Common year starting on Monday

A common year starting on Monday is any non-leap year (i.e., a year with 365 days) that begins on Monday, 1 January, and ends on Monday, 31 December. Its dominical letter hence is G. The most recent year of such kind was 2018 and the next one will be 2029 in the Gregorian calendar, or likewise, 2013, 2019, and 2030 in the obsolete Julian calendar. The century year, 1900, was also a common year starting on Monday in the Gregorian calendar. See below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year of this type contains two Friday the 13ths in April and July. Leap years starting on Sunday share this characteristic, but also have another in January.

Calendars

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

January
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
February
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728
 
March
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
April
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
2930  
 
May
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
June
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
July
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
August
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
September
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
October
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
November
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
December
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  

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

January
Wk Mo Tu We Th Fr Sa Su
01 01020304050607
02 08091011121314
03 15161718192021
04 22232425262728
05 293031  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01020304
06 05060708091011
07 12131415161718
08 19202122232425
09 262728  
   
March
Wk Mo Tu We Th Fr Sa Su
09 01020304
10 05060708091011
11 12131415161718
12 19202122232425
13 262728293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 01
14 02030405060708
15 09101112131415
16 16171819202122
17 23242526272829
18 30  
May
Wk Mo Tu We Th Fr Sa Su
18 010203040506
19 07080910111213
20 14151617181920
21 21222324252627
22 28293031  
   
June
Wk Mo Tu We Th Fr Sa Su
22 010203
23 04050607080910
24 11121314151617
25 18192021222324
26 252627282930
   
July
Wk Mo Tu We Th Fr Sa Su
26 01
27 02030405060708
28 09101112131415
29 16171819202122
30 23242526272829
31 3031  
August
Wk Mo Tu We Th Fr Sa Su
31 0102030405
32 06070809101112
33 13141516171819
34 20212223242526
35 2728293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 0102
36 03040506070809
37 10111213141516
38 17181920212223
39 24252627282930
   
October
Wk Mo Tu We Th Fr Sa Su
40 01020304050607
41 08091011121314
42 15161718192021
43 22232425262728
44 293031  
   
November
Wk Mo Tu We Th Fr Sa Su
44 01020304
45 05060708091011
46 12131415161718
47 19202122232425
48 2627282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 0102
49 03040506070809
50 10111213141516
51 17181920212223
52 24252627282930
01 31  

Applicable years

Gregorian calendar

In the (currently used) Gregorian calendar, along with Sunday, Wednesday, Friday or Saturday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Monday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Monday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic)1590—
17th century 16011607161816291635164616571663167416851691
18th century 17031714172517311742175317591770—178117871798
19th century 1810—1821182718381849185518661877188318941900
20th century 1906191719231934194519511962197319791990—
21st century 20012007201820292035204620572063207420852091
22nd century 21032114212521312142215321592170—218121872198

Julian calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters (one for January and February and the other for March to December, as 29 February has no letter). This sequence occurs exactly once within a cycle, and every common letter thrice.

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). Years 6, 12 and 23 of the cycle are common years beginning on Monday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Monday.

Julian common years starting on Monday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 14031414142514311442145314591470—148114871498
16th century 15091515152615371543155415651571158215931599
17th century 1610—162116271638164916551666167716831694
18th century 170517111722173317391750—17611767177817891795
19th century 1806181718231834184518511862187318791890—
20th century 19011907191819291935194619571963197419851991
21st century 2002201320192030—2041204720582069207520862097

References
  1. Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.