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Every Year Divisible by 4 is not a LEAP YEAR ! Why ?

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Most of us believe that if an year is divisible by 4 then it is a leap year. But it is not ? The proof of this statement is that year 1700, 1800 an 1900 were not leap year. But year 2000 was a leap year. How is it so ? It is because our most believed definition of leap year is incomplete. The complete definition of leap year will certainly enlighten you, and once you know the reason behind that definition, you will feel the mathematicians born centuries ago have really done some tremendous calculations to make a scientific calendar for our usage.

Definition of Leap Year

An year divisible by four is a leap year, except those which are divisible by 100. But those years which are divisible by 400 will be a leap year.

Note: Most of us believe that actual length of an year is 365 days and 6 hours. Normal year have 365 days, while the remaining 6 hours of each year creates one complete day in the 4th year. But the truth is that one solar year is 365 days 5 hours 48 minutes 46 seconds, which is responsible for above given definition of leap year.

Now most probably you have known the reason behind every 100th year not being a leap year and every 400th year being a leap year.

If still there is some confusion, the i will try to sort it down. Reading the following points might help you.

  • 1 day = 24 x 60 x 60 seconds = 86400 seconds
  • 1 year = 365 days = 365 x 86400 seconds =  31536000 seconds
  • Length of solar year = 365 days 5 hours 48 minutes 46 seconds
         Extra time = 5 hours 48 minutes 46 seconds
                    = (5x60x60) + (48x60) + 46 seconds
                    = 18000 + 2880 + 46 seconds
                    = 20926 seconds
  • It means that a normal year leaves 20926 seconds aside.
  • 20926 x 4 = 83704 seconds
  • Every 86400 seconds makes a day, and 83704 is almost near it, so we add an extra day in Feb after every four years.
  • But while doing so we are adding additional (86400-83704) i.e. 2696 seconds in every four years. 
  • 25 times 4 years creates 100 years.
  • 2696 x 25 = 67400 seconds. So in every 100 years we will add 67400 excess seconds.
  • If we don't consider 100th year as leap year then these extra seconds can be compensated.
  • When we don't make the 100th year a Leap Year. We are left with 86400-67400=19000 seconds
  • It means that after spending 100 years and considering 100th year as a non-leap year, we are setting aside 19000 seconds.
  • In 400 years this time will become 4 x 19000 = 76000 seconds . This extra time adds one day on every 400th year, thus making it a leap year. However one day is equal to 86400 seconds. So still 10400 seconds are excess here, but this time is neglected here.
  • Thus the modern calendar repeats itself after every 400 years.
If we look precisely then our calendar system is still inaccurate, as we are using 10400 excess seconds in every 400 years. It means we are using excess 3 hours (approximately), in every 400 years. It means till 3200 years we will add excess 1 day. So, as we know that year 3200 is a leap year as per present system, but we will need to make it a normal year for the sake of our calculations. And this problem may continue as we will go to much larger numbers. Year 3200 is very far, so no body has taken it seriously yet. 
If you feel something went wrong in above calculation then you may put some light in the comments section. Knowledge worth sharing should be shared.

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