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This is the only common year with three occurrences of Friday the 13th: those three in this common year occur in February, March, and November. Leap years starting on Sunday share this characteristic, for the months January, April and July. From February until March in this type of year is also the shortest period (one month) that runs between two instances of Friday the 13th. Additionally, this is the one of only two types of years overall where a rectangular February is possible, in places where Sunday is considered to be the first day of the week. Common years starting on Friday share this characteristic, but only in places where Monday is considered to be the first day of the week.
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What is a Leap Year?
Why Do We Have LEAP YEARS? | What Is A LEAP YEAR? | The Dr Binocs Show | Peekaboo Kidz
Counting the Number of Wednesdays and Leap Year Struggle
What Is a Leap Year?
To check leap year in python programming ( python for beginners )
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 common 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
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
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 common year starting on Thursday (dominical letter D)
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
14
15
16
17
18
04
19
20
21
22
23
24
25
05
26
27
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
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
09
01
10
02
03
04
05
06
07
08
11
09
10
11
12
13
14
15
12
16
17
18
19
20
21
22
13
23
24
25
26
27
28
29
14
30
31
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
14
01
02
03
04
05
15
06
07
08
09
10
11
12
16
13
14
15
16
17
18
19
17
20
21
22
23
24
25
26
18
27
28
29
30
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
18
01
02
03
19
04
05
06
07
08
09
10
20
11
12
13
14
15
16
17
21
18
19
20
21
22
23
24
22
25
26
27
28
29
30
31
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
23
01
02
03
04
05
06
07
24
08
09
10
11
12
13
14
25
15
16
17
18
19
20
21
26
22
23
24
25
26
27
28
27
29
30
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
27
01
02
03
04
05
28
06
07
08
09
10
11
12
29
13
14
15
16
17
18
19
30
20
21
22
23
24
25
26
31
27
28
29
30
31
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
31
01
02
32
03
04
05
06
07
08
09
33
10
11
12
13
14
15
16
34
17
18
19
20
21
22
23
35
24
25
26
27
28
29
30
36
31
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
36
01
02
03
04
05
06
37
07
08
09
10
11
12
13
38
14
15
16
17
18
19
20
39
21
22
23
24
25
26
27
40
28
29
30
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
40
01
02
03
04
41
05
06
07
08
09
10
11
42
12
13
14
15
16
17
18
43
19
20
21
22
23
24
25
44
26
27
28
29
30
31
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
44
01
45
02
03
04
05
06
07
08
46
09
10
11
12
13
14
15
47
16
17
18
19
20
21
22
48
23
24
25
26
27
28
29
49
30
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
49
01
02
03
04
05
06
50
07
08
09
10
11
12
13
51
14
15
16
17
18
19
20
52
21
22
23
24
25
26
27
53
28
29
30
31
Applicable years
Gregorian Calendar
In the (currently used) Gregorian calendar, alongside Tuesday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Thursday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.
This type of year has 53 weeks in the week-day format of the ISO 8601 standard.
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 3, 14 and 20 of the cycle are common years beginning on Thursday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Thursday.
Labour Day falls on its latest possible date, September 7 – this is the only common year when Victoria Day and Labour Day are sixteen weeks apart (they are fifteen weeks apart in all other common years)
Labor Day falls on its latest possible date, September 7 – this is the only common year when Memorial Day and Labor Day are fifteen weeks apart (they are fourteen weeks apart in all other common years)