Leap year starting on Tuesday

From Wikipedia, the free encyclopedia

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 letter hence is FE, such as the years 1952, 1980, 2008, 2036, 2064, 2092, and 2104 in the Gregorian calendar[1] or, likewise, 1992 and 2020 in the obsolete Julian calendar.

Calendars

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

01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31  
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29
 
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31  
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30  
 
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
 
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30  
 
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31  
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30  
 
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31  
 
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30  
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 


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

01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30  
 
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31  
 
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29
 
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31  
 
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30  
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30  
 
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31  
 

Applicable years

Gregorian Calendar

Leap years that begin on Tuesday occur at a rate of approximately 14.4% (14 out of 97) of all total leap years in a 400 year cycle. Their overall occurrence is thus 3.5% (14 out of 400).

Gregorian leap years starting on Tuesday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
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

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.

Sequence of year types in the Julian calendar
Year 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
DL G F E DC B* A G FE D C B AG F E D CB A G F ED C B A GF E D C BA
1 Jan Mo Tu We Th Sa Su Mo Tu Th Fr Sa Su Tu We Th Fr Su Mo Tu We Fr Sa Su Mo We Th Fr Sa
31 Dec Fr We Mo Sa Th Tu Su

The final two digits of Julian years repeat after 700 years, i.e. 25 cycles.

Julian leap years starting on Tuesday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1404 1432 1460 1488
16th century 1516 1544 1572 1600
17th century 1628 1656 1684
18th century 1712 1740 1768 1796
19th century 1824 1852 1880
20th century 1908 1936 1964 1992
21st century 2020 2048 2076
22nd century 2104 2132 2160 2188

References

  1. ^ a b Robert van Gent (2005). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. 
  2. ^ Robert H. van Gent (2005). "Mathematics of the ISO calendar". Department of Mathematics at Utrecht University. 
Retrieved from "https://en.wikipedia.org/w/index.php?title=Leap_year_starting_on_Tuesday&oldid=756858925"
This content was retrieved from Wikipedia : http://en.wikipedia.org/wiki/Leap_year_starting_on_Tuesday
This page is based on the copyrighted Wikipedia article "Leap year starting on Tuesday"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA