".

The modern Hebrew calendar has been designed to ensure that certain holy days and festivals do not fall on certain days of the week. As a result, there are only four possible patterns of days on which festivals can fall.

References

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