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This is the only type of year in which all dates (except 29 February) fall on their respective weekdays the minimal 56 times in the 400 year Gregorian Calendar cycle. Additionally, these types of years are the only ones which contain 54 different calendar weeks (2 partial, 52 in full) in areas of the world where Sunday is considered the first day of the week, and also the only type of year to contain 53 full weekends.
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What is a Leap Year?
Seconds/Minutes/Hours/Days/Weeks/Month/Year
Leap Year and finding number of Days during Leap Years
How to use "a leap year" in a sentence - "a leap year" sentence examples with pronunciation
Why Is There a Leap Day Every Four Years?
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 Saturday, 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 Saturday (dominical letter BA)
January
Wk
Mo
Tu
We
Th
Fr
Sa
Su
52
01
02
01
03
04
05
06
07
08
09
02
10
11
12
13
14
15
16
03
17
18
19
20
21
22
23
04
24
25
26
27
28
29
30
05
31
February
Wk
Mo
Tu
We
Th
Fr
Sa
Su
05
01
02
03
04
05
06
06
07
08
09
10
11
12
13
07
14
15
16
17
18
19
20
08
21
22
23
24
25
26
27
09
28
29
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
09
01
02
03
04
05
10
06
07
08
09
10
11
12
11
13
14
15
16
17
18
19
12
20
21
22
23
24
25
26
13
27
28
29
30
31
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
13
01
02
14
03
04
05
06
07
08
09
15
10
11
12
13
14
15
16
16
17
18
19
20
21
22
23
17
24
25
26
27
28
29
30
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
18
01
02
03
04
05
06
07
19
08
09
10
11
12
13
14
20
15
16
17
18
19
20
21
21
22
23
24
25
26
27
28
22
29
30
31
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
22
01
02
03
04
23
05
06
07
08
09
10
11
24
12
13
14
15
16
17
18
25
19
20
21
22
23
24
25
26
26
27
28
29
30
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
26
01
02
27
03
04
05
06
07
08
09
28
10
11
12
13
14
15
16
29
17
18
19
20
21
22
23
30
24
25
26
27
28
29
30
31
31
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
31
01
02
03
04
05
06
32
07
08
09
10
11
12
13
33
14
15
16
17
18
19
20
34
21
22
23
24
25
26
27
35
28
29
30
31
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
35
01
02
03
36
04
05
06
07
08
09
10
37
11
12
13
14
15
16
17
38
18
19
20
21
22
23
24
39
25
26
27
28
29
30
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
39
01
40
02
03
04
05
06
07
08
41
09
10
11
12
13
14
15
42
16
17
18
19
20
21
22
43
23
24
25
26
27
28
29
44
30
31
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
44
01
02
03
04
05
45
06
07
08
09
10
11
12
46
13
14
15
16
17
18
19
47
20
21
22
23
24
25
26
48
27
28
29
30
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
48
01
02
03
49
04
05
06
07
08
09
10
50
11
12
13
14
15
16
17
51
18
19
20
21
22
23
24
52
25
26
27
28
29
30
31
Applicable years
Gregorian Calendar
Leap years that begin on Saturday, along with those starting on Monday 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 Saturday 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).