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, such as the years 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, and 2104 in the Gregorian calendar[1] or, likewise, 1964, 1992, and 2020 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this leap year occurs in June. Common years starting on Wednesday share this characteristic.
Contents
1 Calendars
2 Applicable years
2.1 Gregorian Calendar
2.2 Julian Calendar
3 References
Calendars
Calendar for any leap year starting on Tuesday, | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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ISO 8601-conformant calendar with week numbers for | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Applicable years
Gregorian Calendar
Leap years that begin on Tuesday, like those that start on Wednesday, occur at a rate of approximately 14.4% of all total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is 3.5% (14 out of 400).
| 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 | ||||||
| Year starts | Common years | Leap years | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 Jan | Count | Ratio | 31 Dec | DL | DD | Count | Ratio | 31 Dec | DL | DD | Count | Ratio | ||
Sun | 58 | 14.50 % | Sun | A | Tue | 43 | 10.75 % | Mon | AG | Wed | 15 | 03.75 % | ||
Sat | 56 | 14.00 % | Sat | B | Mon | 43 | 10.75 % | Sun | BA | Tue | 13 | 03.25 % | ||
Fri | 58 | 14.50 % | Fri | C | Sun | 43 | 10.75 % | Sat | CB | Mon | 15 | 03.75 % | ||
Thu | 57 | 14.25 % | Thu | D | Sat | 44 | 11.00 % | Fri | DC | Sun | 13 | 03.25 % | ||
Wed | 57 | 14.25 % | Wed | E | Fri | 43 | 10.75 % | Thu | ED | Sat | 14 | 03.50 % | ||
Tue | 58 | 14.50 % | Tue | F | Thu | 44 | 11.00 % | Wed | FE | Fri | 14 | 03.50 % | ||
Mon | 56 | 14.00 % | Mon | G | Wed | 43 | 10.75 % | Tue | GF | Thu | 13 | 03.25 % | ||
| ∑ | 400 | 100.0 % | 303 | 75.75 % | 97 | 24.25 % | ||||||||
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).
| 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 |
References
^ abc Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
