leap year calculation

Question

In order to find leap years, why must the year be indivisible by 100 and divisible by 400? I understand why it must be divisible by 4. Please explain the algorithm.

Answer 1

I'm sure Wikipedia can explain it better than I can, but it is basically to do with the fact that if you added an extra day every four years we'd get ahead of the sun as its time to orbit the sun is less than 365.25 days so we compensate for this by not adding leap days on years that are not divisible by 400 eg 1900.

Hope that helps

Answer 2

Here comes a rather obsqure idea. When every year dividable with 100 gets 365 days, what shall be done at this time? In the far future, when even years dividable with 400 only can get 365 days.

Then there is a possibility or reason to make corrections in years dividable with 80. Normal years will have 365 day and those dividable with 400 can get 366 days. Or is this a loose-loose situation.

Answer 3

Return true if the input year is a leap year

Basic modern day code:

  If year mod 4 = 0, then leap year
  if year mod 100 then normal year
  if year mod 400 then leap year
  else normal year

Todays rule started 1582 AD Julian calendar rule with every 4th year started 46BC but is not coherent before 10 AD as declared by Cesar. They did however add some leap years every 3rd year now and then in the years before: Leap years were therefore 45 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC, 27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC, 8 AD, 12 AD Before year 45BC leap year was not added. http://www.wwu.edu/depts/skywise/leapyear.html

The year 0 do not exist as it is ...2BC 1BC 1AD 2AD... for some calculation this can be an issue.

function isLeapYear(year: Integer): Boolean;
begin
  result := false;
  if year > 1582 then // Todays calendar rule was started in year 1582 
    result := ((year mod 4 = 0) and (not(year mod 100 = 0))) or (year mod 400 = 0)
  else if year > 10 then // Between year 10 and year 1582 every 4th year was a leap year 
    result := year mod 4 = 0
  else //Between year -45 and year 10 only certain years was leap year, every 3rd year but the entire time
    case year of
      -45, -42, -39, -36, -33, -30, -27, -24, -21, -18, -15, -12, -9:
        result := true;
    end;
end;

Answer 4

Leap years are arbitrary, and the system used to describe them is a man made construct. There is no why.

What I mean is there could have been a leap year every 28 years and we would have an extra week in those leap years ... but the powers that be decided to make it a day every 4 years to catch up.

It also has to do with the earth taking a pesky 365.25 days to go round the sun etc. Of course it isn't really 365.25 is it slightly less (365.242222...), so to correct for this discrepancy they decided drop the leap years that are divisible by 100.