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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 Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF. The current year, 2024, is a leap year starting on Monday in the Gregorian calendar. The last such year was 1996 and the next such year will be 2052 in the Gregorian calendar[1] or, likewise, 2008 and 2036 in the obsolete Julian calendar. 29 February falls on Thursday.
Additionally, this type of year has three months (January, April, and July) beginning exactly on the first day of the week, in areas which Monday is considered the first day of the week, Common years starting on Friday share this characteristic on the months of February, March, and November.
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What is a Leap Year?
What Is a Leap Year?
Why Do We Have Leap Years?
Why Do We Have LEAP YEARS? | What Is A LEAP YEAR? | The Dr Binocs Show | Peekaboo Kidz
53 Sundays , 52 Sundays , 53 Mondays - How to find the Probability of Leap and Non Leap year??
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 Monday, 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
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
February
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
20
21
22
23
24
25
26
27
28
29
March
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
20
21
22
23
24
25
26
27
28
29
30
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
20
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
14
15
16
17
18
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
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
July
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
20
21
22
23
24
25
26
27
28
29
30
31
August
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
20
21
22
23
24
25
26
27
28
29
30
31
September
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
20
21
22
23
24
25
26
27
28
29
30
October
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
20
21
22
23
24
25
26
27
28
29
30
31
November
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
20
21
22
23
24
25
26
27
28
29
30
December
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
20
21
22
23
24
25
26
27
28
29
30
31
ISO 8601-conformant calendar with week numbers for any leap year starting on Monday (dominical letter GF)
January
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
February
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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 starting on Saturday and Thursday, 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).
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).
Daylight saving ends on its latest possible date, April 7 – the period of daylight saving which ends on April 7 of a leap year starting on Monday is the only period ending in any year to last 27 weeks in Australia and 28 weeks in New Zealand; in all other instances, the period of daylight saving lasts only 26 weeks in Australia and 27 weeks in New Zealand
Columbus Day falls on its latest possible date, October 14 (this is the only year when Martin Luther King Jr. Day and Columbus Day are 39 weeks apart) They are 38 weeks apart in all other years
Thanksgiving Day falls on its latest possible date, November 28 (this is also the only year when Martin Luther King Jr. Day and Thanksgiving are 318 days apart) They are 311 days apart in all other years