Leap year starting on Tuesday

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.

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.

In this leap 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, the leap day is on a Friday, Saint Patrick's Day is on Monday, Memorial day is on May 26, U.S. Independence Day and Halloween are on a Friday, Labor Day is on its earliest possible date, September 1, Thanksgiving in Canada and Columbus Day in the USA are on October 13, Armistice Day is on a Tuesday, Thanksgiving in the USA is on November 27, and Christmas is on a Thursday.

The Election Day in the USA is on November 4th, as well in common years starting on Wednesday.

CalendarsEdit

Calendar for any leap year starting on Tuesday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
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  
 
February
Su Mo Tu We Th Fr Sa
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
 
March
Su Mo Tu We Th Fr Sa
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  
April
Su Mo Tu We Th Fr Sa
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  
 
May
Su Mo Tu We Th Fr Sa
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
 
June
Su Mo Tu We Th Fr Sa
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  
 
July
Su Mo Tu We Th Fr Sa
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  
 
August
Su Mo Tu We Th Fr Sa
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  
September
Su Mo Tu We Th Fr Sa
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  
 
October
Su Mo Tu We Th Fr Sa
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  
 
November
Su Mo Tu We Th Fr Sa
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  
December
Su Mo Tu We Th Fr Sa
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)
January
Wk Mo Tu We Th Fr Sa Su
01 01 02 03 04 05 06
02 07 08 09 10 11 12 13
03 14 15 16 17 18 19 20
04 21 22 23 24 25 26 27
05 28 29 30 31  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01 02 03
06 04 05 06 07 08 09 10
07 11 12 13 14 15 16 17
08 18 19 20 21 22 23 24
09 25 26 27 28 29
   
March
Wk Mo Tu We Th Fr Sa Su
09 01 02
10 03 04 05 06 07 08 09
11 10 11 12 13 14 15 16
12 17 18 19 20 21 22 23
13 24 25 26 27 28 29 30
14 31  
April
Wk Mo Tu We Th Fr Sa Su
14 01 02 03 04 05 06
15 07 08 09 10 11 12 13
16 14 15 16 17 18 19 20
17 21 22 23 24 25 26 27
18 28 29 30  
   
May
Wk Mo Tu We Th Fr Sa Su
18 01 02 03 04
19 05 06 07 08 09 10 11
20 12 13 14 15 16 17 18
21 19 20 21 22 23 24 25
22 26 27 28 29 30 31  
   
June
Wk Mo Tu We Th Fr Sa Su
22 01
23 02 03 04 05 06 07 08
24 09 10 11 12 13 14 15
25 16 17 18 19 20 21 22
26 23 24 25 26 27 28 29
27 30  
July
Wk Mo Tu We Th Fr Sa Su
27 01 02 03 04 05 06
28 07 08 09 10 11 12 13
29 14 15 16 17 18 19 20
30 21 22 23 24 25 26 27
31 28 29 30 31  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01 02 03
32 04 05 06 07 08 09 10
33 11 12 13 14 15 16 17
34 18 19 20 21 22 23 24
35 25 26 27 28 29 30 31
   
September
Wk Mo Tu We Th Fr Sa Su
36 01 02 03 04 05 06 07
37 08 09 10 11 12 13 14
38 15 16 17 18 19 20 21
39 22 23 24 25 26 27 28
40 29 30  
   
October
Wk Mo Tu We Th Fr Sa Su
40 01 02 03 04 05
41 06 07 08 09 10 11 12
42 13 14 15 16 17 18 19
43 20 21 22 23 24 25 26
44 27 28 29 30 31  
   
November
Wk Mo Tu We Th Fr Sa Su
44 01 02
45 03 04 05 06 07 08 09
46 10 11 12 13 14 15 16
47 17 18 19 20 21 22 23
48 24 25 26 27 28 29 30
   
December
Wk Mo Tu We Th Fr Sa Su
49 01 02 03 04 05 06 07
50 08 09 10 11 12 13 14
51 15 16 17 18 19 20 21
52 22 23 24 25 26 27 28
01 29 30 31  
   

Applicable yearsEdit

Gregorian CalendarEdit

Leap years that begin on Tuesday, like those that start on Wednesday, occur at a rate of approximately 14.43% of all total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is 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

400 year cycle

century 1: 8, 36, 64, 92

century 2: 104, 132, 160, 188

century 3: 228, 256, 284

century 4: 324, 352, 380

Julian CalendarEdit

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
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
14th century 1320 1348 1376
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

ReferencesEdit

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