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| A '''leap year starting on Monday''' is any year with 366 days (i.e. it includes 29 February) that begins on ], 1 January, and ends on ], 31 December. Its ]s hence are '''GF''', such as the years ], ], ], ], ], ], ], and ] in the ]<ref name="math">{{cite web|url=http://www.staff.science.uu.nl/~gent0113/calendar/isocalendar.htm |author=Robert van Gent |title=The Mathematics of the ISO 8601 Calendar |publisher=Utrecht University, Department of Mathematics |date=2017 |accessdate=20 July 2017}}</ref> or, likewise, ] and ] in the obsolete ]. | |||
| Any leap year that starts on ], ] or ] has two Friday the 13ths. Like ], this leap year contains two Friday the 13ths in ] and ]. | |||
| == Calendars == | |||
| {{calendar|year=2024|show_year=off|title=Calendar for any ] starting on Monday,<br />presented as common in many English-speaking areas}} | |||
| {{calendar|year=2024|show_year=off|format=iso|row=3|zero=0|title=]-conformant calendar with ] for<br />any leap year starting on Monday (dominical letter GF)}} | |||
| == Applicable years == | |||
| === Gregorian Calendar === | |||
| Leap years that begin on Monday, along with those that start on ], occur least frequently: 13 out of 97 (≈ 13.4%) total leap years in a 400-year cycle of the ]. Their overall occurrence is thus 3.25% (13 out of 400). | |||
| {| class="wikitable" | |||
| |+ Gregorian leap years starting on Monday<ref name=math/> | |||
| !scope=row| Decade | |||
| ! 1st !! 2nd !! 3rd !! 4th !! 5th !! 6th !! 7th !! 8th !! 9th !! 10th | |||
| |- style="opacity: 0.5;" | |||
| ! style="background-color:#efefef;" | ] | |||
| | || || ] || || || ] || || ] || || | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || ] || || || ] || || || ] || || | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || ] || || || ] || || || ] || || | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || ] || || ] || || || ] || || || ] | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || || ] || || || ] || || ] || || | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || ] || || || ] || || || ] || || | |||
| |} | |||
| {{List of calendars}} | |||
| === Julian Calendar === | |||
| Like all leap year types, the one starting with 1 January on a Monday occurs exactly once in a ] 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). | |||
| {| class="wikitable" | |||
| |+ Julian leap years starting on Monday | |||
| !scope=row| Decade | |||
| ! 1st !! 2nd !! 3rd !! 4th !! 5th !! 6th !! 7th !! 8th !! 9th !! 10th | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || ] || || || ] || || || ] || || | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | ] || || || ] || || ] || || || ] || | |||
| |- | |||
| ! style="background-color:#efefef;" | ] | |||
| | || ] || || || ] || || || ] || || ] | |||
| |- | |||
| ! style="background-color:#efefef;" | 18th century | |||
| | || || 1728 || || || 1756 || || || 1784 || | |||
| |- | |||
| ! style="background-color:#efefef;" | 19th century | |||
| | || 1812 || || 1840 || || || 1868 || || || 1896 | |||
| |- | |||
| ! style="background-color:#efefef;" | 20th century | |||
| | || || 1924 || || || 1952 || || 1980 || || | |||
| |- | |||
| ! style="background-color:#efefef;" | 21st century | |||
| | 2008 || || || 2036 || || || 2064 || || || 2092 | |||
| |- | |||
| ! style="background-color:#efefef;" | 22nd century | |||
| | || 2120 || || || 2148 || || || 2176 || || | |||
| |} | |||
| ==References== | |||
| {{reflist}} | |||
| {{DEFAULTSORT:Leap Year Starting On Monday}} | |||
| ] | |||
| ] | |||
| ] | |||