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A leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC. The most recent year of such kind was 2004 and the next one will be 2032 in the Gregorian calendar[1] or, likewise, 2016 and 2044 in the obsolete Julian calendar.
This is the only year in which February has five Sundays, as the leap day adds that extra Sunday.
This is the only leap year with three occurrences of Tuesday the 13th: those three in this leap year occur three months (13 weeks) apart: in January, April, and July. Common years starting on Monday share this characteristic, in the months of February, March, and November.
Along with it's common year counterpart, the gap between July of this year until the next common year (14 months) is the longest time between Tuesday the 13th's, so from July of this year until September of the next year, as in 2004-05 or 2032-33 for example. This also applies for common years starting on Friday, unless the next leap year falls on a Saturday, in this case, the gap is reduced to only 11 months, as in 2027-28 for example.
If this year occurs, the leap day falls on a Sunday (similar to its common year equivalent), transitioning it from what it would appear to be a common year starting on Thursday to the next common year after the previous one, so March 1 would start on a Monday, like it would be on its common year equivalent (March to December of this type of year aligns with the common year equivalent, that should've happened 5 years earlier in order for this type of leap year to start due to the cyclical nature of the calendar.) The previous leap year would have to have been on a Saturday due to the Gregorian Calendar's cyclical nature.
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What is a Leap Year?
Seconds/Minutes/Hours/Days/Weeks/Month/Year
Why Is There a Leap Day Every Four Years?
Leap Year and finding number of Days during Leap Years
If the 1st January of a certain year, which was not a leap year, was a Thursday, then what day o...
Transcription
A calendar year is made of three hundred and
sixty five days -- a number that refuses to
be divide nicely, which is why we end up with
uneven months of either 30 or 31 days. Except
for February -- the runt of the litter -- which
only gets 28... except when it gets 29 and
then the year is 366 days long.
Why does that happen? What kind of crazy universe
do we live in where some years are longer
than others?
To answer this we need to know: just what
is a year?
Way oversimplifying it: a year is the time
it takes Earth to make one trip around the
sun. This happens to line up with the cycle
of the seasons.
Now, drawing a little diagram like this showing
the Earth jauntily going around the sun is
easy to do, but accurately tracking a year
is tricky when you're on Earth because the
universe doesn't provide an overhead map.
On Earth you only get to see the seasons change
and the obvious way to keep track of their
comings and goings is to count the days passing
which gives you a 365 day calendar.
But as soon as you start to use that calendar,
it slowly gets out of sync with the seasons.
And with each passing year the gap gets bigger
and bigger and bigger.
In three decades the calendar will be off
by a week and in a few hundred years the seasons
would be flipped -- meaning Christmas celebrations
taking place in summer -- which would be crazy.
Why does this happen? Did we count the days
wrong? Well the calendar predicts that the
time it takes for the Earth to go around the
sun is 8,760 hours. But, if you actually timed
it with a stopwatch you'd see that a year
is really longer than the calendar predicts
by almost six hours. So our calendar is moving
ever-so-slightly faster than the seasons actually
change.
And thus we come to the fundamental problem
of all calendars: the day/night cycle, while
easy to count, has nothing to do with the
yearly cycle.
Day and night are caused by Earth rotating
about its axis. When you're on the side faceing
the sun, it's daytime and when you're on the
other side it's night. But this rotation is
no more connected to the orbital motion around
the sun than a ballerina spinning on the back
of a truck is connected to the truck's crusing
speed.
Counting the number of ballerina turns to
predict how long the truck takes to dive in
a circle might give you a rough idea, but
it's crazy to expect it to be precise.
Counting the days to track the orbit is pretty
much the same thing and so it shouldn't be
a surprise when the Earth dosen't happen to
make exactly 365 complete spins in a year.
Irritatingly, while 365 days are too few 366
days are too many and still cause the seasons
to drift out of sync, just in the opposite
way.
The solution to all this is the leap year:
where February gets an extra day, but only
every four years.
This works pretty well, as each year the calendar
is about a quarter day short, so after four
years you add an extra day to get back in
alignment.
Huzzah! The problem has been solved.
Except, it hasn't.
Lengthening the calendar by one day every
four years is slightly too much, and the calendar
still falls behind the seasons at the rate
of one day per hundred years.
Which is fine for the apathetic, but not for
calendar designers who want everything to
line up perfectly.
To fix the irregularity, every century the
leap year is skipped.
So 1896 and 1904 were leap years but 1900
wasn't.
This is better, but still leaves the calendar
ever-so-slightly too fast with an error of
1 day in 400 years.
So an additional clause is added to the skip
the centuries rule that if the century is
divisible by 400, then it will be a leap year.
So 1900 and 2100 aren't leap years, but 2000
is.
With these three rules, the error is now just
one day off in almost eight thousand years
which the current calendar declares 'mission
accomplished' and so calls it a day.
Which is probably quite reasonable because
eight thousand years ago humans were just
figuring out that farming might be a good
idea and eight thousand years from now we'll
be hopefully be using a calendar with a better
date tracking system.
But perhaps you're a mathematician and a 0.0001
percent error is an abomination in your eyes
and must be removed.
"Tough luck" says The Universe because the
length of a day isn't even constant. It randomly
varies by a few milliseconds and on average
and very slowly decreases by about 1 millisecond
per hundred years. Which means it's literally
impossible to build a perfect calendar that
lasts forever.
In theory the length of a day will expand
to be as long as a curent month -- but don't
worry in practice it will take tens of billions
of years, and our own expanding sun will destroy
the earth long before that happens.
Sorry, not quite sure how we got from counting
the days of the months to the fiery unavoidable
end of all human civilization -- unless of
course we have an adequately funded space
program (hint, hint) -- but there you have
it.
For the next eight millennia Leap years will
keep the calendar in sync with the seasons
but in a surprisingly complicated way.
You can learn a lot more about orbits, different
kinds of years and supermassive black holes
and over at Minute Physics. As always, Henry
does a great job of explaining it all in his
new video. Check it out.�
Calendars
Calendar for any leap year starting on Thursday, 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
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13
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21
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23
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25
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29
30
31
February
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
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05
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09
10
11
12
13
14
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16
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18
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20
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22
23
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29
March
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
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08
09
10
11
12
13
14
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16
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25
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27
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29
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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
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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
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15
16
17
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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
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16
17
18
19
20
21
22
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24
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28
29
30
July
Su
Mo
Tu
We
Th
Fr
Sa
01
02
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04
05
06
07
08
09
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11
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29
30
31
August
Su
Mo
Tu
We
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Sa
01
02
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10
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12
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September
Su
Mo
Tu
We
Th
Fr
Sa
01
02
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04
05
06
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08
09
10
11
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October
Su
Mo
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Sa
01
02
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06
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November
Su
Mo
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We
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Sa
01
02
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05
06
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December
Su
Mo
Tu
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Sa
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31
ISO 8601-conformant calendar with week numbers for any leap year starting on Thursday (dominical letter DC)
January
Wk
Mo
Tu
We
Th
Fr
Sa
Su
01
01
02
03
04
02
05
06
07
08
09
10
11
03
12
13
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17
18
04
19
20
21
22
23
24
25
05
26
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28
29
30
31
February
Wk
Mo
Tu
We
Th
Fr
Sa
Su
05
01
06
02
03
04
05
06
07
08
07
09
10
11
12
13
14
15
08
16
17
18
19
20
21
22
09
23
24
25
26
27
28
29
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
10
01
02
03
04
05
06
07
11
08
09
10
11
12
13
14
12
15
16
17
18
19
20
21
13
22
23
24
25
26
27
28
14
29
30
31
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
14
01
02
03
04
15
05
06
07
08
09
10
11
16
12
13
14
15
16
17
18
17
19
20
21
22
23
24
25
18
26
27
28
29
30
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
18
01
02
19
03
04
05
06
07
08
09
20
10
11
12
13
14
15
16
21
17
18
19
20
21
22
23
22
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25
26
27
28
29
30
23
31
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
23
01
02
03
04
05
06
24
07
08
09
10
11
12
13
25
14
15
16
17
18
19
20
26
21
22
23
24
25
26
27
27
28
29
30
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
27
01
02
03
04
28
05
06
07
08
09
10
11
29
12
13
14
15
16
17
18
30
19
20
21
22
23
24
25
31
26
27
28
29
30
31
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
31
01
32
02
03
04
05
06
07
08
33
09
10
11
12
13
14
15
34
16
17
18
19
20
21
22
35
23
24
25
26
27
28
29
36
30
31
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
36
01
02
03
04
05
37
06
07
08
09
10
11
12
38
13
14
15
16
17
18
19
39
20
21
22
23
24
25
26
40
27
28
29
30
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
40
01
02
03
41
04
05
06
07
08
09
10
42
11
12
13
14
15
16
17
43
18
19
20
21
22
23
24
44
25
26
27
28
29
30
31
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
45
01
02
03
04
05
06
07
46
08
09
10
11
12
13
14
47
15
16
17
18
19
20
21
48
22
23
24
25
26
27
28
49
29
30
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
49
01
02
03
04
05
50
06
07
08
09
10
11
12
51
13
14
15
16
17
18
19
52
20
21
22
23
24
25
26
53
27
28
29
30
31
Applicable years
Gregorian Calendar
Leap years that begin on Thursday, along with those starting on Monday and Saturday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).
For this kind of year, the corresponding ISO year has 53 weeks, and the ISO week 10 (which begins March 1) and all subsequent ISO weeks occur earlier than in all other years, and exactly one week earlier than common years starting on Friday, for example, June 20 falls on week 24 in common years starting on Friday, but on week 25 in leap years starting on Thursday, despite falling on Sunday in both types of year. That means that moveable holidays may occur one calendar week later than otherwise possible, e.g. Gregorian Easter Sunday in week 17 in years when it falls on April 25 and which are also leap years, falling on week 16 in common years.[2]
Like all leap year types, the one starting with 1 January on a Thursday 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).
Orangeman's Day falls on a Monday. This is the only year when Orangeman’s Day falls in ISO week 29. They fall in ISO week 28 in all other years
Daylight saving ends on its latest possible date, October 31. This is the only year when Daylight Saving Time ends in ISO week 44. They end in ISO week 43 in all other years
Daylight saving begins on its latest possible date, March 14. This is the only year when Daylight Saving Time begins in ISO week 11. They begin in ISO week 10 in all other years.
Victoria Day falls on its latest possible date, May 24. This is the only year when Victoria Day falls in ISO week 22. They fall in ISO week 21 in all other years. This is also the only year when Labour Day that precedes this type of year to Victoria Day in this type of year are 38 weeks apart. They are 37 weeks apart in all other years. This is also the only year when Father’s Day that precedes this type of year to Victoria Day in this type of year are 344 days apart. They are 337 days apart in all other years.
Daylight saving ends on its latest possible date, November 7. This is the only year when Daylight Saving Time ends in ISO week 45. They end in ISO week 44 in all other years.
Daylight saving begins on its latest possible date, March 14. This is the only year when Daylight Saving Time begins in ISO week 11. They begin in ISO week 10 in all other years. This is also the only type of year where Labor Day that precedes this type of year to start of Daylight Saving Time is 195 days apart. They are 188 days apart in all other years. This is also the only type of year where Grandparent’s Day that precedes this type of year to start of Daylight Saving Time is 27 weeks apart. They are 26 weeks apart in all other years. This is also the only type of year where Father’s Day that precedes this type of year to start of Daylight Saving Time is 39 weeks apart. They are 38 weeks apart in all other years.
Memorial Day falls on its latest possible date, May 31. This is the only year when Memorial Day falls in ISO week 23. They fall in ISO week 22 in all other years. This is also the only type of year where Labor Day that precedes this type of year to Memorial Day in this type of year are 39 weeks apart. They are 38 weeks apart in all other years. This is also the only type of year where Grandparent’s Day that precedes this type of year to Memorial Day in this type of year are 267 days apart. They are 260 days apart in all other years. This is also the only type of year where Father’s Day that precedes this type of year to Memorial Day in this type of year is 351 days apart. They are 344 days apart in all other years.
Election Day falls on its earliest possible date, November 2. This is the only leap year to have Election Day fall during Daylight Saving Time.
Daylight saving ends on its latest possible date, November 7. This is the only year when Daylight Saving Time ends in ISO week 45. They end in ISO week 44 in all other years
This page was last edited on 14 April 2024, at 00:51