Leap year starting on Monday: Difference between revisions

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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 ].		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. This leap year contains two Friday the 13ths in ] and ]. ] share this characteristic.		Any leap year that starts on ], ] or ] has two Friday the 13ths. This leap year contains two Friday the 13ths in ] and ]. ] share this characteristic.

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Revision as of 02:18, 12 February 2018

A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF, such as the years 1912, 1940, 1968, 1996, 2013, 2024, 2052, 2080, and 2120 in the Gregorian calendar or, likewise, 2008 and 2036 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in September and December. Common years starting on Tuesday share this characteristic.

Calendars

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

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

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	January
01	01	02	03	04	05	06	07
02	08	09	10	11	12	13	14
03	15	16	17	18	19	20	21
04	22	23	24	25	26	27	28
05	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	February
05				01	02	03	04
06	05	06	07	08	09	10	11
07	12	13	14	15	16	17	18
08	19	20	21	22	23	24	25
09	26	27	28	29

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	March
09					01	02	03
10	04	05	06	07	08	09	10
11	11	12	13	14	15	16	17
12	18	19	20	21	22	23	24
13	25	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	April
14	01	02	03	04	05	06	07
15	08	09	10	11	12	13	14
16	15	16	17	18	19	20	21
17	22	23	24	25	26	27	28
18	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	May
18			01	02	03	04	05
19	06	07	08	09	10	11	12
20	13	14	15	16	17	18	19
21	20	21	22	23	24	25	26
22	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	June
22						01	02
23	03	04	05	06	07	08	09
24	10	11	12	13	14	15	16
25	17	18	19	20	21	22	23
26	24	25	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	July
27	01	02	03	04	05	06	07
28	08	09	10	11	12	13	14
29	15	16	17	18	19	20	21
30	22	23	24	25	26	27	28
31	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	August
31				01	02	03	04
32	05	06	07	08	09	10	11
33	12	13	14	15	16	17	18
34	19	20	21	22	23	24	25
35	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	September
35							01
36	02	03	04	05	06	07	08
37	09	10	11	12	13	14	15
38	16	17	18	19	20	21	22
39	23	24	25	26	27	28	29
40	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	October
40		01	02	03	04	05	06
41	07	08	09	10	11	12	13
42	14	15	16	17	18	19	20
43	21	22	23	24	25	26	27
44	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	November
44					01	02	03
45	04	05	06	07	08	09	10
46	11	12	13	14	15	16	17
47	18	19	20	21	22	23	24
48	25	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	December
48							01
49	02	03	04	05	06	07	08
50	09	10	11	12	13	14	15
51	16	17	18	19	20	21	22
52	23	24	25	26	27	28	29
01	30	31

Applicable years

Gregorian Calendar

Leap years that begin on Monday, along with those that start on Tuesday or Thursday, occur least frequently: 13 out of 97 (≈ 13.4%) total leap years of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400, with dominical letter FE).

Gregorian leap years starting on Monday
Decade	2nd	3rd	4th	5th	6th	7th	8th	10th
17th century		1624			1652		1680
18th century	1720			1748			1776
19th century	1816			1844			1872
20th century	1912		1940			1968		1996
21st century	2013	2024			2052		2080
22nd century	2120			2148			2176

Gregorian year types per leap cycle by Dominical letter (DL) and Doomsday (DD)

1 Jan	Count	Ratio	31 Dec	DL	DD	Count	Ratio	31 Dec	DL	DD	Count	Ratio
Year starts			Common years					Leap years
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 %

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

Julian Calendar

Like all leap year types, the one starting with 1 January on a Monday 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 Monday
Decade	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
15th century		1420			1448			1476
16th century	1504			1532		1560			1588
17th century		1616			1644			1672		1700
18th century			1728			1756			1784
19th century		1812		1840			1868			1896
20th century			1924			1952		1980
21st century	2008			2036			2064			2092
22nd century		2120			2148			2176

References

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

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