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- 1. Very very complex!!!
- 2. A leap year (or intercalary year) is a year containing one extra day (or, in the case of lunisolar calendars, a month) in order to keep the calendar year synchronized with the astronomical or seasonal year. For example, in the Gregorian calendar (common calendar), February in a leap year has 29 days instead of the usual 28, so the year lasts 366 days instead of the usual 365.
- 3. However, some exceptions to this rule are required since the duration of a solar year is slightly less than 365.25 days. Years that are evenly divisible by 100 are not leap years, unless they are also evenly divisible by 400, in which case they are leap years. For example, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. Similarly, 2100, 2200, 2300, 2500, 2600, 2700, 2900 and 3000 will not be leap years, but 2400 and 2800 will be. By this rule, the average number of days per year will be 365 + 1/4 − 1/100 + 1/400 = 365.2425, which is 365 days, 5 hours, 49 minutes &12 seconds. In 2100, the pattern will be broken, and a new 29 day cycle starts in 2104.
- 4. In the Gregorian calendar, the current standard calendar in most of the world, most years that are evenly divisible by 4 are leap years. In each leap year, the month of February has 29 days instead of 28. Adding an extra day to the calendar every four years compensates for the fact that a period of 365 days is shorter than a solar year by almost 6 hours. The Gregorian calendar was designed to keep the vernal equinox on or close to March 21, so that the date of Easter (celebrated on the Sunday after the 14th day of the Moon—i.e. a full moon—that falls on or after March 21) remains correct with respect to the vernal equinox.The vernal equinox year is about 365.242374days long (and is increasing).
- 5. The marginal difference of 0.000125 days between the Gregorian calendar average year and the actual year means that, in 8,000 years, the calendar will be about one day behind where it is now. But in 8,000 years, the length of the vernal equinox year will have changed by an amount that cannot be accurately predicted. Consider a little astronomy and arithmetic. It turns out that in a year, the time it takes for the earth to make a single revolution around the sun, is very close to 365.2423749 days. If we simply make every fourth year a leap year, we have 365.25 day years, not far off and that .0078 day difference is only about 11 minutes and 14 seconds. (You can check that by multiplying .0078 day x 24 hours/day x 60 minutes/hour.) However that small annual accumulation of .0078 day will lead to a full day in about 128 years. (Enter .0078 in your calculator and press the 1/x key, immediately converting days/year to years/day.) To further correct for this, our current Gregorian calendar makes two adjustments: 1. even though they are clearly divisible by four, years divisible by 100 are not leap years, 2. except for those divisible by 400 which are leap years. Thus 1900 was not a leap year, but this year we have the most unusual case of all -- 2000 is divisible by 400 so it is a leap year. This remarkable situation will not occur again until the year 2400.
- 6. A simple way to check if a year is a leap year
- 7. Thank YouBy Aayush Gala

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