How does a leap year go when it happens. Leap years - list

A leap year occurs once every four years. But why then was 1904 a leap year, 1900 was not, and 2000 was again?

In a leap year, the Summer Olympics are held - where did this order come from? And why do we need any special "extended" years? How are they different from normal ones? Let's figure it out.

Who introduced leap years into the calendar?

Ancient Roman astronomers were well aware that a year on Earth lasts 365 days and a few more hours. Because of this, the calendar year, which then consisted of a constant number of days, did not coincide with the astronomical one. The surplus of hours gradually accumulated, turning into days. Calendar dates gradually shifted and deviated from natural phenomena - for example, the equinoxes. A group of astronomers led by Sosigenes, who worked at the court of Julius Caesar, proposed to correct the calendar. According to the new chronology, every fourth year was extended by one day. This year is called bis sextus which in Latin means "second sixth" . In Russian, this word has been transformed into "leap year" That's what we call it to this day.

By order of Julius Caesar, a new calendar was introduced starting from the year 45 BC. After the death of the emperor, there was a failure in the calculation of leap years, and the countdown began again from the 8th year of our era. Therefore, in our time, even years are leap years.

It was decided to add a day to the last, shortest month of the year, which already "did not have enough days." In ancient Rome, the New Year was celebrated on March 1, so an extra 366th day was added to February. The new calendar began to be called "Julian" in honor of Caesar. By the way, the Orthodox and some other churches still live according to the Julian calendar - this is a tribute to tradition.

And again the calendar changes

Astronomical observations continued, methods became more and more accurate. Over time, astrologers realized that the duration of the earth's year is not 365 days and 6 hours, but a little less. (It is now known that a year lasts 365 days 5 hours 48 minutes and 46 seconds).


The use of the Julian chronology led to the fact that the calendar began to be late from the real flow of time. Astronomers have noticed that the spring equinox occurs much earlier than the day allotted for it according to the calendar, that is, March 21. There was a need to correct the calendar, which was done by decree of Pope Gregory XIII in 1582.

To compensate for the discrepancy, we decided to set leap years according to a new rule. It was necessary to reduce their number, which was done. From that moment on, all years divisible by 4, except those that are divisible by 100, are still considered leap years. For even more accurate chronology, years that are divisible by 400 are still considered leap years.

This is why 1900 (like 1700 and 1800) was not a leap year, but 2000 (like 1600) was.

The new calendar was named in honor of the Pope Gregorian - it is currently used by all countries of the world. The Julian calendar is used by a number of Christian churches, including the Russian Orthodox Church.

Rule for determining leap years

So, leap years are determined by a simple algorithm:

If a year is divisible by 4 but not divisible by 100, it is a leap year;

If a year is divisible by 100, it is not considered a leap year;

If a year is divisible by 100 and also by 400, it is a leap year.

How is a leap year different from others?

Only one - it has 366 days, and an additional day is assigned to February. Despite the fact that the year now starts on January 1, which means that the last month of the year is December, we still give an extra day to February. He is the shortest - we will regret him!

And we will rejoice for those who were born on February 29 in a leap year. These "lucky ones" celebrate their birthday every four years, which makes this event more long-awaited and desired than other people.

What happens in a leap year?

Leap years were chosen to host the main sporting event of mankind - the Olympics. Now, in leap years, only the Summer Games are held, and the Winter Games are held with a two-year shift. The sports community adheres to the oldest tradition, which was established by the first Olympians - the ancient Greeks.


It was they who decided that such a grandiose event should not take place too often - once every four years. The four-year cycle coincided with the alternation of leap years, so the modern Olympics began to be held in leap years.

sharky:
03/25/2013 at 16:04

and why is 1900 not a leap year? A leap year occurs every 4 years, i.e. Divisible by 4, it's a leap year. And no more divisions by 100 or 400.

Asking questions is normal, but before you say something, study the materiel. The earth revolves around the sun in 365 days 5 hours 48 minutes 46 seconds. As you can see, the rest is not exactly 6 hours, but 11 minutes 14 seconds less. This means that by making a leap year we add extra time. Somewhere in 128 years, extra days accumulate. Therefore, every 128 years in one of the 4-year cycles, a leap year is not necessary to get rid of these extra days. But to simplify, a leap year is not made every 100th year. Is the idea clear? Okay. But how then to proceed, because an extra day is added every 128 years, and we cut it every 100 years? Yes, we cut off more than it should be, and this must be returned sometime.

If the first paragraph is clear and still interesting, then read on, but it will be more difficult.

So, in 100 years, 100/128=25/32 days of excess time accumulate (this is 18 hours 45 minutes). We do not make a leap year, that is, we subtract one day: we get 25/32-32/32 = -7/32 days (this is 5 hours and 15 minutes), that is, we subtract the excess. After four cycles of 100 years each (after 400 years) we will subtract an extra 4*(-7/32)=-28/32 days (this is minus 21 hours). On the 400th year, we make a leap year, that is, we add a day (24 hours): -28/32+32/32=4/32=1/8 (this is 3 hours).
We make every 4 years a leap year, but at the same time every 100 years is not a leap year and at the same time every 400 years is a leap year, but still every 400 years an extra 3 hours are added. After 8 cycles of 400 years, that is, after 3200 years, an extra 24 hours will accumulate, that is, one day. Then one more obligatory condition is added: every 3200th year should not be a leap year. 3200 years can be rounded up to 4000, but then again you have to play with added or truncated days.
3200 years have not passed, so this condition, if it is made so, is not yet spoken of. But 400 years have already passed since the approval of the Gregorian calendar.
Years divisible by 400 are always leap years (for now), other years divisible by 100 are not leap years, other years divisible by 4 are leap years.

My calculation shows that in the current state, an error of one day accumulates over 3200 years, but this is what Wikipedia writes about this:
“An error of one day compared to the year of the equinoxes in the Gregorian calendar will accumulate in about 10,000 years (in the Julian - in about 128 years). A frequently encountered estimate, leading to a value of the order of 3000 years, is obtained if we do not take into account that the number of days in a tropical year changes with time and, in addition, the ratio between the lengths of the seasons changes. From the same Wikipedia, the formula for the length of the year in days with fractions paints a good picture:

365,2425=365+0,25-0,01+0,0025=265+1/4-1/100+1/400

The year 1900 was not a leap year, but 2000 was, and special, because such a leap year happens once every 400 years.

I hope you had a great New Year's Eve and are now in a great holiday mood. At least this is how it is for me - we didn’t drink any alcohol, and at midnight we clinked glasses of water from a five-liter canister, so we woke up, took a walk, and then I remembered one of yesterday’s New Year’s greetings:

I wish that at the end of each year, remembering what happened over the past 366 if ((year%4 == 0 and year%100 != 0) or (year%400 == 0)) else 365 days, think about myself:

Oh, nifiga yourself, what an action was. I will definitely tell my grandchildren or write a book about it later.

So, above is a fairly simple inline way to determine the number of days in a year (year variable), which, in fact, fully reveals their essence: in the Gregorian calendar, leap years are those years whose serial number is either a multiple of 4, but not a multiple of 100 , or divisible by 400. In other words, if the year is divisible by 4 without a remainder, but divisible by 100 only with a remainder, then it is a leap year, otherwise it is not a leap year, except if it is divisible by 400 without a remainder, then it is still a leap year.

For example, 2013 is a common year, 1700, 1800 and 1900 are again common years, but 2000, 2004, 2008 and 2012 are leap years.

But what if we don't remember how many days there are in leap years (366 days) and common years (365 days), or we just want to write the definition of the number of days in a year as quickly as possible? Is it possible to do this in Python? Of course you can.

So, Python has a calendar module. It is just great for finding out if a particular year is a leap year (or, for example, how many leap years are in a certain interval), determining the number of days in a month, getting the number of the day of the week for a certain date, and so on.

In particular, we can get the number of days in each month of the year, and simply add them up.

The calendar.monthrange function takes the year number as the first argument and the month number as the second argument. Returns the number of the day of the week on the first day of the given month and the number of days in the given month:

>>> import calendar >>> calendar.monthrange(2013, 1) (1, 31)
Accordingly, we can calculate the total number of days for all 12 months, and thus obtain the number of days for a given year:

>>> import calendar >>> year = 2013 >>> sum(map(lambda x: calendar.monthrange(year, x), range(1, 13))) 365
But if you think about how exactly this line is executed, it becomes obvious that this solution is very inefficient if you need to count the number of days for a large number of years.

We check with the timeit module.

To complete it 1 million times, it takes 13.69 seconds if import calendar is done once at the beginning. If import calendar is done every time then 14.49 seconds.

Now let's try another option. It requires knowing how many days there are in leap and non-leap years, but it is very short:

>>> import calendar >>> year = 2013 >>> 365+calendar.isleap(year) 365
And, as you might guess, it is already much faster: 0.83 seconds, including import calendar, and 0.26 seconds if import calendar is done once at the beginning.

Let's also see how long the very first option takes, with a "manual" approach: 0.07 seconds for 2012 and 2013 and 0.12 seconds for 2000 (I think everyone understands where such a difference in speed for these years comes from).

It turns out that this is the fastest option out of these three:

>>> import calendar >>> year = 2013 >>> 366 if ((year%4 == 0 and year%100 != 0) or (year%400 == 0)) else 365 365
Of course, in most cases, you can use either of these options - after all, when determining the number of days in one, two, ten, or a hundred years, you are unlikely to feel any difference.

Write, optimize, improve, test and evaluate performance - but don't forget about the readability of your program sources.

Happy New Year! Good luck, happiness, joy and self-improvement in the new year.

Leap year (lat. bis sextus - “second sixth”) - a year in the Julian and Gregorian calendars, the duration of which is 366 days - one day more than the duration of a regular, non-leap year. In the Julian calendar, a leap year is every fourth year; in the Gregorian calendar, there are exceptions to this rule.

A year is a conventional unit of time, which historically meant a single cycle of seasons (spring, summer, autumn, winter). In most countries, the calendar length of the year is 365 or 366 days. At present, the year is also used as a temporal characteristic of the revolution of planets around stars in planetary systems, in particular the Earth around the Sun.

The calendar year in the Gregorian and Julian calendars is 365 days in non-leap years and 366 days in leap years. The average length of the year is 365.2425 days for the Gregorian and 365.25 days for the Julian calendar.

The calendar year in the Islamic calendar contains 353, 354 or 355 days - 12 lunar months. The average length of the year is 354.37 days, which is less than the tropical year, and therefore Muslim holidays "roam" according to the seasons.

The calendar year in the Jewish calendar contains 353, 354 or 355 days in a simple year and 383, 384 or 385 days in a leap year. The average length of the year is 365.2468 days, which is close to the tropical year.

The length of the tropical year (the time between the two vernal equinoxes) is 365 days 5 hours 48 minutes 46 seconds. The difference in the duration of the tropical year and the average Julian calendar year (365.25 days) is 11 minutes 14 seconds. Of these 11 minutes and 14 seconds, approximately 128 years add up to one day.

As the centuries passed, a shift in the day of the vernal equinox, with which church holidays are associated, was noticed. By the 16th century, the vernal equinox occurred about 10 days earlier than March 21, which is used to determine the day of Easter.

To compensate for the accumulated error and to avoid such a shift in the future, in 1582, Pope Gregory XIII reformed the calendar. In order to better match the average calendar year to the solar year, it was decided to change the leap year rule. As before, a year remained a leap year, the number of which is a multiple of four, but an exception was made for those that were a multiple of 100. From now on, such years were leap years only when they were also divided by 400.

In other words, a year is a leap year in two cases: either it is a multiple of 4, but not a multiple of 100, or it is a multiple of 400. A year is not a leap year if it is not a multiple of 4, or it is a multiple of 100, but not a multiple of 400.

The last years of centuries ending in two zeros are not leap years in three cases out of four. So, the years 1700, 1800 and 1900 are not leap years, since they are a multiple of 100 and not a multiple of 400. The years 1600 and 2000 are leap years, since they are a multiple of 400. The years 2100, 2200 and 2300 are non-leap years. In leap years, an extra day is introduced - February 29. The Catholic world lives according to the Julian calendar. Unlike the Julian calendar, the Gregorian calendar takes into account only one object - the Sun.

Now we live according to the Julian calendar (new style), before the revolution we lived according to the Gregorian (old style). The difference between the old and new styles was 11 days in the 18th century, 12 days in the 19th century, and 13 days in the 20th-21st centuries. In the 22nd century, this difference will already be 14 days. The Gregorian calendar was introduced under Soviet rule on February 14, 1918 (after January 31, it was no longer February 1, but immediately the 14th). The last leap year was , the next one will be .

1996, 1992, 1988, 1984, 1980, 1976, 1972, 1968, 1964, 1960, 1956, 1952, 1948, 1944, 1940, 1936, 1932, 1928, 1924, 1920, 1916, 1912, 1908, 1904, in Gregoriansky 1900 is a non-leap year, Julian is a leap year. 1896.

Note: For most computer and mobile systems, valid dates are from December 13, 1901, 20:45:54 GMT to January 19, 2038, 03:14:07 GMT. (These dates correspond to the minimum and maximum value of a 32-bit signed integer). For Windows, valid dates are from 01-01-1970 to 01-19-2038.

First a note. Not every 4th year is a leap year. Why - we will explain later.

In a normal year there are 365 days. In a leap year, there are 366 days - one day more, due to the addition of an additional day at the number 29 to the month of February, as a result of which those born on this day experience certain difficulties in celebrating their birthday.

A year is the time during which the planet Earth makes one revolution around the Sun in relation to the stars (apparently measured as the interval between two successive passages of the Sun through the vernal equinox).

A day (or often in everyday speech - a day) is the time during which the Earth makes one revolution around its axis. As you know, there are 24 hours in a day.

It turns out that the year does not fit an even number of days. There are 365 days, 5 hours, 48 ​​minutes and 45.252 seconds in a year. If the year is taken equal to 365 days, then it turns out that the Earth in its orbital movement will not "reach" the point at which the circle "closes", i.e. it takes another 5 hours, 48 ​​minutes and 45.252 seconds to fly in orbit. These extra about 6 hours in 4 years will just be collected in one additional day, which was introduced into the calendar to eliminate the backlog, receiving every 4th year leap year- a day longer. He did this on January 1, 45 BC. e. Roman dictator Gaius Julius Caesar, and the calendar has since been called Julian. In fairness, it must be said that Julius Caesar introduced a new calendar only by authority, and, of course, astronomers calculated and proposed it.

The Russian word "leap" comes from the Latin expression "bis sextus" - "the second sixth". The ancient Romans counted the days of the month until the beginning of the next month. So the day of February 24 was the sixth before the beginning of March. In a leap year, an additional, second (bis sextus) sixth day was inserted between February 24 and February 25. Later, this day began to increase towards the end of the month, on February 29.

So, according to the Julian calendar, every 4th year is a leap year.

But it is easy to see that 5 hours, 48 ​​minutes and 45.252 seconds is not exactly 6 hours (11 minutes 14 seconds are missing). Of these 11 minutes and 14 seconds in 128 years, another extra day will “run in”. This was noticed from astronomical observations on the shift of the day of the vernal equinox, relative to which church holidays are calculated, in particular Easter. By the 16th century, the backlog was 10 days (today it is already 13 days). To eliminate it, Pope Gregory XIII reformed the calendar ( Gregorian calendar), according to which not every 4th year was a leap year. There were no leap years, multiples of one hundred, that is, ending in two zeros. The only exceptions were years divisible by 400.

So, leap years are years: 1) divisible by 4, but not by 100 (for example, 2016, 2020, 2024),

Note that the Russian Orthodox Church refused to switch to the Gregorian calendar and lives according to the old, Julian calendar, which is 13 days behind the Gregorian. If the church continues to refuse to switch to the generally accepted Gregorian calendar, then in a few hundred years the shift will become such that, for example, Christmas will be celebrated in the summer.